CN112861332B - Cluster dynamics prediction method based on graph network - Google Patents
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Abstract
The invention discloses a cluster dynamics prediction method based on a graph network, which comprises the following steps: simulating the motion of the self-driven cluster according to the Viscek model to generate a data set; processing the data set into graph structure data through data preprocessing, wherein the graph structure data comprise nodes, edges and global attributes; the preliminary extraction of the characteristics and the dimension reduction of the data are realized; using a graph network block, selecting a multilayer perceptron as an updating function, and transmitting information on a graph through a certain rule; restoring the information to obtain graph structure data; and training the graph network by using an optimization algorithm with descending random gradients, and automatically learning parameters in the graph network. The invention integrates the traditional physical science and deep learning technology, can realize the simulation and reasoning of the objects and the relation in the self-driven cluster system, and only determines the long-term evolution of the system from the initial positions of the particles without any manual characteristics.
Description
Technical Field
The invention relates to the technical field of deep learning, in particular to a cluster dynamics prediction method based on a graph network.
Background
Active substance systems are not limited by thermodynamic rules such as delicate equilibrium conditions or the fluctuating dissipation theorem and thus exhibit rich and complex dynamics such as mass movements that are widespread in spatial dimensions, in nature (e.g., animals, microorganisms and cells), in human society (e.g., collective human behavior and social networks) and in multi-body intelligent systems (e.g., multi-robot systems and multi-vehicle cooperative control) to name a few examples. Typical cluster motion models can simulate many forms of motion of matter, including the motion of birds and fish. The model system taking cluster movement behaviors as a research object is a set consisting of a large number of autonomous individuals, and the individuals are updated by considering the influence of neighbors and disturbance factors in the environment, so that the overall model system presents complex behaviors. At sufficiently high densities and noise below a certain critical value, a phenomenon of cluster synchronization can be observed, and understanding the physical nature behind this phenomenon has been an important research direction in the field of soft matter and unbalanced statistical physics.
Over the last few years, active substance research has begun using machine learning methods. The progress of applying machine learning to scientific research provides a powerful tool for active substance research, and can identify optimal and alternative strategies, realize classification and characterization of active substances, and locate and track particles. Reinforcement learning and deep reinforcement learning have been used to find swimming strategies that minimize energy consumption in simulated fish populations. However, when solving the above problem, conventional machine learning generally maps graph structure data into a simple representation, which makes the preprocessing stage possible to lose topology information of the structure itself, and affects the final prediction result.
In view of the foregoing, it is desirable to provide a method that fully considers local interaction forces between an individual and a neighbor from the perspective of network topology, and can predict a kinetic phase transition process from only the initial position of a particle in a system without undergoing complex molecular dynamics evolution.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a cluster dynamics prediction method based on a graph network aiming at the defects in the prior art.
The technical scheme adopted by the invention for solving the technical problems is as follows: a graph network-based cluster dynamics prediction method is constructed, and comprises the following steps:
simulating the motion of the self-driven cluster according to the Viscek model to generate a data set;
processing the data set into graph structure data through data preprocessing, wherein the graph structure data comprise nodes, edges and global attributes;
the preliminary extraction of the characteristics and the dimension reduction of the data are realized;
using a graph network block, selecting a multilayer perceptron as an updating function, and transmitting information on a graph through a certain rule;
restoring the information to obtain graph structure data;
and training the graph network by using an optimization algorithm with descending random gradients, and automatically learning parameters in the graph network.
In the Viscek model, N individuals which can be regarded as particles move on a plane of a two-dimensional periodic boundary condition of L x L at the same speed, the positions of each individual are randomly distributed in the plane area at the initial moment, the moving directions are randomly distributed among [ -pi, pi ], the angle of each individual is updated according to the vector average of the angles of the neighbors at each moment t +1, and random disturbance is added to the average moving direction in the neighborhood;
in the step of simulating the self-driven cluster movement according to the Viscek model, the definition of the neighbor is expressed by the following formula:
N i (t)＝{j|d ij (t)<r}
wherein N is i (t) represents the neighborhood of the individual i at time t, r represents the radius of the field of view, d ij (t) represents the distance between two individuals;
each individual is moved at a constant rate v throughout the plane, the position change using the following formula:
wherein theta is i (t) is the angle of movement of the individual i at time t;
the angle update adopts the following formula:
θ i (t+1)＝<θ i (t)> r +Δθ
wherein Δ θ represents the interval [ - η/2, η/2 with uniform probability]η represents noise in the environment;<θ i (t)> r the average speed direction of all individuals (including the individual i) in the view radius r by taking the individual i as the center of a circle;
the following formula is used to calculate the average velocity direction of all individuals (including the individual i itself) within the radius r of the visual field:
the cluster dynamics prediction network based on the graph network consists of three modules, namely a node processing module, an edge processing module and a global state processing module;
the edge processing module is used for updating the state of each edge, comprises an updating function and realizes the updating of each edge according to the characteristics of a given edge, the node characteristics and the global characteristics;
the node processing module is used for updating the state of each node, comprises an aggregation function and an updating function, aggregates the characteristics of edges around the node by using the aggregation function, and updates the node based on the aggregation of the node characteristics and the associated edge characteristics and the influence of the global characteristics;
the global state processing module is used for updating a global state and comprises two aggregation functions and an updating function, the receiving parameter of the first aggregation function is a set of all edges, the receiving parameter of the second aggregation function is a set of all points, and global updating is achieved based on global features, aggregation of all nodes and aggregation of edges.
Wherein, the updating function contained in the three processing functions is a multilayer perceptron of a fully-connected neural network, and the multilayer perceptron consists of three layers:
1) the number of neurons of an input layer in the node processing module is 32, the number of neurons of a hidden layer is 64, and the number of neurons of an output layer is 32;
2) the number of neurons of an input layer in the edge processing module is 32, the number of neurons of a hidden layer is 64, and the number of neurons of an output layer is 32;
3) the neuron number of the input layer in the global state module is 32, the neuron number of the hidden layer is 64, and the neuron number of the output layer is 1.
Wherein the aggregation function is a summation of the features.
Compared with the prior art, the invention provides a cluster dynamics prediction method based on a graph network, which comprises the following steps: simulating the motion of the self-driven cluster according to the Viscek model to generate a data set; processing the data set into graph structure data through data preprocessing, wherein the graph structure data comprise nodes, edges and global attributes; the preliminary extraction of the characteristics and the dimension reduction of the data are realized; using a graph network block, selecting a multilayer perceptron as an updating function, and transmitting information on a graph through a certain rule; restoring the information to obtain graph structure data; and training the graph network by using an optimization algorithm with descending random gradients, and automatically learning parameters in the graph network. By the method and the device, simulation and reasoning of the objects and the relations in the self-driven cluster system can be realized, and long-term evolution of the system is determined only from the initial particle position without any manual characteristics.
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The invention will be further described with reference to the accompanying drawings and examples, in which:
fig. 1 is a schematic step diagram of a graph network-based cluster dynamics prediction method provided by the present invention.
Fig. 2 is a graph network model diagram of a cluster dynamics prediction method based on a graph network provided by the present invention.
Fig. 3 is a diagram network block diagram of a graph network-based cluster dynamics prediction method provided by the invention.
Detailed Description
For a more clear understanding of the technical features, objects and effects of the present invention, embodiments of the present invention will now be described in detail with reference to the accompanying drawings.
As shown in fig. 1, the present invention designs a graph network-based cluster dynamics prediction method, including:
simulating the motion of the self-driven cluster according to the Viscek model to generate a data set;
processing the data set into graph structure data through data preprocessing, wherein the graph structure data comprise nodes, edges and global attributes;
the preliminary extraction of the characteristics and the dimension reduction of the data are realized;
using a graph network block, selecting a multilayer perceptron as an updating function, and transmitting information on a graph through a certain rule;
restoring the information to obtain graph structure data;
and training the graph network by using an optimization algorithm with descending random gradients, and automatically learning parameters in the graph network.
Simulating the motion of the self-driven cluster according to the Vicsek model to generate a data set, wherein the data set comprises;
in the Vicsek model, N individuals, which can be regarded as particles, move at the same rate on a plane of a two-dimensional periodic boundary condition of L × L, at an initial instant, the position of each individual is randomly distributed in the area of the plane, the direction of movement is randomly distributed between [ -pi, pi), at each instant t +1, the angle of each individual is updated according to the vector average of the angles of the neighbors, and some random perturbations are added to the average direction of movement in its neighborhood;
the definition of the neighbor is expressed by the following formula:
N i (t)＝{j|d ij (t)<r}
wherein N is i (t) represents the neighborhood of the individual i at time t, r represents the radius of the field of view, d ij (t) represents the distance between two individuals;
each individual is moved at a constant rate v throughout the plane, the position change using the following formula:
wherein theta is i (t) is the angle of movement of the individual i at time t;
the angle update adopts the following formula:
θ i (t+1)＝<θ i (t)> r +Δθ
wherein Δ θ represents the interval [ - η/2, η/2 with uniform probability]η represents noise in the environment;<θ i (t)> r the average speed direction of all individuals (including the individual i) in the view radius r by taking the individual i as the center of a circle;
the following formula is used to calculate the average velocity direction of all individuals (including the individual i itself) within the radius r of the visual field:
processing the data set into graph structure data through data preprocessing, wherein G is (u, V, E), G represents a graph, u represents a global attribute, V represents an attribute of a node, and E represents an attribute of an edge, including;
g is constructed based on the distance between the particles, and since the field of view radius of the Vicsek model is 1, two particles with a distance less than this threshold are connected by an edge. The motion angle of the particles is the characteristic of the node, the relative distance between the particles is the characteristic of the edge of the graph, and the resultant velocity after each iteration is the global characteristic.
The method comprises the steps of realizing the preliminary extraction of features and the dimension reduction of data, including;
an encoder (encoder) is used to receive the input and output a feature vector, which is in fact another representation of the input features and information.
Using a graph network block, selecting a multilayer perceptron as an updating function, and transmitting information on a graph through a certain rule, including;
the graph network block consists of three modules, namely a node processing module, an edge processing module and a global state processing module;
the edge processing module is used for updating the state of each edge, comprises an updating function and realizes the updating of each edge according to the characteristics of a given edge, the node characteristics and the global characteristics;
the node processing module is used for updating the state of each node, comprises an aggregation function and an updating function, aggregates the characteristics of edges around the node by using the aggregation function, and updates the node based on the aggregation of the node characteristics and the associated edge characteristics and the influence of the global characteristics;
the global state processing module is used for updating a global state and comprises two aggregation functions and an updating function, the receiving parameter of the first aggregation function is a set of all edges, the receiving parameter of the second aggregation function is a set of all points, and global updating is achieved based on global features, aggregation of all nodes and aggregation of edges.
Wherein, the updating function contained in the three processing functions is a multilayer perceptron of a fully-connected neural network, and the multilayer perceptron consists of three layers:
1) the number of neurons of an input layer in the node processing module is 32, the number of neurons of a hidden layer is 64, and the number of neurons of an output layer is 32;
2) the number of neurons of an input layer in the edge processing module is 32, the number of neurons of a hidden layer is 64, and the number of neurons of an output layer is 32;
3) the neuron number of the input layer in the global state module is 32, the neuron number of the hidden layer is 64, and the neuron number of the output layer is 1.
Wherein the aggregation function is a summation of the features.
Restoring the information to obtain graph structure data including;
the processed information is extracted by a decoder (decoder) and restored to the graph structure data.
Training a graph network by using an optimization algorithm, and automatically learning parameters in the graph network, including;
and (3) using MAE (mean absolute error) and MSE (mean square error) between the real value and the predicted value as loss functions, and using an optimization algorithm to train the graph network and automatically learn the parameters therein. The optimization algorithm may be a gradient-based optimization algorithm, such as a random gradient descent method, Adam, or the like.
Next, as shown in fig. 2 and 3, the embodiment of the present invention will be further explained.
Graph networks, as a general modular framework for deep learning, can be seen as a superset of the previous graph-based neural networks, the advantage of Graphynetwork (GN) is its versatility, which can be analyzed with GN if the structure of the target problem can be coded in the form of a graph, or a priori knowledge of the relationships between the input entities can itself be described as a graph. GNs also have strong combinatorial and generalization capabilities, and the GN blocks support deep or recursive permutations, where information can be propagated in the graph network to allow more information to perform computations, enabling complex functions. At the same time, the calculations are not performed on a macroscopic level of the whole system, but are multiplexed on the entities and relations, which enables the network to have a good fit to the unknown data set.
The graph network model diagram of the cluster dynamics prediction method based on the graph network is shown in FIG. 2, and in order to realize feature extraction and data dimension reduction, an encoder is added in front of a GN block to preprocess input, so that the method is found to improve the training speed and precision of the model. In the GN block, three multi-layer perceptrons are used for realizing updating of edge, point and global attributes respectively, and residual error connection is added to the GN block for solving the problems of gradient explosion and gradient disappearance in the deep network training process. The GN block is circulated n times to realize complex calculation, and the processed information is extracted by a decoder to be restored into graph structure data. In the last step, edges, points and global properties are concatenated and passed through the Dense layer to produce the final output.
The graph network block structure of cluster dynamics prediction disclosed by the invention is shown in fig. 3, GN is a graph-to-graph function, and an output graph and an input graph of the graph have the same node and edge structures. For a self-driven cluster system, this graph is constructed based on the distance between individuals, and the edges are defined by the relative distance between particles. The GN block comprises three modules of an edge, a point and a global, the modules are composed of a plurality of layers of perceptrons, and the modules are associated through a certain rule to realize the updating of the graph. Including 6 internal functions, three update functions and three aggregation functions.
First, e' k The edge block computes an output for each edge, which is updated with attributes from itself, its connected individuals, and the global state, as follows:
wherein phi e Is an update function of the edge. Next, for each vertex, the vertex block aggregates all the edges pointing to it into
As follows:
where ρ is e→v Is an aggregation function of directed edges directed to each receiving node,
is a set of all directed edges pointing to nodes indexed by i, and computes the output v 'of each node' i The attributes of each node are updated by using its own attributes, the edges connected to it, and the global state vector u:
wherein phi is v Is an update function of the point. Next, in the global block, the outputs at both edge and node level are aggregated to compute global features:
where ρ is e→v Is the aggregation function of all edges on the graph, p v→u Is the aggregation function of all points on the graph, phi u Is an update function of the global property. Thus, the output of GN is the set of all edge, node and graph level features, G '═ u', V ', E'.
Update function phi e ，Φ v Phi of sum u The choice directly determines the performance of the model in the actual task. In the self-driven cluster powerIn the network model of the scholastic graph, we select a multi-layer perceptron as the update function.
The invention constructs a self-driven cluster dynamics model based on a graph network, integrates the traditional physical science and deep learning technology, and can realize the simulation and reasoning of objects and relations in the self-driven cluster system, thereby completing the long-term prediction of the system.
While the present invention has been described with reference to the embodiments shown in the drawings, the present invention is not limited to the embodiments, which are illustrative and not restrictive, and it will be apparent to those skilled in the art that various changes and modifications can be made therein without departing from the spirit and scope of the invention as defined in the appended claims.
Claims (7)
1. A cluster dynamics prediction method based on a graph network is characterized by comprising the following steps:
simulating the motion of the self-driven cluster according to the Viscek model to generate a data set; in the Viscek model, N individuals which can be regarded as particles move on a plane of a two-dimensional periodic boundary condition of L x L at the same speed, the positions of each individual are randomly distributed in the plane area at the initial moment, the moving directions are randomly distributed among [ -pi, pi ], the angle of each individual is updated according to the vector average of the angles of the neighbors at each moment t +1, and random disturbance is added to the average moving direction in the neighborhood;
processing the data set into graph structure data through data preprocessing, wherein G is (u, V, E), G represents a graph, u represents a global attribute, V represents an attribute of a node, and E represents an attribute of an edge;
the preliminary extraction of the characteristics and the dimension reduction of the data are realized;
using the graph network block, selecting a multilayer perceptron as an updating function, and transmitting information on the graph through an updating rule of the graph network block;
restoring the information to obtain graph structure data;
training a graph network by using an optimization algorithm of random gradient descent, and automatically learning parameters in the graph network;
the graph network block is composed of three modules, namely a node processing module, an edge processing module and a global state processing module, and the updating rule of the graph network block is as follows:
the edge processing module is used for updating the state of each edge, comprises an updating function and realizes the updating of each edge according to the characteristics of a given edge, the node characteristics and the global characteristics;
the node processing module is used for updating the state of each node, comprises an aggregation function and an updating function, aggregates the characteristics of edges around the node by using the aggregation function, and updates the node based on the aggregation of the node characteristics and the associated edge characteristics and the influence of the global characteristics;
the global state processing module is used for updating a global state and comprises two aggregation functions and an updating function, the receiving parameter of the first aggregation function is a set of all edges, the receiving parameter of the second aggregation function is a set of all points, and global updating is achieved based on global features, aggregation of all nodes and aggregation of edges.
2. The graph network-based cluster dynamics prediction method according to claim 1, characterized in that in the step of simulating self-driven cluster motion according to the Vicsek model, the definition of the neighbors is expressed by the following formula:
N i (t)＝{j│d ij (t)＜r}
wherein N is i (t) represents the neighborhood of the individual i at time t, r represents the radius of the field of view, d ij (t) represents the distance between two individuals;
each individual is moved at a constant rate v throughout the plane, the position change using the following formula:
wherein theta is i (t) is the angle of movement of the individual i at time t;
the angle update adopts the following formula:
θ i (t+1)＝<θ i (t)> r +Δθ
wherein Δ θ represents the interval [ - η/2, η/2 with uniform probability]η represents noise in the environment;<θ i (t)> r the average speed direction of all individuals in the visual field radius r by taking the individual i as the center of a circle, wherein all the individuals comprise the individual i per se;
the following formula is adopted for calculating the average speed direction of all individuals within the visual field radius r of the individual i:
3. the graph network-based cluster dynamics prediction method according to claim 1, wherein in the step of implementing the preliminary extraction of features and the dimensionality reduction of data, an encoder (encoder) is used to receive input and output a feature vector, wherein the feature vector is actually another representation of the input features and information.
4. The graph network-based cluster dynamics prediction method of claim 1, wherein the update function is substantially a multi-layered perceptron of a fully-connected neural network, the multi-layered perceptron consisting of three layers:
1) the number of neurons of an input layer in the node processing module is 32, the number of neurons of a hidden layer is 64, and the number of neurons of an output layer is 32;
2) the number of neurons of an input layer in the edge processing module is 32, the number of neurons of a hidden layer is 64, and the number of neurons of an output layer is 32;
3) the neuron number of the input layer in the global state module is 32, the neuron number of the hidden layer is 64, and the neuron number of the output layer is 1.
5. The graph network-based cluster dynamics prediction method of claim 1, wherein the aggregation function is a summation of features.
6. The graph network-based cluster dynamics prediction method of claim 1, wherein in the step of obtaining graph structure data by implementing information reduction, a decoder (decoder) is used to extract processed information and reduce the processed information to graph structure data.
7. The graph network-based cluster dynamics prediction method according to claim 1, wherein MAE (mean absolute error) and MSE (mean square error) between the real value and the predicted value are used as loss functions, and an optimization algorithm is used for training the graph network to automatically learn parameters therein.
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