CN117634363B - Flow field reconstruction method based on quantum Koopman analysis - Google Patents
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Abstract
The invention discloses a flow field reconstruction method based on quantum Koopman analysis, which comprises the steps of inputting flow field data into a trained quantum Koopman analysis model to output a flow field reconstruction result; the training process of the quantum Koopman analysis model is as follows: s1: constructing a training set; s2: constructing a nonlinear mapping function and constructing mapped flow field data based on quantum circuitsIs a query interface of (1)To implement a mapping function; s3: to query interfaceAs input, computation based on quantum dynamic modal decomposition algorithmIs the main characteristic value of (2)And principal eigenvector; S4: based on principal eigenvaluesAnd principal eigenvectorReconstructing mapped flow field dataObtaining flow field data after reconstruction; the flow field reconstruction method reduces the reconstruction cost and improves the accuracy of the reconstructed fluid.
Description
Technical Field
The invention relates to the technical field of flow field reconstruction, in particular to a flow field reconstruction method based on quantum Koopman analysis.
Background
Flow field reconstruction is an important research problem in hydrodynamic research, and a specific task is to reconstruct flow field evolution according to observed flow field data. With the development of flow field research in large scale, high precision, strong coupling and the like, the dimension of generated flow field data is continuously increased, and too much computing resources are needed for analyzing flow field data and reconstructing the flow field by using a classical computer, so that the computing power of the classical computer may be exceeded.
Quantum computing has powerful data processing capability, and various quantum algorithms for accelerating data analysis tasks have been developed, such as a quantum support vector machine [ PHYSICAL REVIEW LETTERS 113.13.13 (2014): 130503], a quantum principal component analysis method [ nature Physics 10.9 (2014): 631-633], a quantum algorithm for analyzing data topology and geometric characteristics [ Nature communications 7.1.1 (2016): 10138], and a quantum dynamic modal decomposition algorithm for analyzing high-dimensional time series data [ INTELLIGENT COMPUTING (2023): 0045].
However, the quantum algorithm has some limitations when directly applied to the problem of flow field reconstruction: the defects of inaccurate flow field data and high reconstruction cost are caused by the fact that the nonlinear characteristics of the flow field data cannot be extracted, the algorithm optimization cost is too high, and the like.
Disclosure of Invention
Based on the technical problems in the background technology, the invention provides a flow field reconstruction method based on quantum Koopman analysis, which reduces the reconstruction cost and improves the accuracy of the reconstructed fluid.
According to the flow field reconstruction method based on quantum Koopman analysis, flow field data are input into a trained quantum Koopman analysis model to output flow field reconstruction results;
The training process of the quantum Koopman analysis model is as follows:
s1: constructing a training set, and setting flow field data in the training set Stored in a quantum data structure, and a data query interface/>, is constructed by querying the quantum data structure，/>Representing flow field data/>Middle/>Data corresponding to flow field observational quantity of moment,/>，/>Representing the number of time steps;
s2: constructing a nonlinear mapping function and constructing mapped flow field data based on quantum circuits Query interface/>To realize mapping function based on query interface/>Flow field data/>Mapping to post-mapping flow field data/>，，/>Represents the/>Data of time of day/>Vector after mapping by the mapping function;
s21: introducing parameters to be optimized to construct a mapping function, and constructing flow field data based on the mapping function Corresponding mapped flow field data/>The parameters to be optimized are subjected to parameter optimization in the training process;
S22: query interface based on quantum arithmetic operation Go/>Any element/>, is calculated by secondary queryRealize inquiry interface/>First operation/>Wherein/>Representing vectors/>First/>A component;
s23: preparation method based on quantum state amplitude for multiple data Amplitude encoded state preparation of (a) to obtain mapped vectorsAmplitude encoding state of (a) to realize inquiry interface/>Second operation/>；
S24: quantum arithmetic operation based pair dataIs/is > ofCalculating to obtain a vector/>Is/is > ofRealize inquiry interface/>Third operation/>；
S3: to query interfaceAs input, calculating/>, based on a quantum dynamic modal decomposition algorithmPrincipal eigenvalues/>And principal eigenvector/>，/>Representing Koopman operators;
s31: preparation of the initial state Wherein, the method comprises the steps of, wherein,Representing a trace operation on matrix H,/>Respectively represent data/>Is a singular value, a left singular vector, a right singular vector,/>，/>；
S32: in an initial stateAs input state, pair/>Executing a quantum singular value estimation algorithm and performing post-processing to obtain a quantum state/>，/>Wherein/>Representation will/>Matrix after hermitization,/>Representing intermediate process parameters,/>Representation/>Is the transposed conjugate of (2);
S33: for quantum state Sampling, and calculating/>, based on the sampling resultLow-dimensional projection matrix/>And pair/>And (3) performing characteristic decomposition: /(I)Wherein/>Representation/>Is/are of the eigenvectors of (1)Representation/>Is a characteristic value of (2);
S34: matrix of low-dimensional projection As/>Principal eigenvalues/>Each score/>；
S35: by projecting the matrix in low dimensionsAnd query interface/>Performing operator linear combination to obtain/>Principal eigenvector/>Each component/>Amplitude encoded states/>；
S4: based on principal eigenvaluesAnd principal eigenvector/>Reconstructing mapped flow field data/>And obtaining the flow field data after reconstruction.
Further, in step S1,，/>Representing the grid number of the flow field,/>Indicating time step number and inquiring interfaceThe following are provided:
wherein, Represents the/>Time 1/>Observation data corresponding to each grid,/>Representation data/>Is used for the amplitude encoding state of (a),，/>Representation data/>Is a binary norm of (c).
Further, in step S21, the mapping function is defined as:
wherein, Representing transpose,/>Representing parameters to be optimized,/>Constant representing nonlinear order,/>Representing tensor product operation;
Construction of flow field data based on mapping function Mapped flow field data。
Further, in step S23, for a plurality of dataAmplitude encoded states/>The preparation method specifically comprises the following steps:
First preparing quantum state Wherein/>，/>Representing parameters to be optimized;
Executing intermediate parameters Obtaining the quantum stateGenerate data/>Amplitude encoded states/>，/>Right and left vector symbols of dirac in quantum mechanics are represented;
In step S24, two norms The calculation formula of (2) is as follows:
wherein, Constant representing nonlinear order,/>Representing the sum index.
Further, in step S4, specifically:
S41: based on principal eigenvalues Each score/>And principal eigenvector/>Each component/>Amplitude encoding state of (2)Reconstructing the vector/>, at each momentTo reconstruct/>Recorded as reconstruction data/>Will reconstruct data/>Collecting to obtain flow field data after reconstruction;
s42: by reconstructing data Performing operator linear combination to prepare the quantum state/>；
Reconstructing dataThe calculation formula of (2) is as follows:
wherein, Representing the cut-off order,/>First/>, representing initial coefficientsThe elements.
Further, in the quantum Koopman analysis model training process, constructing a loss function to optimize parameters to be optimized in the mapping function, wherein the loss functionThe formula of (2) is as follows:
wherein, Representing the number of time steps,/>Representing vectors/>Reconstructed data after reconstruction.
The flow field reconstruction method based on quantum Koopman analysis has the advantages that: the flow field reconstruction method based on quantum Koopman analysis provided by the invention calculates the main characteristic value of the Koopman operator by using a quantum Koopman analysis modelAnd principal eigenvector/>Based on principal eigenvalue/>And principal eigenvector/>Reconstructing the mapped flow field data, thereby outputting a flow field reconstruction result; the flow field data after mapping is reconstructed based on the quantum Koopman analysis model, so that the nonlinear characteristics of the flow field data can be particularly focused and reconstructed, and the accuracy of the flow field data after reconstruction and the accuracy of evolution based on the flow field data after reconstruction are improved.
Drawings
FIG. 1 is a schematic diagram of the structure of the present invention;
FIG. 2 is a schematic diagram of a training flow of a quantum Koopman analytical model;
FIG. 3 is a flow diagram of a quantum dynamic modal decomposition algorithm;
fig. 4 is a schematic diagram of flow field data reconstruction for example cylindrical bypass flow.
Detailed Description
In the following detailed description of the present invention, numerous specific details are set forth in order to provide a thorough understanding of the present invention. The invention may be embodied in many other forms than described herein and similarly modified by those skilled in the art without departing from the spirit or scope of the invention, which is therefore not limited to the specific embodiments disclosed below.
As shown in figures 1 to 4, the flow field reconstruction method based on the quantum Koopman analysis, provided by the invention, inputs flow field data into a trained quantum Koopman analysis model, and the quantum Koopman analysis model calculates a main characteristic value of a Koopman operatorAnd principal eigenvector/>Based on principal eigenvalue/>And principal eigenvector/>Reconstructing the mapped flow field data, thereby outputting a flow field reconstruction result.
The flow field data is reconstructed based on the quantum Koopman analysis model, so that the nonlinear characteristics of the flow field data can be particularly focused and reconstructed, and the accuracy of the reconstructed flow field data and the accuracy of evolution based on the reconstructed flow field data are improved.
The flow field reconstruction is solved based on quantum acceleration in a quantum Koopman analysis model, and specifically comprises the following steps: firstly, selecting a proper mapping function and giving out a quantum circuit implementation mode; then using quantum calculation to accelerate solving of main eigenvalue of Koopman operatorAnd principal eigenvector/>; Reconstructing mapped flow field data according to the main feature value and the main feature vector obtained by the Koopman operator; and constructing a loss function by using the reconstructed flow field data and the mapped flow field data, and carrying out parameter optimization on parameters to be optimized in the mapping function by the loss function to obtain an optimal mapping function. In the actual use process of the quantum Koopman analysis model, mapping is carried out on the original flow field data based on an optimal mapping function to obtain mapped flow field data, and the quantum Koopman analysis model calculates a main characteristic value and a main characteristic vector of the mapped flow field data, so that the reconstructed flow field data can be obtained.
Based on training the quantum Koopman analysis model to optimize parameters to be optimized of the mapping function, the training process of the quantum Koopman analysis model is as follows from S1 to S4.
S1: constructing a training set, and setting flow field data in the training setStored in a quantum data structure, and a data query interface/>, is constructed by querying the quantum data structure；
Observed flow field data is defined asRepresenting flow field data/>Middle/>Data corresponding to flow field observed quantity at moment, wherein the data can be observed pressure, vorticity and other data,/>，/>Expressed/>Is/>，/>Representing the grid number of the flow field,/>Representing the number of time steps. In the quantum algorithm/>Stored in a quantum data structure, a data query interface/>, comprising the following operations, can be realized by querying the quantum data structure：
Wherein,Represents the/>Time 1/>Observation data corresponding to each grid,/>Representation data/>Is used for the amplitude encoding state of (a),，/>Representation data/>Is a binary norm of (c).
S2: constructing a nonlinear mapping function and constructing mapped flow field data based on quantum circuitsQuery interface/>To realize mapping function based on query interface/>Flow field data/>Mapping to post-mapping flow field data/>Comprising steps S21 to S24;
s21: introducing parameters to be optimized to construct a mapping function, and constructing flow field data based on the mapping function Corresponding mapped flow field data/>The parameters to be optimized are subjected to parameter optimization in the training process;
koopman analysis first uses flow field data Mapping to New flow field data/>，，/>The representation represents the/>Data of time of day/>Vector mapped by mapping function,/>，/>Representing the number of time steps; /(I)Representing a mapping function,/>Is flow field data/>And mapping the data after mapping by the mapping function. Because the flow field evolution equation is a nonlinear differential equation, the mapping function needs to be selected as a nonlinear function when solving the flow field reconstruction problem. In addition, in order to obtain an optimal mapping function, parameters to be optimized are introduced into the mapping function, and the expression of the mapping function is as follows:
wherein, Represents the/>Data of time of day/>Vector data mapped by mapping function,/>Representing flow field dataMiddle/>Data corresponding to flow field observational quantity of moment,/>Representing transpose,/>Is a parameter to be optimized,/>Is a constant representing nonlinear order,/>Representing tensor product operations.
S22: query interface based on quantum arithmetic operationGo/>Any element/>, is calculated by secondary queryRealize inquiry interface/>First operation/>Wherein/>Representing vectors/>First/>A component; the quantum arithmetic operations are quantum addition operations and quantum multiplication operations;
due to Each element may pass through at most/>Personal/>Calculated by the elements of/>, thenQuery/>The times can calculate any/>The arithmetic process can be realized by using quantum arithmetic operationThe first operation:。
s23: preparation method based on quantum state amplitude for multiple data Amplitude encoded state preparation of (a) to obtain mapped vectorsAmplitude encoding state of (a) to realize inquiry interface/>Second operation/>；
Amplitude encoded states pass through multiple copies/>Is prepared in the amplitude encoded state. First, quantum state/>Wherein/>，/>Representing parameters to be optimized; then execute/>To obtain the quantum state/>Generate mapped data/>Amplitude encoded states/>I.e. can be realized by quantum arithmetic operations-Second operation/>；/>Representing dirac right and left vector symbols in quantum mechanics,/>Represent right vector/>Multiplying the left vector/>；
Wherein U defined by this formula implements a series of controlled unitary operators, i.e. control bits areWhen execution/>, on the target bitAnd (3) operating.
S24: quantum arithmetic operation based pair dataIs/is > ofCalculation to obtain/>Is/is > ofRealize inquiry interface/>Third operation/>；
Through inquiry interfaceObtain/>Is/is > ofThen based on quantum addition, multiplication and open square operation, the/>Is a binary norm of (c).
Two normsThe calculation formula of (2) is as follows:
wherein, Constant representing nonlinear order,/>Representing the sum index.
Query interface constructed through steps S22 to S24The following are provided:
by constructing a query interface Mapping function is realized through quantum circuit, and finally flow field data/>Mapped flow field data/>Is mapped to the mapping of (a).
S3: to query interfaceAs input, calculating/>, based on a quantum dynamic modal decomposition algorithmPrincipal eigenvalues/>And principal eigenvector/>，/>Representing Koopman operators;
As shown in FIG. 3, a query interface is constructed After that, realizeMapping to/>, by a nonlinear mapping functionIs a process of (2). Assumption/> in Koopman analysisThe evolution of (c) can be expressed in terms of linear operators, specifically expressed as: /(I)Wherein/>Representing Koopman operator,/>，/>. The task of Koopman analysis is to calculate/>Principal eigenvalues/>And principal eigenvector/>Wherein/>Representing the number of truncation steps.
The implementation process of the quantum computing acceleration Koopman analysis is realized by a quantum dynamic modal decomposition algorithm, and the method is toAs input, executing a quantum dynamic modal decomposition algorithm to obtain/>Principal eigenvalues/>And principal eigenvector/>Each component/>Amplitude encoded states/>; The implementation process of the quantum dynamic modal decomposition algorithm is as follows:
s31: preparation of the initial state Wherein/>，/>Can also be expressed asWherein/>Representing matrix,/>Representation will/>Matrix after hermitization,/>Represents the transposed conjugate of G,/>Representing intermediate process parameters,/>，/>Representation/>Transposed conjugate of/>Representing a trace operation on matrix H,/>Respectively express/>A singular value of (a), a left singular vector, a right singular vector;
S32: in an initial state As input state, pair/>Executing a quantum singular value estimation algorithm and performing post-processing to obtain a quantum state/>；
S33: for quantum stateSampling, and calculating a low-dimensional projection matrix/>, of the Koopman operator through sampling resultsAnd pair/>And (3) performing characteristic decomposition: /(I)Wherein/>Representation/>Is/are of the eigenvectors of (1)Representation/>Is a characteristic value of (2); wherein the sampling result is the principal eigenvalue of the Koopman operator and the amplitude encoding state of the principal singular vector, and then the low-dimensional projection matrix of the Koopman operator is calculated by a series of vector inner product operations.
S34: matrix of low-dimensional projectionAs/>Principal eigenvalues/>Each score/>；
S35: by projecting the matrix in low dimensionsAnd query interface/>Performing operator linear combination to obtain/>Principal eigenvector/>Each component/>Amplitude encoded states/>; The operator represents a quantum operator, and the operator linear combination is a basic quantum algorithm module, namely a given operator/>The operator can be realized by the operator linear combination technology。
S4: based on principal eigenvaluesAnd principal eigenvector/>Reconstructing mapped flow field data/>Obtaining flow field data after reconstruction; specifically S41 to S42:
S41: based on principal eigenvalues Each score/>And principal eigenvector/>Each component/>Amplitude encoding state of (2)Reconstructing the vector/>, at each momentTo reconstruct/>Recorded as reconstruction data/>Will reconstruct data/>Collecting to obtain flow field data after reconstruction;
Reconstructing data The calculation formula of (2) is as follows:
wherein, Representing the cut-off order,/>Representing the initial coefficient/>(1 /)Element,/>Is to satisfy/>/>The element of (1) is then the initial coefficient/>By/>And/>And (5) calculating.
S42: by reconstructing flow field dataPerforming operator linear combination to prepare the quantum state/>；
Wherein the operators represent quantum operators, and the linear combination of the operators is a basic quantum algorithm module, i.e. a given operatorOperator/>, can be realized by an operator linear combination technique。
Through the steps S1 to S4, the quantum Koopman analysis model is used for accelerating the flow field reconstruction problem through quantum calculation after training, so that a fluid reconstruction result can be obtained more quickly and accurately.
In the quantum Koopman analysis model training process, mainly for optimizing parameters to be optimized in the mapping function, the embodiment designs a loss function to optimize the parameters, and the loss function is as follows:
loss function The formula of (2) is as follows:
wherein, Representing the number of time steps,/>Representation data/>Reconstructed data after reconstruction.
Can be calculated by a Hadamard test. Then pass/>Parameters to be optimized in optimizing mapping functionAnd obtaining the optimal mapping function. And finally, performing quantum Koopman analysis after optimization to complete a flow field reconstruction task, namely obtaining an optimal mapping function based on the loss function, and performing a quantum Koopman analysis model of the optimal mapping function in the actual use process to perform quantum Koopman analysis.
As an embodiment
As shown in fig. 4, consider the reynolds numberA cylindrical bypass problem, the data set being generated by an IBPM flow field solver.
The data set information is: Wherein/> ，/>Represents the/>At the moment, the flow field space is divided into/>Grid,/>Each element/>Indicating the vorticity of the corresponding flow field grid. Will/>Spread into one dimension, i.e./>. The embodiment solves the problem as follows:
(1) And (3) selecting and realizing a nonlinear mapping function: mapping function Middle/>Get 3, then/>The writing is as follows:
Each of which is Can be written as at most/>Personal/>The product of the elements is multiplied by a constant, thus by query/>The quantum data structure of (a) gets the corresponding/>The elements in (2) are then calculated using quantum arithmetic operationsThereby realizing; In addition/>Is a series/>And/>By querying/>Is prepared by preparing a quantum data structure of (2), and further preparing/>I.e. realizing/>; Finally/>By querying/>Obtained of the quantum data structure of/>Then calculate/>, using quantum arithmetic operationsNamely realize. The above is/>Implementation details of (a).
(2) Quantum computation accelerates Koopman analysis: for mapped dataExecution of the cut-off order/>The main characteristic value/>, of the Koopman operator is obtained by the quantum dynamic modal decomposition algorithm of (2)And principal eigenvectorAmplitude encoded states/>。
(3) Reconstructing a flow field: next solve the system of linear equationsObtain vector/>; Then prepare/>, using an operator linear combination techniqueQuantum state/>。
(4) And (3) optimizing mapping function parameters: defining a loss function，/>Representing the number of time steps, in this case/>. Next calculate/>, by Hadamard testThen pass/>Optimizing mapping function parameters/>And obtaining the optimal mapping function.
(5) And finally, executing an optimized quantum Koopman analysis model to complete a flow field reconstruction task of cylindrical bypass flow: inputting the flow field data of the cylindrical bypass flow into an optimized quantum Koopman analysis model, calculating the flow field data by the model to obtain a main characteristic value and a main characteristic vector, and reconstructing the flow field data after mapping based on the main characteristic value and the main characteristic vector, so as to output a flow field reconstruction result of the cylindrical bypass flow.
The foregoing is only a preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art, who is within the scope of the present invention, should make equivalent substitutions or modifications according to the technical scheme of the present invention and the inventive concept thereof, and should be covered by the scope of the present invention.
Claims (6)
1. A flow field reconstruction method based on quantum Koopman analysis is characterized in that flow field data are input into a trained quantum Koopman analysis model to output flow field reconstruction results;
The training process of the quantum Koopman analysis model is as follows:
s1: constructing a training set, and setting flow field data in the training set Stored in a quantum data structure, and a data query interface/>, is constructed by querying the quantum data structure，/>，/>Representing flow field data/>Middle/>Data corresponding to flow field observational quantity of moment,/>，/>Representing the number of time steps;
s2: constructing a nonlinear mapping function and constructing mapped flow field data based on quantum circuits Query interface/>To realize mapping function based on query interface/>Flow field data/>Mapping to post-mapping flow field data/>，/>，/>Represents the/>Data of time of day/>Vector after mapping by the mapping function;
s21: introducing parameters to be optimized to construct a mapping function, and constructing flow field data based on the mapping function Corresponding mapped flow field data/>The parameters to be optimized are subjected to parameter optimization in the training process;
S22: query interface based on quantum arithmetic operation Go/>Any element/>, is calculated by secondary queryRealizing inquiry interfaceFirst operation/>Wherein/>Representing vectors/>First/>Components of the grid;
s23: preparation method based on quantum state amplitude for multiple data Amplitude encoded state preparation of (a) to obtain mapped vector/>Amplitude encoding state of (a) to realize inquiry interface/>Second operation/>；
S24: quantum arithmetic operation based pair dataIs/is > ofCalculating to obtain a vector/>Is/is > ofRealize inquiry interface/>Third operation/>；
S3: to query interfaceAs input, calculating/>, based on a quantum dynamic modal decomposition algorithmPrincipal eigenvalues/>And principal eigenvector/>，/>Representing Koopman operators;
s31: preparation of the initial state Wherein/>Representing a trace operation on matrix H,/>Respectively represent data/>A singular value of (a), a left singular vector, a right singular vector,，/>；
S32: in an initial stateAs input state, pair/>Executing quantum singular value estimation algorithm and performing post-processing to obtain quantum state，/>Wherein/>Representation will/>Matrix after hermitization,/>Representing intermediate process parameters,/>Representation/>Is the transposed conjugate of (2);
S33: for quantum state Sampling, and calculating/>, based on the sampling resultLow-dimensional projection matrix/>And pair/>And (3) performing characteristic decomposition: /(I)Wherein/>Representation/>Is/are of the eigenvectors of (1)Representation/>Is a characteristic value of (2);
S34: matrix of low-dimensional projection As/>Principal eigenvalues/>Each score/>；
S35: by projecting the matrix in low dimensionsAnd query interface/>Performing operator linear combination to obtain/>Principal eigenvector/>Each component/>Amplitude encoded states/>；
S4: based on principal eigenvaluesAnd principal eigenvector/>Reconstructing mapped flow field data/>And obtaining the flow field data after reconstruction.
2. The method for reconstructing a flow field based on quantum Koopman analysis according to claim 1, wherein, in step S1,，/>Represents the grid number of the flow field, inquires interface/>The following are provided:
wherein, Represents the/>Time 1/>Observation data corresponding to each grid,/>Representation data/>Is used for the amplitude encoding state of (a),，/>Representation data/>Is a binary norm of (c).
3. The method of flow field reconstruction based on quantum Koopman analysis according to claim 1, wherein in step S21, the mapping function is defined as:
wherein, Representing transpose,/>Representing parameters to be optimized,/>Constant representing nonlinear order,/>Representing tensor product operation;
Construction of flow field data based on mapping function Mapped flow field data，/>Representing the mapping function.
4. The method for reconstructing a flow field based on quantum Koopman analysis according to claim 3, wherein in step S23, for a plurality of dataAmplitude encoded states/>The preparation method specifically comprises the following steps:
First preparing quantum state Wherein/>，/>Representing parameters to be optimized;
performing intermediate operations To obtain the quantum state/>Generating a vector/>Amplitude encoded states/>，/>Right and left vector symbols of dirac in quantum mechanics are represented;
In step S24, two norms The calculation formula of (2) is as follows:
wherein, Constant representing nonlinear order,/>Representing the sum index.
5. The flow field reconstruction method based on quantum Koopman analysis according to claim 1, wherein in step S4, specifically:
S41: based on principal eigenvalues Each score/>And principal eigenvector/>Each component/>Amplitude encoded states/>Reconstructing the vector/>, at each momentTo reconstruct/>Recorded as reconstruction data/>Will reconstruct data/>Collecting to obtain flow field data after reconstruction;
s42: by reconstructing data Performing operator linear combination to prepare the quantum state/>；
Reconstructing dataThe calculation formula of (2) is as follows:
wherein, Representing the cut-off order,/>First/>, representing initial coefficientsThe elements.
6. The flow field reconstruction method based on quantum Koopman analysis according to claim 1, wherein in the quantum Koopman analysis model training process, a loss function is constructed to optimize parameters to be optimized in the mapping function, the loss functionThe formula of (2) is as follows:
wherein, Representing the number of time steps,/>Representing vectors/>Reconstructed data after reconstruction.
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