DE102022209903A1 - SAFE CONTROL OF TECHNICAL-PHYSICAL SYSTEMS - Google Patents

Abstract

A method for estimating a hidden system state of a technical-physical system using a machine-learned algorithm is disclosed. Depending on at least one predetermined criterion, an estimate of the machine-learned algorithm for the hidden system state for an input vector is either permitted or blocked. The at least one predetermined criterion takes into account a position (85) of the input vector in the corresponding input vector space (71).

Description

TECHNICAL FIELD

Various examples concern techniques to enable control of technical-physical systems. Various examples concern techniques for estimating a hidden system state of such technical-physical systems and, if necessary, determining an associated uncertainty.

BACKGROUND

Machine-learned algorithms are used in various application areas because the corresponding tasks to be solved by the machine-learned algorithm can be defined by a description of requirements. For example, machine-learned algorithms can be used to control technical-physical systems (i.e. technical systems). The machine-learned algorithm can predict a hidden system state of the technical-physical system (inference).

For example, machine-learned algorithms can be used to control a vehicle, such as a motor vehicle or a train. Machine-learned algorithms can be used to monitor and, if necessary, adjust maintenance intervals for technical-physical systems such as vehicles or infrastructure (e.g. rails, switches, means of passenger transport such as escalators or treadmills, production facilities, etc.).

In such scenarios, it is often possible, for example using an expert's domain knowledge, to identify certain processes in historical data that require an assigned control action for the technical-physical system. This corresponds to the above description of requirements for the control task of the machine-learned algorithm.

The machine-learned algorithm therefore determines one or more output features (typically in the form of an output vector) given the presence of input features (which are typically passed to the machine-learned algorithm in the form of an input vector). To do this, the machine-learned algorithm is trained based on one or more training data sets. A training data set includes several training data pairs of an input vector and associated ground truths. The input vector includes several entries, each of which encodes characteristics of state data of the technical-physical system. The ground truths describe a target position in the vector space of the output vector of the machine-learned algorithm. Training the machine-learned algorithm ensures that the output vector obtained from the machine-learned algorithm matches the target position in vector space as closely as possible.

Due to the success of machine-learned algorithms, they are increasingly being used in areas of application where the lives of people, their health or the environment can be endangered by a malfunction of the machine-learned algorithm. Examples concern, for example, autonomous vehicles that take part in traffic.

It is therefore necessary to train the machine-learned algorithm as well as possible so that malfunctions are avoided.

However, the available training data sets are limited in scope. This means that an associated ground truth is not available for all positions in the vector space of the input vector (input vector space). Therefore, when training a machine-learned algorithm, generalization occurs. This means that during inference (i.e. without available ground truth) an output from the machine-learned algorithm is provided even for previously unknown examples.

With previously known systems, there is a risk that the life or health of people will be endangered during the inference. This happens when incorrect outputs are generated, i.e., for example, a hidden system state of a technical-physical system is incorrectly predicted.

SUMMARY

There is therefore a need for improved techniques for estimating hidden system states of a technical-physical system using machine-learned algorithms. In particular, there is a need for techniques that alleviate the aforementioned disadvantages and limitations.

This task is solved by the features of the independent patent claims. The dependent claims define embodiments.

According to various examples, a machine-learned algorithm that determines output vectors based on input vectors may be used. The input vectors can each encode status data of a technical-physical system. The output vectors can predict a respective hidden system state of the technical-physical system.

The machine-learned algorithm can predict discrete system states (classes), i.e. implement a classifier.

In some examples, regression could also be performed by the machine-learned algorithm.

The input vectors can have two or more dimensions. The output vectors can have two or more dimensions. The position of an input vector in the corresponding vector space (input vector space) defines the position of the associated output vector in the corresponding vector space (output vector space).

According to various examples, contextual data is used for the machine-learned algorithm in inference. The context data provides supplementary information to the machine-learned algorithm. The context data is determined in connection with the training of the machine-learned algorithm. The contextual data can help determine a reliability of an estimate of the hidden system state by the machine-learned algorithm.

In the various examples described herein, the information content of the context data may vary.

The context data are, for example, indicative of areas in the input vector space of the machine-learned algorithm, i.e. define hypervolumes of the input vector space. It can be checked how the input vector is positioned with respect to these areas. From this it can be deduced whether there is a reliable or unreliable prediction of the machine-learned algorithm for this input vector.

The areas can be determined, for example, as a Delaunay triangulation of the input space, so that input vectors of training data pairs of a training data set form corners of the respective surfaces (more precisely, hypersurfaces of any dimensionality; however, for the sake of simplicity, reference is only made to surfaces). As a result, the areas interpolate between the input vectors for which ground truths are also available within the training data pairs.

The context data may also include partitioning the regions into those associated with low uncertainty in estimating the hidden system state and those associated with high uncertainty in estimating the hidden system state. Alternatively, such a partitioning could still be created for inference.

Alternatively or additionally, it would also be conceivable that the context data indexes one or more permitted results for the hidden system state for at least some areas. In other words, this means that the areas can indicate which output vectors of the machine-learned algorithm are allowed.

Such context data can therefore be used during inference - when no ground truth is available - to check the plausibility of the output of the machine-learned algorithm.

The context data can be determined in connection with training the machine-learned algorithm. For example, it would be conceivable that the context data is determined based on input vectors of a training data set. For example, the above-mentioned regions indexed by the context data may be determined by interpolation between positions of the input vectors of the training data set.

However, the context data cannot only be used in connection with inference. For example, it would also be possible to use the context data to determine for which positions in the input vector space further training data pairs - that is, combinations of an input vector and an output vector describing a ground truth - are required.

By using the context data, it can be achieved that the technical-physical system can be controlled in a particularly safe manner. If, for example, it is recognized based on the control data that an output of the machine-learned algorithm is subject to a comparatively high level of uncertainty, the permissible control actions can be restricted and/or the technical-physical system can be transferred to a safe operating mode and/or a warning message can be issued. In addition, the training of the machine-learned algorithm can be particularly targeted, so that reliable estimates of the hidden system state can be obtained more frequently.

According to various examples, techniques are disclosed that make it possible to estimate a hidden system state of a technical-physical system. A machine-learned algorithm is used for this estimation. The estimation of the machine-learned algorithm for the hidden system state is either allowed or blocked, each for a corresponding input vector. This is based on at least one predetermined criterion. The at least one predetermined criterion takes into account a position of the input vector in the corresponding input vector space. This means that depending on the position of the input vector in the input vector space, the output of the machine-learned algorithm can be prevented. This can avoid uncertain output or uncertain estimates for the hidden system state.

A computer-implemented method for estimating a hidden system state of a technical-physical system using a machine-learned algorithm is disclosed.

The method includes obtaining an input vector. The input vector encodes status data of the technical-physical system. The process also includes loading the machine-learned algorithm. The method further includes loading predetermined context data. The predetermined context data is associated with the machine-learned algorithm. The predetermined context data indexes a variety of regions in the vector space of the input vector. The method also includes determining a relative position of the input vector with respect to the plurality of regions. The method further includes selectively processing the input vector in the machine-learned algorithm to estimate the hidden system state or outputting an error indicator. The choice between processing and outputting the error indicator is based on the relative position of the input vector with respect to the plurality of areas.

A device includes at least a processor and a memory. The at least one processor is set up to load program code from memory and to execute the program code. The at least one processor is set up to execute a method for estimating a hidden system state of a technical-physical system using a machine-learned algorithm based on the program code. The method includes obtaining an input vector. The input vector encodes status data of the technical-physical system. The process also includes loading the machine-learned algorithm. The method further includes loading predetermined context data. The predetermined context data is associated with the machine-learned algorithm. The predetermined context data indexes a variety of regions in the vector space of the input vector. The method also includes determining a relative position of the input vector with respect to the plurality of regions. The method further includes selectively processing the input vector in the machine-learned algorithm to estimate the hidden system state or outputting an error indicator. The choice between processing and outputting the error indicator is based on the relative position of the input vector with respect to the plurality of areas.

A computer program or a computer program product or a computer-readable storage medium includes program code. The program code can be loaded and executed by at least one processor. When the processor executes the program code, this causes the processor to execute a method of estimating a hidden system state of a technical-physical system using a machine-learned algorithm. The method includes obtaining an input vector. The input vector encodes status data of the technical-physical system. The process also includes loading the machine-learned algorithm. The method further includes loading predetermined context data. The predetermined context data is associated with the machine-learned algorithm. The predetermined context data indexes a variety of regions in the vector space of the input vector. The method also includes determining a relative position of the input vector with respect to the plurality of areas. The method further includes selectively processing the input vector in the machine-learned algorithm to estimate the hidden system state or outputting an error indicator. The choice between processing and outputting the error indicator is based on the relative position of the input vector with respect to the plurality of areas.

A computer-implemented method for parameterizing a machine-learned algorithm is disclosed. Using the machine-learned algorithm, a hidden system state of a technical-physical system can be estimated. The method includes obtaining a training data set. The training data set includes multiple training data pairs, which in turn include input vectors and ground truths. The input vectors encode state data of the technical-physical system. The basic truths concern the hidden system state of the technical-physical system. The method also includes carrying out training of the machine-learned algorithm. Training is performed based on the training data set. Performing training results in parameter values for the machine-learned algorithm. The method further includes determining a plurality of areas based on the input vectors. The plurality of regions includes regions defined in the vector space of the input vectors. The method further includes generating contextual data for the machine-learned algorithm such that the contextual data is indicative of the plurality of domains. The method also includes storing the machine-learned algorithm and storing the context data associated with the machine-learned algorithm.

A device includes at least a processor and a memory. The at least one processor is set up to load program code from memory and to execute the program code. The at least one processor is set up to execute a method for parameterizing a machine-learned algorithm based on the program code. Using the machine-learned algorithm, a hidden system state of a technical-physical system can be estimated. The method includes obtaining a training data set. The training data set includes multiple training data pairs, which in turn include input vectors and ground truths. The input vectors encode state data of the technical-physical system. The basic truths concern the hidden system state of the technical-physical system. The method also includes carrying out training of the machine-learned algorithm. Training is performed based on the training data set. Performing training results in parameter values for the machine-learned algorithm. The method further includes determining a plurality of areas based on the input vectors. The plurality of regions includes regions defined in the vector space of the input vectors. The method further includes generating contextual data for the machine-learned algorithm such that the contextual data is indicative of the plurality of domains. The method also includes storing the machine-learned algorithm and storing the context data associated with the machine-learned algorithm.

A computer program or a computer program product or a computer-readable storage medium includes program code. The program code can be loaded and executed by at least one processor. When the processor executes the program code, this causes the processor to execute a method of parameterizing a machine-learned algorithm. Using the machine-learned algorithm, a hidden system state of a technical-physical system can be estimated. The method includes obtaining a training data set. The training data set includes multiple training data pairs, which in turn include input vectors and ground truths. The input vectors encode state data of the technical-physical system. The basic truths concern the hidden system state of the technical-physical system. The method also includes carrying out training of the machine-learned algorithm. The training will be based on the Trai ning data set carried out. Performing training results in parameter values for the machine-learned algorithm. The method further includes determining a plurality of areas based on the input vectors. The plurality of regions includes regions defined in the vector space of the input vectors. The method further includes generating contextual data for the machine-learned algorithm such that the contextual data is indicative of the plurality of domains. The method also includes storing the machine-learned algorithm and storing the context data associated with the machine-learned algorithm.

The features set out above and features described below can be used not only in the corresponding combinations explicitly set out, but also in further combinations or in isolation without departing from the scope of the present invention.

BRIEF DESCRIPTION OF THE FIGURES

• 1 schematically illustrates a system comprising a data processing system and a technical-physical system according to various examples.
• 2 schematically illustrates a data processing pipeline with a machine-learned algorithm and associated context data according to various examples.
• 3 illustrates details regarding the contextual data indexing multiple regions in a vector space of input vectors for the machine-learned algorithm.
• 4 is a flowchart of an example method.
• 5A is a flowchart of an example method.
• 5B shows aspects related to a Delaunay triangulation.
• 5C shows aspects related to a Delaunay triangulation.
• 5D shows aspects related to min-max triangulation.
• 5E shows aspects related to regions in the input vector space that are associated with different classes.
• 5F shows aspects related to regions in the input vector space that are associated with different classes.
• 5G shows aspects related to regions in the input vector space that are associated with different classes.
• 5H shows aspects related to regions in the input vector space that are associated with different classes.
• 51 shows aspects related to the plausibility check of context data.
• 6 illustrates input vectors of a training data set in a corresponding vector space.
• 7 illustrates a classification result of a machine-learned algorithm based on the training data set 6 was trained according to various examples.
• 8th illustrates a classification result of a machine-learned algorithm based on the training data set 6 was trained according to various examples.
• 9 illustrates a classification result of a machine-learned algorithm based on the training data set 6 was trained according to various examples.
• 10A illustrates several regions in the vector space of the input vectors 6 can be determined according to various examples.
• 10B illustrates details about one of the areas 10A .
• 10C illustrates an input vector space according to various examples.
• 10D illustrates a region in the input vector space according to 10C is determined.
• 10E illustrates another region in the input vector space according to 10C is determined.
• 11 is a flowchart of an example method.
• 12 illustrates context data according to various examples.
• 13 illustrates context data according to various examples.

DETAILED DESCRIPTION

The characteristics, features and advantages of this invention described above, as well as the manner in which these are achieved, will be more clearly and clearly understood in connection with the following description of the exemplary embodiments, which will be explained in more detail in connection with the drawings.

The present invention is explained in more detail below using preferred embodiments with reference to the drawings. In the figures, the same reference numbers designate the same or similar elements. The figures are schematic representations of various embodiments of the invention. Elements shown in the figures are not necessarily drawn to scale. Rather, the various elements shown in the figures are reproduced in such a way that their function and general purpose are understandable to those skilled in the art. Connections and couplings between functional units and elements shown in the figures can also be implemented as an indirect connection or coupling. A connection or coupling can be implemented in a wired or wireless manner. Functional units can be implemented as hardware, software, or a combination of hardware and software.

Techniques are described below for estimating a hidden system state of a technical-physical system using a machine-learned (ML) algorithm.

For example, the estimation of the hidden system state could be used to control the technical-physical system. This means that the operation of the technical-physical system can be adjusted accordingly based on the prediction of the ML algorithm.

The techniques described herein can be used in various areas of application, i.e. for different technical-physical systems. For example, the techniques described herein could be used to control vehicles, e.g. in rail traffic, public road traffic, in industrial plants or buildings, as well as ships, aircraft or spacecraft. The techniques described herein could be used to adjust maintenance intervals for transportation routes such as rail sections or switches. The techniques described herein can be used to detect fault conditions of rail vehicles or track infrastructure or to allow the release of certain rail/track sections to road users or to control traffic in transport networks. The techniques described herein could be used to monitor the operation of production lines or industrial plants, such as power plants or turbines, to control the distribution of energy or material flows, or to monitor technical components (e.g. surge protection), people (e.g. in industrial manufacturing), To protect company assets (e.g. in economic transactions) or the environment (e.g. from fires). These are just a few examples, and other areas of application are conceivable.

The various techniques described herein use a machine-learned algorithm. For example, the machine-learned algorithm could be a classifier, that is, mapping continuous values of an input vector to discrete classes. The machine-learned algorithm could also provide regression, that is, have continuous values of an output vector.

Different types of machine-learned algorithms can be used in the various examples described herein. For example, a deep neural network, for example with convolutional layers with a trained convolution kernel, could be used. A support vector machine (SVM) could also be used. Based on a training data set, the input space is divided into classes in such a way that the widest possible area between the different classes remains free. Another machine-learned algorithm that can be used would be the “nearest neighbor” classifier. For example, a parameter that describes the number of nearest neighbors to be taken into account can be learned as part of the training of the machine-learned algorithm. Another type of machine-learned algorithm that may benefit from the techniques disclosed herein is the multilayer perceptron or radial basis function network (RBF network).

Techniques are described that make it possible to obtain additional information related to the prediction of the machine-learned algorithm, so-called context data.

In particular, using the techniques described herein, it is possible to use the context data to check whether a prediction of the machine-learned algorithm for a particular input vector is reliable or unreliable. For example, depending on the context data, the input vector can either be processed with the machine-learned algorithm (provided its output is reliable), or an error indicator could be output. The technical-physical system can also be controlled depending on an output of the error indicator. For example, a safe operating mode could be activated. A user review could be triggered. A warning signal can be issued. An autonomously acting functionality such as an economic transaction could be aborted. In this way, the risk to the environment due to an unreliable prediction by the machine-learned algorithm can be avoided.

Using the context data, it is also possible to derive at which positions in the input vector space further training data pairs should be positioned. Such information can also be determined based on the analysis of whether the machine-learned algorithm provides an unreliable prediction for a specific region in the input vector space. This enlarges the subareas of the input space in which the machine-learned algorithm can make a reliable statement, thus enabling greater availability of the technical system in “normal operation”. “Normal operation” refers, for example, to the state of the system in which the system is not in a safe state, but rather fulfills a safety-relevant utility function; This could be, for example, a moving train that does not stop in a safe position at a train station where passengers can get on and off safely. In particular, during training - for example when collecting and recording examples, e.g. through a measurement in the real environment or through the use of a digital twin (e.g. a simulation) - areas in the input vector space can be specifically covered where a generalization of the machine-learned algorithm would otherwise be possible would take place by extrapolation from pairs of training data located distantly in the input vector space. The capture of further examples increases the reliability of the prediction by the machine-learned algorithm and the technical system.

Thus, according to the various techniques disclosed herein, it is possible to either allow or block the estimation of the machine-learned algorithm for the hidden system state depending on at least one predetermined criterion. Blocking the prediction may correspond to the output of the error indicator described above or otherwise suppressing further processing of the output of the machine-learned algorithm. Allowing the estimate may correspond to passing it to subsequent processing steps of a corresponding data processing pipeline.

The at least one criterion for blocking or allowing can take into account the position of the corresponding input vector - which is the basis for the estimate of the machine-learned algorithm. For example, the prediction could be blocked if the position of the input vector corresponds to an extrapolation of the machine-learned algorithm based on state data of the technical-physical system that is included in a training data set for the machine-learned algorithm. This state data can mark corresponding positions (e.g. closest ones) in the input vector space; this can be indicated by the context data. Then the input vector may have a position in the input vector space that is spaced from areas that extend between positions in the input vector space corresponding to the state data. Conversely, a prerequisite for allowing the estimation of the machine-learned algorithm can be that there is no extrapolation, i.e. there is an interpolation. This then means that the input vector has a position in the input vector space, which is arranged in a region that extends between the positions of the state data from the training data set (if the input vector space has the dimension D, then D+1 input vectors each, which a space of dimension D defines a hypervolume T of the input space. The boundary of the hypervolume T is then limited by hypersurfaces, which connect three neighbors of the state data. If the input vector lies within a hypervolume, which is limited by examples of the training set as described above , then we speak of an interpolation based on the training data, but this is not the case, of an extrapolation. In addition to the interpolation, it can also be required that the longest distance between the two or more state data of the technical-physical system between which the interpolation is carried out is not greater than a predetermined threshold value. This means that a upper threshold value for the side length of the hypersurfaces delimiting an area can be required. Another exemplary criterion that can lead to a blocking of the prediction would be falling below a minimum distance to uncertain positions in the input vector space. These uncertain positions could, for example, be determined based on a course of a class boundary between different predicted classes in the input vector space. The positions can therefore be labeled as unsafe.

Various criteria for blocking or allowing the prediction of the machine-learned algorithm have been explained above. As a general rule, it would be conceivable that checking whether one or more such criteria for blocking or allowing are met would be carried out sequentially. For example, a predetermined sequence could be processed, which specifies an order of testing for the different criteria. The prediction of the machine-learned algorithm can then be blocked if a first test produces a negative result; The subordinate second test then no longer has to be carried out. In particular, it would be conceivable, for example, to first check whether the minimum distance to unsafe positions in the input vector space is undershot. Only as a secondary matter could it be checked whether the position of the input vector corresponds to an extrapolation or an interpolation, as described above.

From the above, it can be seen that the regions in the input vector space can be determined that have different certainties with respect to the prediction of the machine-learned algorithm. This is in TAB. 1 summarized. LEVEL SHORT DESCRIPTION EXEMPLARY DETAILS I Edge length + interpolation Regions may be used that extend between positions associated with input vectors of state data of the engineering-physical system included in the training data set for the machine-learned algorithm. This means that in such an area interpolation takes place between the respective state data for which ground truths are available. This already corresponds to a high level of security. In order to further increase the security level, it can also be required that the edge length of such areas does not exceed a predetermined threshold value. This means that only areas that are relatively close to the positions of the state data in the input vector space are taken into account. This avoids the possibility of a double class change occurring within the area. By taking into account the comparatively limited edge length and interpolation, a particularly high level of security can be achieved Reference to the prediction of the machine-learned algorithm can be guaranteed. Optionally, it could also be taken into account that a corresponding area does not fall below a specified minimum distance to unsafe positions in the input vector space. Such a test could, in particular, be described in more detail below (in connection with Box 3020). 11 ), take priority over other components, for example over a check as to whether the edge length of the areas exceeds or does not exceed a predetermined threshold value. II interpolation If only the interpolation - but not the edge length, compare level I - is taken into account, a comparatively high level of security can still be guaranteed, although this is lower than with level I. For example, multiple class changes could occur within a corresponding area; This cannot be ruled out by considering arbitrarily large interpolation areas. III Extrapolation A comparatively low level of certainty in connection with the prediction of the machine-learned algorithm is achieved if the prediction is made for a position in the input vector space that is associated with an extrapolation based on state data included in the training data set. For example, such areas may extend not between positions of input vectors associated with state data in the training data set, but away from such positions.

TAB. 1: Different levels of certainty that can be obtained in the context of prediction by a machine-learned algorithm. Such stages can be described in the context of specific regions in the input vector space defined by contextual data. The areas could be divided into different security levels using an evaluation metric. This can be done either for inference or during training. Determining the areas or applying the evaluation metrics can be done in a quality-assured manner, which means that dangerous loss or falsification of the information can be reliably avoided.

1 illustrates aspects relating to a system 90. The system 90 includes a data processing system 91 and a technical-physical system 95 (e.g. an industrial plant, an air, water, space or ground vehicle, a power plant, a means of passenger transport such as an elevator or a Escalator, a manufacturing machine, a factory, a production line, a system for distributing energy or material flows or a system for controlling traffic, to give just a few examples).

The data processing system 91 has a processor 92 and a non-volatile memory 93. The data processing system 91 also includes a communication interface 94. The processor 92 can communicate with the technical-physical system using the communication interface 94. For example, it would be possible for status data 81 of the technical-physical system 95 to be received via the communication interface 94. The status data 81 could, for example, be measured values from a sensor that monitors certain operating parameters of the technical-physical system 95. The status data 81 could also be operating values of the technical-physical system 95, for example certain control specifications for actuators of the technical-physical system 95. It is also possible for the processor 92 to send control data 82 to the technical-physical system 95 via the communication interface 94. The operation of the technical-physical system can be adjusted using the control data 82.

While in 1 Only one processor 92 is shown, the data processing system 91 can generally have several processors.

To process the status data 81, the processor 92 can load and execute program code from the memory 93. The program code may define a machine-learned algorithm configured to process input vectors encoding the state data 81. The machine-learned algorithm can then provide an output vector that estimates a hidden system state of the engineering-physical system. A corresponding data processing pipeline is also in 2 shown.

2 illustrates aspects relating to a machine-learned algorithm 89. The machine-learned algorithm 89 processes an input vector 85 which encodes state data 81 of the technical-physical system 95. The machine-learned algorithm 89 then provides an output vector 86 ready, which predicts the hidden system state of the technical-physical system 95. This corresponds to an inference.

Using various techniques described herein, it is possible to verify whether the prediction of the hidden system state by the machine-learned algorithm 89 is reliable. In particular, it can be checked a priori, i.e. before or independently of executing the machine-learned algorithm, whether this prediction is reliable.

The check can be based on the position of the input vector 85 in the input vector space and using corresponding context data 50. The context data 50 is associated with, but different from, the machine-learned algorithm 89. Different machine-learned algorithms 89 have different context data 50. The context data 50 may, for example, be determined in connection with training the machine-learned algorithm 89, which will be explained in detail later.

Below are related to 3 Aspects related to checking the position of the input vector 85 in the input vector space using the context data 50 are shown.

3 illustrates aspects related to the position of the input vector 85 in the corresponding input vector space 71 (for illustration, the input vector space 71 is shown in two dimensions, but may be higher dimensional; so the input vector space is strictly speaking a hyperspace).

In 3 Several areas 72 are also shown in the input vector space 71. The areas 72 are delimited from one another by hypersurfaces (or, in the two-dimensional case shown, lines). The input vector 85 has a specific position in relation to these areas 72 (in the example the 3 the input vector 85 is arranged in one of the areas 72).

The areas can be indexed by context data 50 associated with the machine-learned algorithm 89. For example, the context data 50 could indicate the areas between the areas 72.

The areas can have different security levels according to TAB. 1 be associated.

In the various examples described herein, it is possible to determine such a relative position of the input vector with respect to multiple regions 72 and then, based on that relative position, selectively process the input vector machine-learned algorithm 89 and thereby estimate the hidden system state (e.g. if it if it is security level I or II), or to output an error indicator (for example if it is security level III, see TAB. 1). The areas 72 can be indexed by the context data 50 of the machine-learned algorithm 89. The context data 50 can be loaded by the processor 92, for example from the memory 93. The context data 50 can be created in connection with the training of the machine-learned algorithm, ie when parameterizing the machine-learned algorithm; please refer 4 .

4 is a flowchart of an example method. 4 illustrates different phases of using a machine-learned algorithm such as machine-learned algorithm 89.

Parameterization takes place in Box 3001.

This includes, for example, the training of the machine-learned algorithm 89. The training can be carried out based on a training data set. The training data set includes training data pairs, each comprising an input vector and an associated output vector. The output vector represents the ground truth for the output of the machine-learned algorithm for the respective input vector. For example, a ground truth can be obtained based on manual annotation by an expert with domain knowledge. There are also techniques for automatically obtaining basic truths, although this can vary depending on the application area, e.g. by means of a simulation of the technical-physical system.

Based on the training, parameter values for the machine learned algorithm are obtained. Different parameter values may be used for different types of machine-learned algorithms can be obtained (for example, for a deep neural network with one convolutional layer, the convolution kernel can be determined).

The training can be carried out using previously known techniques, which typically include an iterative optimization of the various parameter values to minimize a loss function. A gradient descent method for optimization with backward adjustment of the parameters (backpropagation) can be carried out. The loss function describes a distance of the output vector of the machine-learned algorithm in the current separation state compared to the corresponding ground truth vector of a corresponding training data pair.

The parameterization 3001 may also include generating the context data 50 for the machine-learned algorithm. These can be determined based on the input vectors of the training data set. This means that the context data is specific to the respective machine-learned algorithm that has undergone a certain training. Different machine-learned algorithms then have different context data (see also vertical dashed arrow in 2 ).

It is then possible to store both the machine-learned algorithm and the context data 50 for the machine-learned algorithm in a memory such as memory 93 for later inference in box 3002.

Box 3002 is where the inference takes place. This inference takes into account both the previously trained machine-learned algorithm 89 in order to estimate, if necessary, a hidden system state of the technical-physical system; as well as the context data 50 to determine whether an output of the machine learned algorithm is secure or unsafe. No ground truth is available as part of the inference in Box 3002. That is, the machine-learned algorithm 89 outputs an output vector 86 that cannot be compared to a ground truth.

Aspects related to Box 3001 are described below. Aspects related to Box 3002 are then described.

5A is a flowchart of an example method. 5A illustrates aspects related to parameterizing a machine-learned algorithm according to Box 3001 4 .

For example, the procedure could be: 5A are executed by processor 92 based on program code loaded from memory 93 and then executed by processor 92.

First, a training data set is obtained in box 3505. The training data set includes several pairs of training data. Each pair of training data has a corresponding input vector, corresponding to input vector 85 (see 2 ). The input vector encodes status data of a technical-physical system. A ground truth is assigned to each input vector, for a corresponding hidden system state of the technical-physical system. The basic truths are in the form of output vectors (compare output vector 86 in 2 ) before.

In box 3510, the training of the machine-learned algorithm is then carried out based on the training data set. This is done to obtain parameter values for the machine-learned algorithm. Details about the training have already been described above in connection with Box 3001.

Multiple ranges are then determined in box 3515 based on the input vectors of the training data set.

At least some of the areas are determined in such a way that they are arranged between the positions of the input vectors in the corresponding input vector space. This means that the input vectors each define the outer boundaries of the areas. This means that the areas extend between the input vectors. So - to determine the areas - interpolation is carried out between the positions of the input vectors in the input vector space.

For example, it would be conceivable that the areas are formed based on triangular areas of a triangular network, the nodes of which are determined by the input vectors. A triangulation, for example a Delaunay triangulation, could be used. The context data 50 can then be generated, which is indicative of the areas. For example, the context data 50 could be the triangle areas of the triangular network. The areas can therefore be delimited by surfaces (more precisely: hypersurfaces) that extend between the positions of neighboring input vectors in the corresponding input vector space.

As a general rule, the so-called KD-Trees algorithm could be used to find the nearest neighbors. However, there are all sorts of other options for this. Other classic tree structures would be conceivable, such as quadtrees or R-trees. Approximate nearest neighbor methods such as locality-sensitive hashing are suitable for particularly high-dimensional data.

In some examples, it would be conceivable that at least some of the areas are determined in such a way that a position in the input vector space that is recognized as unsafe is surrounded. If a position is recognized as unsafe, the extent of such an area can be determined based on a specified distance measure (parameter “b”). The parameter b supports the control of class boundary problems in applications with a strong imbalance in the importance of certain types of errors. An example is a safety-relevant function that regulates driving through a traffic light. Running a red light can endanger people's lives and health. If, on the other hand, a vehicle stops at a traffic light, then there is only an availability problem for the vehicle because it does not always run then. The parameter “bk” then defines a “safety distance” from an example from a class “k”. All examples that are less than b _k away in the input space from an example of class “k” are then assigned to class “k”. Accordingly, for examples that are less than b _k away from an uncertain position, the use of the prediction of the machine-learned algorithm is blocked, ie, for example, no prediction is calculated or the prediction is discarded. It is not necessary in all variants that the areas around uncertainly recognized positions are also determined. Sometimes the areas extending between positions of input vectors could also be evaluated accordingly via an evaluation metric (see Box 3520) (this will be explained later).

In some examples, it would be conceivable that the context data 50 are also indicative of permitted results of the machine-learned algorithm if a corresponding input vector is arranged in one of the areas. These permitted results can be determined in box 3516. There are several techniques to determine the allowed results in Box 3516. For example, a special algorithm could be used that determines the permitted results depending on the geometric properties of the respective area. For example, a corresponding additional machine-learned algorithm could be used. A multilayer perceptron or a support vector machine could be used. A classic rule-based algorithm could also be used. For example, the allowed results could be determined based on ground truths for the input vectors of the training data pairs used to determine the ranges. For example, if a particular region is bounded by three input vectors associated with the ground truths “yellow,” “yellow,” and “blue,” then the corresponding region could be characterized in the contextual data such that the output vectors of the machine-learned algorithm are either “ yellow” or “blue”. In other words, for regions formed by a triangular mesh, the allowed outcomes of the hidden system state can be determined based on the ground truths associated with the nodes of the triangular mesh. Corresponding aspects will be discussed later in connection with 12 and 13 explained in more detail.

Optionally, the areas could be partitioned into first areas and second areas in box 3520 based on a predetermined evaluation metric, for example according to TAB. 1, security level I or security level II. For example, the first ranges in terms of the evaluation metric may be associated with a comparatively low uncertainty for the estimation of the hidden system state by the machine-learned algorithm; while the second areas are associated with a comparatively large uncertainty for estimating the hidden system state in terms of the evaluation metric. The context data that is then saved can also be indicative of the partitioning of the areas. The context data could, for example, be the security level according to TAB. Show 1.

It is not necessary in all examples for the areas to be partitioned as part of the parameterization in Box 3001. Rather, it would be conceivable that the partitioning of the areas is carried out in box 3002 as part of the inference. The explanations set out above and below in connection with the determination of the partitioning in box 3520 can be applied accordingly to a partitioning that is only carried out for inference (cf. e.g 11 : Box 3020).

Basically, there are different options for implementing the evaluation metric.

For example, the evaluation metric could include a component that evaluates the plurality of areas based on their distance from positions recognized as unsafe. For example, if an area lies within a distance b _k from a position recognized as unsafe, the area can be classified as unsafe.

For example, the evaluation metric could include a component that partitions the plurality of areas based on an edge length of edges of the areas (see TAB. 1: Security level I vs. II). For example, the longer the individual edges of an area, there might be a tendency for that area to be classified as unsafe. This is based on the knowledge that the probability of a significant change in the output of the machine-learned algorithm is greater the larger the areas are, i.e. the greater the edge length of the edges of the area. The longer the edge length, the greater the probability of a double class change along the respective edge, for example from a first class to a second class and back. So - in other words - a critical threshold a could be defined, which determines a distance in the input vector space below which the ML algorithm can generalize safely. This is based, among other things, on the assumption that if the distance is smaller than a in the input vector space, there will be no double change in the output class. Areas that are classified as safe then have edge lengths that are all smaller than the threshold value a. Areas that are classified as unsafe have at least one side edge that is greater than the threshold value a.

In some examples, the threshold a could be fixed for the different positions in the input space. However, it would also be possible for the threshold value to be chosen as a function of the position in the input space.

If the input vector space has D dimensions (i.e. the input vector includes D entries), then with a number of D+1 training data pairs there will also be a corresponding number of input vectors. These are arranged at different positions in the input vector space. The connection vectors starting from one input vector to the other input vector span an e-dimensional hypervolume of the input vector space if the connection vectors are linearly independent of each other, i.e. none of the connection vectors can be formed by a linear combination of the other connection vectors. Mathematically, it is then said that the “D+1” positions of the input vectors are in a “general position” relative to one another. It can happen that the connection vectors are non-linearly independent. If the D+1 input vectors do not yet span a D-dimensional hypervolume, neighboring points in the input space can be added until a D-dimensional space is spanned. Then this set of points defines a hypervolume for which a generalization can be made and an evaluation of the area can be carried out.

This initial situation enables the triangulation to be set up. The triangulation divides the input vector space into hypervolumes (or areas), whereby the boundary of a hypervolume is defined by the area (more precisely: hypersurface) that lies between three points of the triangulation. The respective hypervolume (i.e. the respective area in the input vector space) is then delimited between the areas of D+1 points adjacent to the triangulation (which are each in a general position relative to one another in accordance with the specifications for the triangulation).

Different types of triangulations may be used in the various examples described herein. This means that different algorithms can be used to determine triangulation. Depending on the choice of triangulation, different areas can be obtained; e.g. is in 5B shows how four points can be triangulated differently (solid vs. dashed lines).

An example of a triangulation is the Delaunay triangulation. The Delaunay triangulation can be carried out using the Bowyer-Watson algorithm. An example of Delaunay triangulation is in 5C shown. The Delaunay triangulation is formed with the so-called circumference condition. The following applies: The circumference of a triangle of the network must not contain any other points from the specified point set. This, mathematically speaking, “maximizes the smallest interior angle across all triangles.” What is achieved is that the smallest angle in the triangles becomes as large as it can be in this triangle network. However, no statement is made about the other angles. Another example of one Triangulation is the so-called min-max triangulation. This is related to 5D explained for three different examples (in 5D are different examples associated with different positions in the input vector space; the positions in the input vector space are marked by the crosses). With min-max triangulation, for example, the triangles are chosen so that the largest edge of the triangle becomes minimal. This helps to choose the maximum side length of the area as small as possible, which is helpful when considering the threshold comparison with the threshold value a. However, it can sometimes happen that several possible triangulations can take place and thus a certain position in the input vector space can be assigned to different areas - depending on the triangulation. If there are several possible assignments and at least one of these assignments can be associated with an uncertain state, the output of the machine-learned algorithm (e.g. a classifier) can be blocked as a result. Accordingly, if there are several possible expenses, there are two options. The classifier can be set to favor either the safest or the most useful output. In the second case, you would of course have to define “usefulness” in terms of prioritized expenditure.

In other words: There is potential for optimization in the possible ambiguity when determining the areas. If for an input vector for which inference is to be made, the position vector in the input vector space lies in two areas, both of which enable a secure assignment (e.g. all edge lengths less than "a", cf. TAB. 1: Example I), then the for the Application “more useful” output of the two areas (i.e. the one with the lower cost) will be used. This would be e.g 5D the case if the top point were “yellow” and the bottom three points were “blue” (as examples of class assignment). In this case, when evaluating the upper triangle (left part of the illustration 5D ) the output “blue” or “yellow” is possible. However, the triangle in the middle representation allows us to safely conclude that the output is “blue”. Then the ML algorithm is allowed to output the output “blue” because this output is done through a secured interpolation since all edge lengths are smaller than a. This variant increases the availability of the system without compromising security.

In summary, a general triangulation without additional conditions can lead to ambiguity. The Delaunay triangulation solves the ambiguity with the circumference condition: There must not be any other points within the circumference of a triangle. Although this reduces the occurrence of very “pointed” triangles, it does not necessarily ensure that the edge length is as small as possible. On the other hand, in order to comply with the above-mentioned threshold value for the edge length, it may be desirable in the various examples described herein to determine the triangles with the shortest possible edge length. This is achieved through min-max triangulation. This minimizes the largest edge of a triangle (“MinMaxEdge”). The choice of the triangle in which a point lies depends only on the position of this point.

If there are not enough training data pairs to define the areas, additional training data pairs can be collected. For example, if problems arise when setting up the triangulation (e.g. because examples are not in a suitable position relative to one another), then further neighboring points are added to the set under consideration until the input vectors of this set of examples span a space with the same dimension as the input space. The positions of the input vectors then define the boundary of a hypervolume for which an output and an assessment of the security of the output can be determined (see TABLE 1).

If D+1 input vectors of the training data set are all less than the critical threshold a apart, then these examples B for the hypervolume H, which is enclosed by the hypersurfaces connecting them, define a hypervolume for which a reliable statement about the internal system state is possible (see TABLE 1). In this case, in some examples it may be possible to take into account permitted results for the prediction or the hidden system state. For example, it would be conceivable that the predicted hidden system state may only assume values that can also be assumed by the examples B in the output that limit the hypervolume; or when estimating the hidden system state, the output value can only take values that are no more than o _d away from such examples B. The approximate function is continuous in this hypervolume H, and in special embodiments it is even Lipschitz continuous. If all “D+1” input vectors belong to the same class K (ie have the same ground truth K), then all other input vectors that lie within the hypervolume can be safely assigned to this class K in accordance with the above statements.

A scenario was described above in which the evaluation metric performs the partitioning of the areas based on their edge length. Alternatively or additionally, the applicant could tion metrics evaluate the variety of domains based on local variation in ground truths. This means that, for example, it can be checked whether and, if so, to what extent the basic truths change within or at the edge of the respective area. For example, it could be checked whether there is a double change in an output class for a classifier as a machine-learned algorithm. This is based on the knowledge that a greater variation in the ground truth in a certain region in the input vector space of the input vector can be indicative of a corresponding increased uncertainty in the prediction of the machine-learned algorithm.

In various examples it would be conceivable that the evaluation metric used in Box 3520 is parameterized. This means that there may be a parameter whose value influences the results of the evaluation. The parameter value can then be selected depending on the area of application or situation-specific. For example, a predetermined threshold value for the side edges (the value a) could be selected based on at least one criterion.

Some exemplary criteria are explained below that can serve as a basis for choosing the threshold value for the edge length. The following explains how the threshold value can be determined.

The criterion could, for example, include a minimum distance between the different input vectors of the training data set that are associated with the different system states. This means that an analysis of the distances between the different input vectors in the training data set can be carried out. In particular, it can be checked what the minimum distance is for input vectors that provide different results, for example different classes, for the hidden system state. Then the predetermined threshold value could be chosen to be less than or equal to this minimum distance.

A corresponding example is in 5E shown. 5E is a two-dimensional representation of the input vector space (generally formulated, the input vector space could also have a higher dimensionality) and shows different regions 691-694 in which input vectors that belong to a specific class are arranged. For example, the input vectors located in region 691 of the input vector space belong to a first class (e.g., “green”), while the input vectors located in a region 692 of the input vector space belong to another, second class (e.g., “red ") belong. In 5E The minimum distance 699 between two positions in the input vector space that are associated with input vectors of different classes is also shown (in the example shown 5E this distance 699 is defined by two input vectors in regions 691 and 693). For example, corresponding information could be provided through a histogram-like evaluation. The distance between all pairs of input vectors that belong to different classes can be plotted in the histogram. The smallest distance between two input vectors that are assigned to different classes can then be determined from the histogram. Accordingly, a histogram can also be created showing the distance at which a double class change occurs. To do this, it is determined for every two examples whether there is an example that lies between these examples (that is, it is closer to the first two examples mentioned) and that has a different class to at least one of the first mentioned examples. This distance 699 can then be selected as a predetermined threshold value between the smallest distance between two examples that are assigned to different classes and the smallest distance with a double class change.

The example of 5E is characterized by good separation of regions 691-694 in the input vector space. This means that the distance 699 and thus the threshold value is comparatively large. This makes it possible to make a reliable prediction of the hidden system state of the technical-physical system in comparatively large parts of the input vector space using the machine-learned algorithm.

In some examples, it may be possible to improve such separation of regions associated with different classes through appropriate preprocessing of state data; so that the input vectors, which are determined based on the state data of the technical-physical system, have the correspondingly large separation. Such progressive separation through different preprocessing is shown in the examples 5F , 5G and 5H shown. For example, it would be possible to define a corresponding quality indicator that is indicative of the separation of the different regions 691-694. Then the preprocessing could be optimized with regard to an optimization function that includes the quality indicator. For example, certain transformations of the state data could be carried out to determine the input vectors. Transformations could also occur in the output space. Corresponding examples are described, for example, in: German patent application 10 2021 207 613.0 .

Alternatively or additionally, the at least one criterion could be determined based on domain knowledge. For example, if the dimensionality of the input vector space is comparatively low, a minimum distance between different classes could be determined based on domain knowledge. As an example: For example, a camera-based route detection for rail vehicles could detect features in images that firstly indicate parallel rails (corrected if necessary by an optical transfer function of a camera), secondly rail sleepers arranged at a certain distance from one another and thirdly the presence of ballast of a defined size between the thresholds. As a concrete example: Using a Hough transformation, for example, the radius of curvature of the rails can be determined using extended parallel linear structures; The frequency of the threshold sequence and the size of the gravel can be determined using a Garbor filter. If in this 3-D input space (radius of curvature of long slender linear parallel objects, frequency of thresholds, size of gravel) three examples differed less than the threshold value determined based on domain knowledge, then a route was recognized. It would then be conceivable that the permissible feature range for recognized rails/tracks is determined based on this domain knowledge and the threshold value is selected based on this.

Alternatively or additionally, the at least one criterion for determining the threshold value could include, for example, a design specification of a development process of the technical-physical system. For example, at least one criterion could specify which security level should be achieved for the operation of the technical-physical system. For example, if a certain security level - for example a probability of a misclassification or an incorrect control action - is required as part of the development process for the technical-physical system, then depending on this specification, a stricter or less strict criterion for the parameterization of the evaluation metric can be used be used.

In Box 3525, the areas determined in Box 3515 and optionally evaluated in Box 3520 can optionally be checked for plausibility. This means that it can be checked/validated whether the classification into “safe” and “unsafe”, for example, is accurate or inaccurate.

For example, the threshold value for the edge length (i.e. the parameter a) can be checked for plausibility based on one or more further training data pairs. These one or more further training data pairs can therefore go beyond the training data set and have further input vectors at positions that have a distance to a position of an input vector of the training data pairs of the original training data set that is smaller than the minimum distance. These additional pairs of training data can then be used to check whether the output of the machine-learned algorithm matches the corresponding ground truth. If this is not the case, the plausibility check may produce a negative result.

This is also in 5I shown. In 5I The circles represent input vectors of the training data set in a first class (e.g. “green”) and the triangles represent input vectors of the training data set in a second class (e.g. “red). Then the areas identified as safe for the first class are shown with a dashed fill (bottom left to top right) and the areas identified as safe for the second class are shown with a different dashed fill (top left to bottom right), see TAB . 1: Security level I. Areas classified as unsafe (here TABLE 1: Security level II) - too large due to class change at the corner points and/or edge length - are shown without filling. The peripheral region (TAB. 1: Security level III) is also shown; No reliable prediction can be made for corresponding input vectors (diamonds) because this would correspond to an extrapolation based on input vectors of the training data set.

The plausibility of the division into the areas identified as safe is then carried out with further pairs of training data, i.e. further input vectors for which the basic truths are known. These additional input vectors are identified with the crosses + circle. An error is detected for one of these additional input vectors (highlighted with an arrow): the ground truth indexes the second class, while this input vector is arranged in an area that is safely classified with respect to the first class.

If an error is detected during the plausibility check in box 3525, the feedback loop could be executed via box 3526. In this case, in box 3526, the side edge threshold (the value a) can be reduced and the areas reclassified.

In box 3530, one or more additional positions in the input vector space can optionally be determined at which additional training data pairs should be positioned. In other words, this means that it can be determined where additional training data pairs are helpful in promoting a reliable prediction of the hidden system state by the machine-learned algorithm. The training data set can therefore be expanded in a targeted manner.

In particular, the evaluation of the areas within the framework of a corresponding partitioning from Box 3520 can be used. As part of such an evaluation, areas in the input vector space can be determined that are associated with a large uncertainty with respect to a corresponding evaluation metric. It would then be possible for further pairs of training data to be arranged in such a way that they lead to a reassessment of these areas that are subject to great uncertainty.

The one or more further positions can be selected in the vector space so that after a redetermination of the large number of areas, taking into account the training data pairs and the further training data pairs, a total size of the first areas increases to the maximum. This could be determined, for example, as part of an optimization algorithm.

There are different options for obtaining such additional training data. For example, a human-machine interface could be controlled to obtain an annotation of ground truths for the hidden system state for the further training data. This means that in a labeling process, those labeling candidates from the set of available input vectors that are determined to be useful based on the partitioning can be given higher priority. This means that a learning curve that describes the accuracy of the machine-learned algorithm as a function of the annotation iterations can be particularly steep. The number of annotations required can be comparatively small. A software simulation of the technical-physical system could also be suitably set in order to obtain the ground truth for the hidden system state for the further training data pairs.

If further pairs of training data are received, Box 3510 and the subsequent boxes can be carried out again (in 5A shown by the feedback dashed arrow).

In Box 3535 it is then possible to store the trained machine-learned algorithm obtained by executing Box 3510, as well as the context data 50 obtained from Box 3515 and, if applicable, Box 3520.

The foregoing was in connection with 5A Aspects related to determining contextual data indicating areas are explained. Based on these areas, it can be determined whether a prediction from the machine-learned algorithm is reliable or unreliable. This effect of the areas is explained in more detail below, using a practical example 6-10 (here also shown in two dimensions for illustration purposes; in practical examples there is a higher dimensionality of the corresponding input vector space 71).

6 illustrates an example of the positioning of input vectors 511-513 and 521-523 in input vector space 71. The true hidden system state can be divided into two classes corresponding to regions 531, 532.

For example, area 531 could correspond to a properly functioning motor for a track switch; while area 532 could correspond to a stalled engine. The input vectors 511-513 and 521-523 could correspond, for example, based on measured values for a current flow through the motor as well as measured data from a vibration sensor. This is just a specific example and other examples are possible.

The input vectors 511-513 and 521-523 are part of a training data set. The training data set therefore comprises several pairs of training data, each of which includes a corresponding input vector 511-513 and 521-523, as well as an associated output vector as ground truth for the input vectors 511-513 displays a first output class (e.g. “motor defective”) and for the input vectors 521-523 displays a second output class (e.g. “motor not defective”).

In 6 Another input vector 550 is also shown. This input vector 550 is not part of the training data set. This means that there is no ground truth for the input vector 550. Input vector 550 actually corresponds to the second output class, as do input vectors 521-523. However, it will be shown below that different machine-learned algorithms 89, which are trained based on the input vectors 511-513 and 521-523, can make an incorrect prediction for the input vector 550.

This is initially in 7 shown for a nearest neighbor classifier. The input vector 550 is in the immediate vicinity of the input vector 513; which was trained during training as belonging to the first output class. So the nearest neighbor classifier would incorrectly predict the first class based on the input vector 550.

This also applies to a machine-learned algorithm 89 implemented by a multilayer perceptron, as in 8th shown. In 8th shows how such a machine-learned algorithm 89 - trained based on the input vectors 511-513, 521-523 - predicts the class boundary 565. There is a discrepancy in the area of the input vector 550, resulting in an incorrect prediction.

The same also applies to an SVM implementation of the machine-learned algorithm, see 9 . In 9 the corresponding class limit 567 is shown. Here too there is a misclassification for the input vector 550.

The following shows how, based on the areas indicated by the context data 50, such an uncertain prediction is made by the machine-learned algorithm 89 in the implementations according to 7-9 can be anticipated.

In 10A The areas 571-574 are shown, which result from an interpolation between the input vectors 511-513 and 521-524. The areas are obtained by triangulation, whereby, as already described above, different triangulations can be used. Examples are a min-max triangulation or a Delaunay triangulation.

Furthermore, in 10A the critical edge length 590 is shown. In the example shown, this critical edge length 590 is determined so that it corresponds to the smallest distance between two input vectors 511-513 and 521-524 of the training data set for which a class change is observed (that is between input vector 512 and input vector 523).

As a general rule, different distance metrics may be used in the various examples described herein. For example, the Euclidean distance can be used. However, the so-called p-norm could also be used.

As a general rule, the critical edge length 590 can be chosen so that no double class change for the output of the machine-learned algorithm can occur within the corresponding length in the input vector space. See TAB. 1: Security level I.

In 10A It can be seen that the areas 571, 572 and 574 have edge lengths that are not below the critical edge length 590. Accordingly, these areas 571, 572, 574 (see TABLE 1: Security level I) are rated as unsafe. For example, for the area 574 in 10B an enlarged illustration of how a different class may appear along the line connecting input vectors 524 and 522 in region 574--1; So there is a double class change. An input vector that lies within these areas 571, 573, 574 causes an uncertain prediction of the associated hidden system state using the machine-learned algorithm. An error indicator can then be output, based on which, for example, a warning or a transfer of the controlled technical-physical system to a safe operating state can occur.

A different situation exists for area 573 (cf. 10A) . The area 573 only has edges that are shorter than the critical edge length 590. The area 573 can therefore be assessed as safe, see TAB. 1 security level I).

Out of 10A It can also be seen that the further input vector 550 does not lie within any of the areas 571-573. Therefore, no reliable prediction can be made for the further input vector 550 using the machine-learned algorithm (see TAB. 1: Security level III) - which is consistent with the observations presented above 7 , 8th and 9 covers.

A variant was explained above in which the areas are arranged between positions of input vectors. Another variant is in 10C shown. The input vector space 71 is shown there and positions of input vectors 662 for a first class and of input vectors 663 for a second class, as well as the class boundary 660. Inference for an input vector 661 could give an incorrect result (first class). This could - if the threshold value for the edge length of the areas that extend between the positions of the input vectors 662 is chosen to be too large (see TAB. 1: Example I) - be incorrectly classified as safe. To prevent this, an area 670 - cf. 10D - are determined, which surrounds the position of the input vector 663 marked with a cross and delimits a distance b to this position. The inference for all input vectors (including input vector 661) within this area 670 can then be recognized as unsafe. Alternatively, the interpolated areas 671 (cf. 10E) be recognized as unsafe by the evaluation metric because the distance to the position of the unsafe input vector 663 is smaller than b, ie smaller than a distance threshold 679. The area 670 could be determined, for example, based on a course of the class boundary 660. For example, where no ground truth is available in training near a known class boundary, a corresponding area 670 could be arranged.

The context data 50 indicates the areas. This can be the case with inference (cf. 4 : Box 3002). This is explained below.

11 is a flowchart of an example method. 11 can implement Box 3002 for example. 11 concerns inference using a pre-trained machine-learned algorithm based on an input vector for which no ground truth is available. For example, the procedure could be: 11 are executed by the processor 92 after it loads and executes a corresponding program code from the memory 93.

First, an input vector is obtained in box 3005. This can encode status data of the technical-physical system. For example, the input vector could be based on corresponding state data (compare 1 : status data 81), which are received from the technical-physical system, are determined. The input vector can be loaded from memory.

The machine-learned algorithm is loaded into Box 3010. A corresponding program code can be loaded from memory.

The machine-learned algorithm has already been trained at this point, meaning parameter values have been set. Techniques such as those described above in connection with Box 3001, for example, can be used for training 5A and also related to 4 described can be used.

Then context data is loaded into Box 3015. The context data is associated with the machine-learned algorithm. Additionally, the context data indicates multiple regions in the vector space of the input vector. This was discussed above in connection with 10A discussed. The areas can be determined as part of the parameterization of the machine-learned algorithm, as described above in connection with 5A : Box 3515 described.

There are different ways that the context data can index regions in the input vector space. The context data could, for example, specify the areas directly, i.e. define corresponding boundaries for each area. It would also be conceivable that the context data indicates the key points; and then the areas are determined from this using a Delaunay triangulation or another triangulation or another scheme. The context data can indicate the interfaces between the areas.

The context data can also be optimized. The context data can specify the areas in compressed form. For example, areas that have the same properties can be combined in order to determine the hidden system state as efficiently as possible. Such a combination of areas or other optimization/compression of the context data can be done in 5A : box 3515.

In some examples, the context data can also display additional information beyond the areas.

The areas can be divided into first areas and second areas. The first areas (cf. 10A : Regions 573) may be associated with low uncertainty in estimating the hidden system state using the machine-learned algorithm; while the second areas are associated with a comparatively high uncertainty in estimating the hidden system state (cf. 10A : Areas 571, 572).

In principle, it is possible for the context data to already include an indicator that indexes a corresponding partitioning of the areas into the first and second areas. This means that a corresponding partitioning of the areas can already be carried out in connection with the parameterization of the machine-learned algorithm and then this previous partitioning can be used as part of the inference (corresponding aspects were, for example, in connection with Box 3520 in 5A explained). However, in some examples it would also be conceivable that the corresponding partitioning is only determined as part of the inference, namely in box 3020, for example. This means that in box 3020 each of the areas indexed by the context data can be evaluated based on a corresponding evaluation metric . Corresponding evaluation metrics have already been described above in connection with Box 3520. The same evaluation metrics or components of the evaluation metric can also be applied during inference in Box 3020. Such evaluation metrics relate, for example, to an evaluation of the areas based on an edge length of edges of the areas, where this edge length can be compared with a size threshold. For example, the size threshold was used in connection with 10A : critical length 590 discussed. The size threshold can be displayed through the context data. Another exemplary component of the evaluation metric could, for example, concern the classification of an area as safe or unsafe based on a distance to positions in the input vector space that are recognized as unsafe. Such positions in the input vector space that are recognized as uncertain could, as described above, be determined based on a course of class boundaries.

If the evaluation metric includes several components, these components can be ordered hierarchically. This can mean that the partitioning treats a first criterion with a higher hierarchy than a second criterion (i.e. the first criterion has a higher hierarchy level than the second criterion). For example, such a criterion could be checked first; and if it is then determined that a particular area is to be classified as unsafe, for example, it may be unnecessary to assess the area in terms of other criteria of the evaluation metric. For example, it may be particularly desirable to primarily check the distance to positions in the input vector space that are recognized as unsafe with regard to a threshold value (the parameter b; distance 679 in 10D ); and only secondarily to check a consideration of the edge lengths of edges of the regions in relation to the size threshold (the parameter a). The consideration of b can therefore generally take precedence over the other components of the evaluation metric, including the side length with regard to the threshold value a. So you can first place a safety ring around all critical states (ie unsafe positions in the input vector space). This means that even complex interfaces can be treated safely. In the remaining input vector space, one can then work with a comparatively larger threshold value for the edge length (parameter a) (compared to a scenario without taking the distances to positions classified as unsafe into account), since the occurrence of new clusters away from the dividing line between classes is then limited can. In this way, you can ensure safe treatment of the interfaces but also work with a large threshold value for the edge length a to prevent the occurrence of new clusters. It may therefore be desirable to first apply the distance threshold b to classify the areas with the highest priority and then secondarily to evaluate the areas regarding the edge length with regard to the threshold value a.

Performing partitioning for inference in Box 3020 may have certain advantages over performing partitioning during parameterization of the machine-learned algorithm (cf. 5A : Box 3520). In particular, it would be conceivable that the evaluation metric is adjusted during inference based on current circumstances of the physical-technical system. This means that, depending on the operating situation of the physical-technical system, a different partitioning can be determined for the several areas, so that, depending on the operating situation of the physical-technical system, certain areas can be classified as safe or unsafe. In this way, it can be tailored to the current operating situation of the physical-technical system Adapted security level for the control can be achieved based on the machine-learned algorithm.

For example, it would be conceivable that the evaluation metric is parameterized based on an operating mode of the technical-physical system. The operating mode can be associated with the status data. This means that the status data (compare 1 : Status data 81) are currently provided by the physical-technical system and their values depend on which operating mode is activated.

The evaluation metric could thus be parameterized based on an operational safety level of the function to be provided by the technical-physical system, which is specific to the operating mode. This is based on the knowledge that certain technical-physical systems can be operated in different operating modes, which require different operational safety levels for automatic control. An example would be semi-autonomous versus fully autonomous driving. With semi-autonomous controls (e.g. "Level 2" - partially automated driving), the driver retains access to the vehicle, so that the operational safety level for the control can be reduced compared to fully autonomous controls (e.g. "Level 5" - autonomous driving). Accordingly, it would be conceivable that a different evaluation metric would be used to partition the areas for the reliability of the prediction, depending on whether semi-autonomous or fully autonomous driving is implemented based on the prediction of the machine-learned algorithm.

For example, if a division of the areas is based on the edge length compared to a given size threshold (compare 10A : critical length 590), it would be conceivable that this edge length would be chosen to be shorter or longer depending on the operating mode of the technical-physical system. A larger size threshold then results in a larger number of areas for which the machine-learned algorithm is assumed to make a confident prediction.

Examples have been described above in which the context data indexes further information beyond the areas; An example in particular has been described above in which it is possible for the context data to index the partitioning of the areas. In addition to such further information provided by the context data, other information could also be provided by the context data.

In some scenarios, it would be conceivable that the context data for at least some areas of the plurality of areas index one or more permitted results for the hidden system state. This means that - in addition to indicating the different areas in the input vector space - it can also be specified which permissible output values the output vector may assume, provided that the input vector is positioned in a corresponding area. For example, in 12 a scenario is shown in which the context data 50 describes several areas 771-776 (the areas form a triangular network and are represented by corresponding triangular areas - in 12 represented by the lines - limited due to the two-dimensional representation) and specify an indicator 751 for each of the areas 771-776, which partitions the areas into those with a low uncertainty and others with a high certainty of estimating the hidden system state using the machine-learned Algorithm describes. There is also another indicator 752 that indexes one or more allowed outcomes for the estimated hidden system state. The same thing was also done in 5A described in connection with Box 3516.

Outside the areas 771-776 there could be extrapolation (e.g. for point 779) (see TABLE 1: Security level III), so that a reliable prediction is not possible here.

In box 3025 in 11 it is then possible to determine the relative position of the input vector with respect to the areas. For example, it could be checked whether the input vector is in a certain range or outside all ranges. For example, if the context data indexes the regions by the interfaces between the regions, appropriate verification could include forming subspaces in the input vector space based on the corresponding interfaces.

Based on this relative position, it can then be checked in box 3030 whether either - box 3035 - an error indicator should be output (i.e. the output of the machine-learned algorithm is blocked) or in box 3040 the input vector of the machine-learned algorithm should be processed (i.e. the output of the machine-learned algorithm is allowed and further processed).

For example, the error indicator in box 3035 could be output if and only if the input vector is not located in any region (in such a case it may be unnecessary to partition the regions). It would also be conceivable that the error indicator is output even if the input vector lies in a range that is associated with a large uncertainty in estimating the hidden system state, for example as indicated by the corresponding indicator 751 in the context data 750; or as determined by the partitioning in Box 3020. If the error indicator is output in box 3035, this can be taken into account in box 3050 to control the technical-physical system. For example, the technical-physical systems could be transferred to a safe operating state. A warning could be issued to an operator of the technical-physical system. An error log file could be supplemented accordingly.

If the input vector of the machine-learned algorithm is processed in box 3040, an output vector is then obtained as the output of the machine-learned algorithm, which is indicative of the hidden system state of the technical-physical system. In some examples, this output could then be used to control the technical-physical system, Box 3050.

Optionally, it would also be conceivable in Box 3045 to display the hidden system state that is obtained as output from the machine-learned algorithm in Box 3040, based on allowed results for the system state indexed by the context data (compare 12 : indicator 752). For example, averaging could occur, for example when a regression task is performed by the machine-learned algorithm. In a regression task, in addition to the predicted value, information regarding a probability distribution of the predicted value can also be output. This probability distribution may depend on the distance to regions with indicators of other values to the position of the input vector in the input space. Another example is in 13 illustrated. 13 basically corresponds 12 . In the example of 13 However, the context data 50 is structured in such a way that a corresponding indicator 753 is provided in connection with a corner of the areas 771-776, which indexes a respective permitted result for the estimated system state or the output of the machine-learned algorithm. It would then be possible to determine a distance between the position of the input vector in relation to the different corners of the areas 771-776 and to select the respective permitted result (or - for a regression task - the probability distribution) based on these distances. The corners of the areas 771-776 correspond to the positions of corresponding input vectors of the underlying training data set; the permitted outcomes could be chosen here based on the corresponding ground truths. For example, the nearest corner could be taken into account and then based on the indicator 753 associated with that corner, the allowed result for the output of the machine-learned algorithm could be determined (for the in 13 The input vector 85 shown would be “blue”).

These are in 12 and 13 The scenarios presented are just examples. Other techniques would also be conceivable to determine the permitted results for the system status. For example, it would be conceivable that the predicted hidden system state may only assume values that are no further than o _d from the permitted results indicated by the context data 50. This can be particularly helpful for regression tasks

Again referring to 11 : there may be situations where the output of the machine learned algorithm from box 3040 does not match the one or more allowed outcomes determined from the context data 750. It is possible to compare the hidden system state estimated by processing the input vector in the machine-learned algorithm with the corresponding allowed results for the range from the context data, box 3045. If the comparison indexes no or only a reduced match, a Error indicator is output.

Box 3040 and Box 3045 therefore correspond to a two-stage approach. First, in Box 3040, result candidates are determined using the machine-learned algorithm; which can then be corrected in box 3045 if necessary, based on the context data.

In Box 3050, the control of the technical-physical system can then be carried out based on the error indicator (from Box 3035 or, if applicable, from Box 3045) and/or the estimated hidden value a system state from Box 3040. For example, corresponding control data could be sent to the technical-physical system.

In summary, techniques have been described above in which contextual data is generated in connection with the training of a machine-learned algorithm. The contextual data is indicative of regions in the input vector space that are associated with confident or uncertain predictions from the machine-learned algorithm. The areas can be generated, for example, as a Delaunay triangulation between positions of input vectors of a training data set. The areas therefore form hyperspace volumes. Each hyperspace volume can be assigned as a marker the set of output classes of the examples that form the corner points of the hyperspace volume. If the distance between all points in the input space is smaller than “a”, the “safe” feature is also set for the marking. The attribute safe in the marking means that only the outputs that are present in the examples that limit the hyperspace volume can occur. Other outputs cannot occur in this case because of the assumption in “a” that no double class change occurs.

Of course, the features of the previously described embodiments and aspects of the invention can be combined with one another. In particular, the features can be used not only in the combinations described, but also in other combinations or alone, without departing from the field of the invention.

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Cited patent literature

• DE 102021207613 [0102]

Claims (48)

Computer-implemented method for estimating a hidden system state of a technical-physical system using a machine-learned algorithm, the method comprising: - Obtaining an input vector (85, 511, 512, 513, 521, 522, 523, 550) that encodes state data (81) of the technical-physical system (95), - loading the machine learned algorithm (89), - Loading predetermined context data (50) associated with the machine-learned algorithm (89) and containing a plurality of areas (72, 571, 572, 573, 574, 771-776) in the vector space (71) of the input vector (85, 511, 512, 513, 521, 522, 523, 550) index, - determining a relative position of the input vector (85, 511, 512, 513, 521, 522, 523, 550) with respect to the plurality of areas (72, 571, 572, 573, 574, 771-776), and - based on the relative position, either processing the input vector in the machine-learned algorithm to estimate the hidden system state, or outputting an error indicator. Computer-implemented method Claim 1 , wherein one or more first areas (571, 572) of the plurality of areas are associated with a comparatively low uncertainty in estimating the hidden system state, wherein one or more second areas (573) of the plurality of areas are associated with a comparatively high uncertainty in estimating the hidden system status. Computer-implemented method Claim 2 , wherein the context data (50) includes an indicator (751) indexing a partitioning of the plurality of areas into the one or more first areas and the one or more second areas. Computer-implemented method Claim 2 , wherein the method further comprises: - after loading the context data (50) and based on a predetermined evaluation metric, determining (3020) a partitioning of the plurality of areas into the one or more first areas and into the one or more second areas. Computer-implemented method Claim 4 , wherein the method further comprises: - parameterizing the evaluation metric based on an operating mode of the technical-physical system that is associated with the status data (81). Computer-implemented method Claim 5 , wherein the evaluation metric is parameterized based on an operational safety level of the technical-physical system (95), which is specific to the operating mode. Computer-implemented method according to 5 or 6, wherein the evaluation metric includes a component that partitions the plurality of areas based on an edge length of edges of the areas of the plurality of areas, wherein an edge length size threshold (590) that decides between assignment to the plurality of first regions and the plurality of second regions is selected based on the mode of operation. Computer-implemented method according to one of the Claims 4 until 7 , wherein the evaluation metric includes a component that partitions the plurality of regions based on a distance (679) to positions (663) in the input vector space that are recognized as unsafe. Computer-implemented method according to one of the Claims 4 until 8th , where the evaluation metric includes several components that are ordered hierarchically. A computer-implemented method according to any one of the preceding claims, wherein the predetermined context data (50) comprises an indicator (752) that indexes one or more permitted results for the hidden system state for at least some areas of the plurality of areas. Computer-implemented method Claim 10 , the method further comprising: - adjusting (3045) the hidden system state created by processing the input vector in machine-learned algorithm (89) is estimated based on the allowed results for the system state for that area of the plurality of areas in which the input vector is positioned. Computer-implemented method Claim 11 , wherein the method further comprises: - determining a distance of the position of the input vector with respect to edges or corners of that area of the plurality of areas in which the input vector is positioned, the predetermined context data for that area in which the input vector is positioned, index a plurality of allowed outcomes for the hidden system state, where different ones of the plurality of allowed outcomes in the context data are associated with different edges or corners of this region in which the input vector is positioned, and - selecting the one of the plurality of allowed outcomes that corresponds to the Edges or corners of the area in which the input vector is positioned, to which the position of the input vector is the closest distance, the hidden system state is corrected based on the selected allowed result. Computer-implemented method according to a he Claims 11 or 12 , the method further comprising: - comparing the hidden system state estimated by processing the input vector in the machine-learned algorithm with the corresponding allowed system state results for that region of the plurality of regions in which the input vector is positioned, and optionally Output the error indicator based on the comparing. Computer-implemented method according to one of the preceding claims, where the context data describes a triangular network, wherein the areas of the plurality of areas are delimited by triangular areas of the triangular network. Computer-implemented method according to one of the preceding claims, the method further comprising: - Controlling (3050) the technical-physical system (95) based on at least one of the estimated hidden system states or the error indicator. Computer-implemented method for parameterizing a machine-learned algorithm (89) by means of which a hidden system state of a technical-physical system (95) can be estimated, the method comprising: - Obtaining (3505) a training data set containing several training data pairs of state data of the technical-physical system (95) encoding input vectors (85, 511, 512, 513, 521, 522, 523, 550) and ground truths for the hidden system state of the technical-physical System (95) includes, - performing (3510) training of the machine-learned algorithm (89) based on the training data set to obtain parameter values for the machine-learned algorithm, - based on the input vectors (85, 511, 512, 513, 521, 522, 523, 550), determining (3515) a variety of regions (72, 571, 572, 573, 574, 771-776) in the vector space (71 ) of the input vectors, - Generating context data (50) for the machine-learned algorithm so that it is indicative of the variety of areas, and - Storing the machine-learned algorithm (89) and storing the context data (50) associated with the machine-learned algorithm (89). Computer-implemented method according to one of the claims, the method further comprising: - based on a predetermined evaluation metric, determining (3520) a partitioning of the areas of the plurality of areas into first areas and second areas, the first areas being associated with a low uncertainty with respect to the evaluation metric for the estimate of the hidden system state, the second areas of the plurality of areas with respect to the evaluation metric are associated with a large uncertainty for the estimation of the hidden system state, and - based on the partitioning, determining (3530) one or more further positions in the vector space (71) at which further pairs of training data should be positioned. Computer-implemented method Claim 17 , wherein the method further comprises: - Controlling a human-machine interface to obtain an annotation of the ground truths for the hidden system state for the further training data pairs. Computer-implemented method Claim 17 or 18 , wherein the method further comprises: - Setting a software simulation of the technical-physical system in order to obtain the ground truths for the hidden system state for the further training data pairs. Computer-implemented method according to one of the Claims 17 until 19 , wherein the one or more further positions in the vector space (71) are chosen so that after a redetermination of the large number of areas, taking into account the training data pairs and the further training data pairs, a total size of the first areas increases to the maximum. Computer-implemented method according to one of the Claims 16 until 20 , wherein at least some of the plurality of regions are arranged between positions of the input vectors in the corresponding vector space (71). Computer-implemented method according to one of the Claims 16 until 21 , wherein at least some areas of the plurality of areas surround positions of an input vector in the corresponding vector space that are recognized as uncertain. Computer-implemented method Claim 22 , the method further comprising: - Detecting the more uncertain positions based on a gradient of class boundaries. Computer-implemented method according to one of the Claims 16 until 23 , wherein the method further comprises: - based on a predetermined evaluation metric, determining a partitioning of the plurality of areas into first areas and second areas, the first areas being associated with a low uncertainty with respect to the evaluation metric for the estimation of the hidden system state, wherein the second areas of the plurality of areas are associated with a large uncertainty with respect to the evaluation metric for estimating the hidden system state, the context data being indicative of the partitioning of the areas. Computer-implemented method Claim 24 , wherein the evaluation metric includes a component that partitions the plurality of regions based on an edge length of edges of the regions of the plurality of regions. Computer-implemented method Claim 24 or 25 , where the evaluation metric includes a component that partitions the regions based on a local variation of the ground truths for the hidden system state. Computer-implemented method according to one of the Claims 24 until 26 , wherein the evaluation metric includes a component that evaluates the areas based on a distance (679) to a position (663) recognized as unsafe in the vector space of the input vectors. Computer-implemented method Claim 27 , which further includes: - Detecting uncertain positions in the vector space of the input vectors based on a gradient of class boundaries. Computer-implemented method according to one of the Claims 16 until 28 , where the regions are bounded by areas that extend in vector space between the positions of adjacent input vectors. Computer-implemented method according to one of the Claims 16 until 29 , the method further comprising: - determining the areas (72, 571, 572, 573, 574, 771-776) of the plurality of areas (72, 571, 572, 573, 574, 771-776) based on triangular areas of a triangular network , whose nodes are formed by the input vectors (85, 511, 512, 513, 521, 522, 523, 550). Computer-implemented method Claim 30 , where the triangular network is formed by a Delaunay triangulation or a min-max triangulation. Computer-implemented method one of the Claims 24 until 28 , as well as after Claim 30 or 31 , wherein the one or more first areas are limited only by triangular areas that do not have a side edge that is longer than a threshold value predetermined by the evaluation metric. Computer-implemented method Claim 32 , wherein at least one of the one or more second areas is each delimited by at least one triangular area which has at least one side edge that is longer than the predetermined threshold value. Computer-implemented method Claim 32 or 33 , wherein the method further comprises: - parameterizing the evaluation metric, wherein parameterizing the evaluation metric includes: determining the predetermined threshold based on at least one criterion. Computer-implemented method Claim 34 , wherein the at least one criterion comprises a minimum distance between two different input vectors of the training data set that are associated with different hidden system states. Computer-implemented method Claim 35 , wherein the method further comprises: - Checking the plausibility of the minimum distance based on one or more further training data pairs that have input vectors at positions that have a distance to a position of an input vector of the training data pairs that is smaller than the minimum distance. Computer-implemented method according to one of the Claims 34 until 36 , wherein the at least one criterion includes a design specification of a development process of the technical-physical system. Computer-implemented method according to one of the Claims 34 until 37 , wherein the at least one criterion includes a specification for an operational safety level of the technical-physical system. Computer-implemented method according to one of the Claims 34 until 38 , whereby the at least one criterion includes domain knowledge. Computer-implemented method according to one of the Claims 24 until 39 , wherein the context data is generated such that it is indicative of allowed results of the hidden system state for at least some areas of the plurality of areas, the method further comprising: - for each of the at least some areas: determining (3516) the allowed results of the hidden System state based on the ground truths for the hidden system state that are associated with the nodes of the triangular surfaces of the triangular network delimiting the respective area. Computer-implemented method for estimating a hidden system state of a technical-physical system using a machine-learned algorithm, wherein the method includes: - depending on at least one predetermined criterion, optionally allowing or blocking an estimate of the machine-learned algorithm for the hidden system state for an input vector, wherein the at least one predetermined criterion takes into account a position of the input vector in the corresponding input vector space. Computer-implemented method Claim 41 , whereby the prediction is blocked if the position of the input vector corresponds to an extrapolation of the machine-learned algorithm based on state data of the technical-physical system contained in a training data set for the machine-learned algorithm. Computer-implemented method Claim 41 or 42 , whereby the prediction is blocked if the position of the input vector of an interpolation of the machine-learned algorithm between two or more state data of the technical-physical system contained in a training data set for the machine-learned algorithm corresponds and if a distance between the positions in the input vector space corresponding to two or more state data is greater than a predetermined threshold value. Computer-implemented method according to one of the Claims 41 until 43 , wherein the prediction is permitted if the position of the input vector corresponds to an interpolation of the machine-learned algorithm between two or more state data of the technical-physical system included in a training data set for the machine-learned algorithm and if a distance between the two or more state data corresponding positions in the input vector space is smaller than a predetermined threshold value. Computer-implemented method according to one of the Claims 41 until 44 , whereby the prediction is blocked if the position of the input vector falls below a minimum distance (679) to positions (663) in the input vector space that are labeled as uncertain. Computer-implemented method according to one of the Claims 41 until 45 , wherein the at least one criterion comprises a plurality of criteria, the method further comprising: - sequentially checking the plurality of criteria. Device comprising at least one processor and a memory, wherein the at least one processor is configured to load and execute program code from the memory, wherein the at least one processor is configured to execute, based on the program code, a computer-implemented method according to one of Claims 1 until 46 to carry out. Computer program comprising program code that can be loaded and executed by at least one processor, wherein the at least one processor implements a computer-implemented method according to one of the Claims 1 until 46 executes.

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