A physical material dynamic simulation method based on a graph neural network

Abstract

The application relates to a physical material dynamic simulation method based on a graph neural network, and has the characteristics that S101, the dynamic change process of particles of a certain physical material is acquired, and the dynamic change process of the particles in space-time is divided into T time snapshots; S102, the T time snapshots generated in S101 are constructed into T subgraphs; S103, feature embedding is performed on the T subgraphs generated in S102, and the feature vectors of all particles in each subgraph are acquired; and S104, based on all the particle feature vectors generated in S103, a recurrent neural network is used to capture the time characteristics of the particle state change. According to the application, the subgraphs are constructed, the local features and the global features of the physical particles are extracted from the local and global angles by using the graph convolution network and the graph attention network, then the two kinds of features are aggregated into one feature, the extracted feature information is more comprehensive, and more accurate information guarantee is provided for simulation prediction.

Description

Technical Field

[0001] This invention relates to a method for dynamic simulation of physical materials based on graph neural networks. Background Technology

[0002] Physical material simulation has always been a research hotspot in the field of computer graphics. With technological advancements, there is a growing demand for more realistic and grander simulation scenes, as well as real-time and efficient physical material simulation rendering effects. Simultaneously, the rapid development of the domestic film and television, digital twin, and gaming industries has led to a surge in demand for physical material simulation systems from major internet technology companies. In the development of digital twin scenes, the selection and use of a physical material simulation system significantly impacts the overall project development progress. Currently, most domestic development teams use the Unity or Unreal Engine to develop simulation applications, making it essential to develop a physical material simulation system that meets domestic needs to better serve the domestic physical material simulation application development industry.

[0003] In physical materials simulation, the simulation of various complex physical materials has always been crucial. Traditional simulation techniques have the ability to simulate a wide range of physical phenomena such as flow, turbulence, heat transfer, and reactions. Industrial applications range from airflow over aircraft wings to combustion in furnaces, from bubbling towers to drilling platforms, from blood flow to semiconductor production, and from cleanroom design to wastewater treatment plants, and so on.

[0004] As an emerging technology, deep learning also has great potential for application in physical materials simulation, as it can train simulation simulators directly from observed data. However, conventional deep learning algorithms cannot handle the dynamic changes in the vast state space during simulation. Summary of the Invention

[0005] In view of this, the present invention provides a method for dynamic simulation of physical materials based on graph neural networks.

[0006] A physical material dynamic simulation method based on graph neural networks, characterized by including:

[0007] S101. Obtain the dynamic change process of particles in a certain physical material, and divide the dynamic change process of particles in spacetime into T time snapshots, each time snapshot consisting of particles.

[0008] S102. Construct T subgraphs from the T time snapshots generated in S101, wherein each subgraph consists of nodes and undirected edges;

[0009] S103. Perform feature embedding on the T sub-graphs generated in S102 to obtain the feature vectors of all particles in each sub-graph;

[0010] S104. Based on the feature vectors of all particles in the T subgraphs generated in S103, a recurrent neural network is used to capture the temporal characteristics of particle state changes.

[0011] Furthermore, in S101, the particle dynamics process of a certain physical material is obtained through the SPH smooth particle hydrodynamics method, the MPM material point method, and the PDB position-based simulation method.

[0012] Furthermore, in step S102, the T time snapshots are constructed into T subgraphs using a graph structure generation method. The specific process is as follows:

[0013] Graph structure data is generated by adding edges between particles; the subgraph is represented as G. t ={V t E t H t}, where V t It is a set of M nodes in each subgraph, E t H is the set of edges in each subgraph. t ={h1 t h2 t , ..., h N t}∈R M×N The feature matrix represents the set of nodes in the subgraph, where each node V i t ∈V t Each has its corresponding D-dimensional feature vector h i t ;

[0014] The specific process of adding connecting edges includes:

[0015] a. Determine the specific position of each particle in three-dimensional space based on its coordinates (x, y, z);

[0016] b. Define a custom three-dimensional spatial connection radius r;

[0017] c. Calculate the distances between all particle pairs in the subgraph;

[0018] d. For a given particle, connect all particles within its connection radius according to the three-dimensional spatial connection radius.

[0019] Further, in S103, the feature embedding refers to using graph convolutional neural networks and graph attention neural networks to capture the local and global similarities between particles from local and global perspectives, respectively. It uses a message passing mechanism to obtain the attention-based local features and convolution-based global features of the particles, and aggregates the local and global features through an aggregation function to finally generate a particle feature containing local and global information.

[0020] Specifically, the graph convolutional neural network has the following formula:

[0021]

[0022] in, l is the identity matrix. yes The degree matrix, H t+1 ={h1 t+1 h2 t+1 , ..., h N t+1}∈R M×N , represents the feature matrix of the subgraph node set at time t+1;

[0023] Specifically, the graph attention neural network described above has the following formula:

[0024]

[0025] Among them, Q (t) It is a query matrix, K (t) It is a key matrix representation, D (t) It is a value matrix. H (t+1) and H (t) These are the particle characteristic moments at time t+1 and time t, the key matrix, and the value matrix, used for feature transformation and information exchange.

[0026] Specifically, the aggregate function has the following formula:

[0027]

[0028] Furthermore, in S104, the formula for the recurrent neural network is:

[0029]

[0030]

[0031]

[0032] Among them, weight and bias These are all parameters of the model. They are obtained by using the particle states from previous time steps. By concatenating the particle state with the particle state at subsequent time steps, the particle state H at the current time step can be predicted. t .

[0033] This invention presents a dynamic simulation method for physical materials based on graph neural networks. It constructs the dynamic changes of physical materials as sub-graphs and proposes a novel dynamic graph neural network method. Utilizing graph convolutional networks and graph attention networks, it extracts local and global features of physical particles from both local and global perspectives. Then, an aggregation function combines these two types of features into a single feature, resulting in more comprehensive extracted feature information and providing more accurate information for simulation prediction. Finally, in the simulation prediction, a recurrent neural network is used to predict the state of physical particles at a specific moment. This recurrent neural network not only learns the feature information of physical particles before a certain moment but also learns the feature information of physical particles after a certain moment, resulting in extremely high accuracy in simulation prediction. Attached Figure Description

[0034] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0035] Figure 1 This is a schematic diagram of the process of a physical material dynamic simulation method based on graph neural networks provided by the present invention. Detailed Implementation

[0036] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0037] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0038] This embodiment takes fluid simulation as an example and proposes a physical material dynamic simulation method based on graph neural networks, such as... Figure 1 As shown, the method steps include:

[0039] S101. Obtain the dynamic change process of particles in a certain physical material, and divide the dynamic change process of particles in spacetime into T time snapshots, each time snapshot consisting of particles.

[0040] In this embodiment, S101 is to obtain the particle dynamic change process of a certain physical material by using conventional methods in the prior art, such as SPH smoothed particle hydrodynamics, MPM material point method and PDB position-based simulation method.

[0041] S102. Construct T subgraphs from the T time snapshots generated in S101, wherein each subgraph consists of nodes and undirected edges;

[0042] In S102 of this embodiment, T time snapshots are constructed into T subgraphs using a graph structure generation method. The specific process is as follows:

[0043] Graph structure data is generated by adding edges between particles; the subgraph is represented as G. t ={V t E t H t}, where V t It is a set of M nodes in each subgraph, E t H is the set of edges in each subgraph. t ={h1 t h2 t , ..., h N t}∈R M×N The feature matrix represents the set of nodes in the subgraph, where each node V i t ∈V t Each has its corresponding D-dimensional feature vector h i t ;

[0044] The specific process of adding connecting edges includes:

[0045] a. Determine the specific position of each particle in three-dimensional space based on its coordinates (x, y, z);

[0046] b. Define a custom three-dimensional spatial connection radius r;

[0047] c. Calculate the distances between all particle pairs in the subgraph;

[0048] d. For a given particle, connect all particles within its connection radius according to the three-dimensional spatial connection radius.

[0049] S103. Perform feature embedding on the T sub-graphs generated in S102 to obtain the feature vectors of all particles in each sub-graph;

[0050] In S103 of this embodiment, the feature embedding refers to using graph convolutional neural networks and graph attention neural networks to capture the local and global similarities between particles from local and global perspectives, respectively, to obtain the attention-based local features and convolution-based global features of the particles, and then aggregating the local features and global features through an aggregation function to finally generate a particle feature containing local and global information.

[0051] Specifically, the graph convolutional neural network has the following formula:

[0052]

[0053] in, A t It is the adjacency matrix, and l is the identity matrix. yes The degree matrix, H t+1 ={h1 t+1 h2 t+1 , ..., h N t+1}∈R M×N The characteristic matrix representing the set of nodes in the subgraph at time t+1;

[0054] Specifically, the graph attention neural network described above has the following formula:

[0055]

[0056] Among them, Q (t) It is a query matrix, K (t) It is a key matrix representation, D (t) It is a value matrix. H (t+1) and H (t) These are the particle characteristic moments at time t+1 and time t, the key matrix, and the value matrix, used for feature transformation and information exchange.

[0057] Specifically, the aggregate function has the following formula:

[0058]

[0059] Where σ() is the activation function, W is the parameter matrix, MEAN() is the average function, and ∪ represents the concatenation operation.

[0060] S104. Based on the particle feature vectors of the T subgraphs generated in S103, a recurrent neural network method is used to learn the particle feature information at time t-2, t-1, t+1, and t+2, and capture the temporal characteristics of particle state changes.

[0061] The recurrent neural network in S104 of this embodiment can capture not only previous particle state information but also subsequent particle state information; the formula of this recurrent neural network is:

[0062]

[0063]

[0064]

[0065] Among them, weight and bias These are all parameters of the model. They are obtained by using the particle states from previous time steps. By concatenating the particle state with the particle state at subsequent time steps, the particle state H at the current time step can be predicted. t .

Claims

1. A physical material dynamic simulation method based on a graph neural network, characterized in that, S101, obtaining the dynamic change process of particles of a certain physical material, and dividing the dynamic change process of the particles in space-time into T time snapshots, each time snapshot being composed of particles; S102, constructing T subgraphs from the T time snapshots generated in S101, the subgraphs being composed of nodes and undirected edges; S103, performing feature embedding on the T subgraphs generated in S102 to obtain feature vectors of all particles in each subgraph; the feature embedding refers to capturing local similarity and global similarity between particles from a local perspective and a global perspective using a graph convolutional neural network and a graph attention neural network, respectively, obtaining attention-based local features and convolution-based global features of the particles using a message passing mechanism, and aggregating the local features and the global features through an aggregation function to finally generate a particle feature containing local information and global information; S104, based on all particle feature vectors generated in S103, using a recurrent neural network to capture the time characteristics of the particle state changes; the formula of the recurrent neural network is: where the weights and the bias are parameters of the model; the particle state at the current time H t is predicted by concatenating the particle state at the previous time and the particle state at the next time 2. The physical material dynamic simulation method based on a graph neural network according to claim 1, characterized in that, in S101, the dynamic change process of particles of a certain physical material is obtained by using SPH smooth particle hydrodynamics method, MPM material point method and PDB position-based simulation method.

3. The physical material dynamic simulation method based on a graph neural network according to claim 1, characterized in that, in S102, T subgraphs are constructed from T time snapshots by using a graph structure generation method, and the specific process is as follows: By adding edges between particles, graph structure data is generated; sub-graphs are represented as G t = {V t , E t , H t}; where V t is the set of M nodes in each subgraph, E t is the set of edges in each subgraph, H t = {hi t , h2 t ,..., h N t} e R M×N denotes the feature matrix of the set of nodes of a subgraph, each node V i t e V t has its corresponding D-dimensional feature vector h i t .

4. The physical material dynamic simulation method based on a graph neural network according to claim 3, characterized in that, the specific processing process of adding edges between particles includes: a. determining the specific position of the particle in the three-dimensional space according to the coordinates (x, y, z) of each particle; b. defining a three-dimensional space connection radius r; c. calculating the distance between all pairs of particles in the subgraph; d. for a certain determined particle, connecting all particles within its connection radius according to the three-dimensional space connection radius.

5. The physical material dynamic simulation method based on a graph neural network according to claim 1, characterized in that, the formula of the graph convolutional neural network is: wherein, l is the identity matrix, is the degree matrix of H t+1 = {hi t+1 , h2 t+1 ,..., h N t+1} e R M×N , denotes the feature matrix of the subgraph node set t+1 at time.

6. The physical material dynamic simulation method based on a graph neural network according to claim 1, characterized in that, the formula of the graph attention neural network is: where Q (t) is a query matrix, K (t) is a key matrix representation, D (t) is a value matrix, H (t+1) and H (t) are the particle feature matrices at the t+1th and tth time, the key matrix and the value matrix, used for feature conversion and information exchange.

7. The physical material dynamic simulation method based on a graph neural network according to claim 1, characterized in that, the formula of the aggregation function is as follows:

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