Physical system trajectory prediction method and system based on isotropic graph neural network

Abstract

The invention discloses a physical system trajectory prediction method and system based on an isotropic graph neural network, and relates to the technical field of trajectory prediction. The method comprises the following steps: constructing a virtual node corresponding to a real fluid particle node according to a target state at a given moment, and constructing a trajectory prediction model based on an isotropic graph neural network according to the virtual node; the target state comprises characteristics and coordinates of target fluid particles at a given moment; and on the basis of the trajectory prediction model, state data of the real fluid particle nodes are updated firstly, and then state data of the virtual nodes are updated according to the updated state data. The method can improve the prediction accuracy of the physical system trajectory.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of trajectory prediction, in particular to a physical system trajectory prediction method and system based on an equivariant graph neural network. BACKGROUND

[0002] In the field of complex physical system simulation, trajectory prediction of fluid dynamics, molecular dynamics and many-body interaction systems has always been a core problem. Traditional methods usually rely on numerical methods such as finite element, finite difference or smoothed particle hydrodynamics (SPH) to describe physical laws, although they can guarantee a certain accuracy, but the computational complexity is extremely high, and for large-scale long-time simulation, it is difficult to balance efficiency and scalability. In recent years, with the development of deep learning technology, researchers have tried to use neural networks to accelerate physical system simulation. For example, the method based on convolutional neural network (CNN) can predict the evolution of flow field on a fixed grid, but due to its dependence on regular grid structure, it is difficult to handle complex boundaries and irregular geometry. On the other hand, the method based on graph neural network (GNN) learns the dynamics law by constructing the adjacency relationship between particles, and representative works such as Interaction Networks and Graph Network Simulator (GNS) have shown good prediction results in fluid and many-body dynamics tasks. However, this kind of method still has significant defects: the CNN method is limited by the grid and lacks flexibility; the traditional GNN method does not explicitly introduce physical symmetry modeling, so it has poor generalization ability in rotation, translation, reflection and other symmetry scenarios; in complex three-dimensional flow field prediction, ordinary neural network methods often cannot guarantee physical consistency and are prone to energy non-conservation or numerical drift.

[0003] To overcome the above problems, researchers have proposed equivariant graph neural network (Equivariant Graph Neural Network, EGNN), which introduces geometric constraints and tensor operators into the message passing mechanism to realize the preservation of translation, rotation and other symmetries, and has made significant progress in molecular modeling, dynamics prediction and other tasks. However, the equivariant network usually needs high-order tensor product operations in many-body interaction modeling, which is extremely expensive in calculation, making it difficult to apply in large-scale fluid particle simulation. Therefore, the existing methods either have low computational efficiency or lack physical consistency and generalization ability, and cannot balance efficiency and accuracy. SUMMARY

[0004] The purpose of the present application is to provide a physical system trajectory prediction method and system based on an equivariant graph neural network, which aims to solve or improve at least one of the above technical problems.

[0005] To achieve the above purpose, the present application provides the following scheme: A physical system trajectory prediction method based on isometric graph neural network, comprising: According to the target state of a given time, a virtual node corresponding to the real fluid particle node is constructed, and a trajectory prediction model based on isometric graph neural network is constructed according to the virtual node; The target state includes the characteristics and coordinates of the target fluid particle at a given time; Based on the trajectory prediction model, the state data of the real fluid particle node is updated first, and then the state data of the virtual node is updated according to the updated state data.

[0006] Optionally, the state data calculation process of the virtual node is: Based on the four-point positioning principle, the edge feature and distance between any two real fluid particle nodes are calculated, and the multi-layer perception The edge feature is encoded, and then the multi-layer perception And The initialization feature of the virtual node is calculated, and finally the aggregation information of all neighbors for each real fluid particle node is calculated to obtain the coordinates of the virtual node.

[0007] Optionally, the state data calculation formula of the virtual node comprises: Among them, The encoded edge feature is represented as , And The multi-layer perception operation is represented as The feature of the table node i is represented as The feature of the node j is represented as The edge feature is represented as The distance between two nodes is represented as The shared feature of the virtual node is represented as The coordinates of the virtual node are represented as The all-1 vector representation is represented as The coordinates of the real node are represented as The neighborhood of the node i is represented as α i The normalization coefficient is represented as φ Z The multi-layer perception for calculating the coordinate difference weight is represented as

[0008] Optionally, the process of updating the state data of the real fluid particle node is specifically represented as: Among them, The encoded edge message is represented as And This represents the multilayer perceptron operation. Table Node i Features shown, Represents a node j Features Indicates the characteristics of connected edges. Indicates the distance between two nodes. α i Represents the normalization coefficient. Represents a node i The neighborhood, Vector messages representing connected edges This represents a multilayer perceptron for calculating vector feature weights. This represents the aggregated scalar message. This represents the aggregated vector message. Represents the coordinates of the node.

[0009] Optionally, updating the virtual node's state data based on the updated state data specifically involves: Based on the updated state data, an equivalent DeepSet is constructed, the coordinate difference between the virtual node and the real fluid particle node is calculated, and a novel multilayer perceptron is introduced. Constructing complete scalar information Finally, the node features and coordinates are updated sequentially.

[0010] Optionally, the process of updating the state data of the virtual node is specifically represented as follows: in, This represents the coordinate difference between the virtual node and the real node. This represents a vector consisting entirely of 1s. Represents the coordinates of the virtual node. Represents scalar information. This indicates the shared characteristics of virtual nodes. Represents a node j Features Table Node i Features shown, α i Represents the normalization coefficient. Represents a node i The neighborhood, Represents the coordinates of neighboring nodes. This represents a complete multilayer perceptron used for edge message computation. This represents a complete multilayer perceptron used for updating the scalar features of real nodes. This represents a complete multilayer perceptron used for updating the scalar features of virtual nodes. coordinates of real nodes, (v) a multi-layer perceptron representing weights for updating coordinates of virtual nodes using information from virtual nodes, (v) a multi-layer perceptron representing weights for updating coordinates of virtual nodes using information from virtual nodes.

[0011] The application further provides a physical system trajectory prediction system based on an isometric graph neural network, comprising: a model construction unit configured to construct virtual nodes corresponding to real fluid particle nodes according to a target state at a given time, and construct a trajectory prediction model based on an isometric graph neural network according to the virtual nodes; the target state comprises features and coordinates of target fluid particles at the given time; a trajectory prediction unit configured to update state data of the real fluid particle nodes based on the trajectory prediction model, and update state data of the virtual nodes according to the updated state data.

[0012] According to the specific embodiments of the application, the following technical effects are achieved: The application discloses a physical system trajectory prediction method and system based on an isometric graph neural network. The method comprises the following steps: constructing virtual nodes corresponding to real fluid particle nodes according to a target state at a given time, and constructing a trajectory prediction model based on an isometric graph neural network according to the virtual nodes; the target state comprises features and coordinates of target fluid particles at the given time; and updating state data of the real fluid particle nodes based on the trajectory prediction model, and updating state data of the virtual nodes according to the updated state data. The application can improve the prediction accuracy of the trajectory of the physical system. The application firstly introduces a geometric graph as a data structure to model the physical system. In the modeling process, a group of reference datum points is learned for each particle node, other particle coordinates are converted into distance vectors by the four-point positioning principle, and a deep set network is used to efficiently process the distance vector set corresponding to all particle coordinates, so that the complex multi-body action is effectively modeled while the physical symmetry is maintained. The method can balance the physical consistency, prediction accuracy and calculation efficiency, breaks through the bottleneck of the prior art, and has strong practical application value. BRIEF DESCRIPTION OF DRAWINGS

[0013] In order to more clearly illustrate the technical solutions of the embodiments of the application or the prior art, the following will briefly introduce the drawings needed in the embodiments. Obviously, the drawings described below are only some embodiments of the application, and for those skilled in the art, other drawings can also be obtained from these drawings without creative labor.

[0014] Figure 1This is a schematic diagram of the physical system trajectory prediction method based on equivariant graph neural networks of the present invention; Figure 2 This is a schematic diagram showing the position and state of each physical entity in three-dimensional space in this embodiment. Detailed Implementation

[0015] 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, and 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.

[0016] The purpose of this invention is to provide a method and system for predicting the trajectory of a physical system based on an equivariant graph neural network, aiming to solve or improve at least one of the above-mentioned technical problems.

[0017] 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.

[0018] like Figure 1 As shown, this invention provides a method for predicting the trajectory of a physical system based on an isovariant graph neural network. First, virtual nodes are constructed around each node using learnable weights. Second, using the four-point positioning principle, the spatial coordinates of physical entities are transformed into distance vectors from their virtual nodes, and encoded using a DeepSet to obtain the standard form of the geometric graph. This standard form is then embedded into the scalar channel of the neural network, thereby constructing the isovariant graph neural network. This method can effectively model multi-body interactions in complex systems while maintaining physical symmetry, achieving efficient trajectory prediction for physical systems. Specific steps include: Step 100: Construct virtual nodes corresponding to real fluid particle nodes based on the target state at a given time, and construct a trajectory prediction model based on an isotropic graph neural network based on the virtual nodes; the target state includes the characteristics and coordinates of the target fluid particle at a given time.

[0019] Step 200: Based on the trajectory prediction model, first update the state data of the real fluid particle nodes, and then update the state data of the virtual nodes according to the updated state data.

[0020] As a specific implementation method, the following specific processing procedure is provided.

[0021] First, for the graph neural network used to build the trajectory prediction model in this embodiment, a graph is an important data structure used to describe objects and their relationships, consisting of nodes and edges. Nodes represent basic entities in a physical system, such as particles, molecules, or rigid bodies; edges represent the relationships between entities and can have weights to represent the strength, distance, or dependency of the interaction. In a physical system, the interaction between nodes is usually bidirectional, so the system is often represented as an undirected graph to describe the symmetric relationship and interaction rules between particles. Through this graph structure, the trajectory prediction problem of a physical system can be converted into a learning and reasoning task based on a graph neural network, providing an efficient and physically consistent method for modeling and simulating large-scale complex physical systems. The entire physical system can be represented as a geometric graph, which introduces geometric information (such as coordinates, velocities, and other physical properties) on the basis of traditional graph structures. Specifically, it can be represented as where represents the physical entities (such as particles, molecules, or rigid bodies) in the system. is an adjacency matrix (0 1 matrix) that represents the interaction relationship between physical entities, such as which indicates that the physical entity in the system and the physical entity interact and can exchange information. represents the coordinate information of the physical entities in three-dimensional space. Optionally, when the data set contains velocity information, the velocity attribute can also be added to the node features of the geometric graph, similar to the coordinate attribute, to more completely describe the dynamic state of the physical system.

[0022] The trajectory prediction task of a physical system requires predicting the motion trajectory of each physical entity in the system in a three-dimensional space, which needs to satisfy E(3) equivariance. Among them, E(3) represents a special Euclidean group in three-dimensional space (Euclidean Group), which is used to describe the rigid body transformation in three-dimensional space, including translation and rotation. The so-called equivariance means that the prediction result of the physical system will be transformed accordingly with the input rigid body transformation, so as to ensure that the prediction result is independent of the choice of the reference coordinate system; in contrast, invariance refers to the fact that the prediction result remains completely consistent under different coordinate systems, while equivariance requires the output to change accordingly with the input transformation. This equivariance is of key significance in trajectory prediction of physical systems, because the physical laws themselves should remain consistent under spatial transformation, thereby ensuring the physical consistency and generalization ability of the prediction. Existing E(3) equivariant graph neural networks (such as the EGNN model) can fully utilize this property when processing tasks such as molecular dynamics, many-body systems, and fluid dynamics. The model proposed in the present application is also an E(3) equivariant graph neural network, which encodes the geometric information of the nodes to achieve high-precision prediction of the trajectory of the physical system, while ensuring the correctness of the prediction result under translation and rotation transformation.

[0023] As shown in Figure 2 , the task of physical system trajectory prediction is to predict the position and state of each physical entity in the system in three-dimensional space. Assuming that the motion direction of a certain physical entity in the system is initially oriented, when the spatial coordinates of the entity are rotated as a whole (for example, by 90°), the predicted motion direction will also be rotated accordingly, thereby ensuring that the prediction result is consistent with the rotation of the input coordinate system, which embodies the E(3) equivariance of the model.

[0024] The core of physical system trajectory prediction is to predict the state of each physical entity at the next time step based on the given system state at the current time step, which can generally be divided into the following three steps: 1) Construct a virtual node based on each fluid particle node, the specific formula is as follows, wherein represents the coordinates of the virtual node, represents the shared features of the virtual node, and the coordinate difference between the node and the virtual node is calculated: Specifically, in the first row of the formula, the features of node i and the features of node j , as well as the edge feature and the distance , are encoded by a multi-layer perceptron to obtain the edge feature ; in the second row of the formula, a multi-layer perceptron is further introduced to Compute virtual node initialization features; in the third line of the formula, denotes an all-ones vector, then for node i neighborhood All information is aggregated to obtain the coordinates of the virtual node .

[0025] 2) Similar to the normal EGNN, update the features and coordinates of all real fluid particle nodes: where the same symbols as in the first step formula represent the same meaning, and the normalization coefficient denotes the number of nodes in the neighborhood .

[0026] 3) Further update the features and coordinates of the fluid particle nodes and the virtual nodes. This step is equivalent to constructing a DeepSet, and then through the isometric feature basis function to obtain the required objective function: Specifically, where denotes the coordinate difference generated by the virtual node and the real node, and then by introducing a brand new multi-layer perception construct a complete scalar information , and finally update the node features and coordinates in turn.

[0027] Based on the above technical solutions, the following embodiments for vehicle trajectory prediction in a traffic system are provided.

[0028] For all vehicles in an area, each vehicle can be considered as a node, with its vehicle type as the feature of the node, and with corresponding coordinates and speed. Since in general cases, the driving route of a vehicle is only affected by nearby vehicles, a geometric graph can be constructed by building edges according to distance. By inputting the information mentioned above, the position of the vehicle at the subsequent time can be predicted, thereby realizing the prediction task of the vehicle trajectory in the traffic system.

[0029] In addition, the present embodiment also uses the 5-body and Water-3D mini two data sets to detect the effect of the technical solution, and tests the performance of the model and the baseline EGNN, FastEGNN, HEGNN, etc. in different settings of 1-4 layers on each data set.

[0030] 5-body is a commonly used task dataset for evaluating the trajectory prediction of physical systems. Specifically, it is a dataset generated by simulation. In the simulation of the present embodiment, each system contains 5 charged particles, each with a random charge of +1 or -1, and the motion of each particle is driven by Coulomb force. The dataset is divided into: a training set of 5000 samples, a validation set of 2000 samples, and a test set of 2000 samples. The task goal is to predict the positions of all particles after 1000 time steps. The results are shown in Table 1.

[0031] Table 1

[0032] Water-3D is a particle-based large-scale fluid simulation dataset generated using smoothed particle hydrodynamics (SPH), recording the dynamic process of water falling into a box, each system containing an average of 7806 particles and 94999 edges, with a connection cutoff value of 0.035. Due to the large sample size of the original dataset, the present embodiment limits the evaluation range to a subset of 1 / 5, constructing a new evaluation standard Water-3D mini, which contains 3,000 / 300 / 300 samples from the original dataset (15,000 / 1,500 / 1,500) for training, validation, and testing, with a maximum training period of 1,000. The results are shown in Table 2.

[0033] Table 2

[0034] From the above, it can be found that the model of the present embodiment outperforms the traditional baselines EGNN, FastEGNN, and HEGNN on both tasks. In addition, the model of the present embodiment achieves results close to those of other models with 3-4 layers under the setting of 1-2 layers, fully demonstrating the effectiveness of the modeling method for fluid simulation tasks.

[0035] The various embodiments in the specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0036] The principles and implementation modes of the present application are described by applying specific examples in the present specification. The above description of the embodiments is only to help understand the core idea of the present application; at the same time, for those skilled in the art, according to the idea of the present application, the specific implementation mode and application range will be changed. In view of the above, the content of the specification should not be understood as a limitation of the present application.

Claims

1. A method for trajectory prediction of a physical system based on equivariant graph neural networks, the method comprising: The method comprises the following steps: According to the target state at a given time, a virtual node corresponding to a real fluid particle node is constructed, and a trajectory prediction model based on an equivariant graph neural network is constructed according to the virtual node; the target state comprises the characteristics and coordinates of a target fluid particle at a given time; Based on the trajectory prediction model, the state data of the real fluid particle node is first updated, and then the state data of the virtual node is updated according to the updated state data.

2. The isometric graph neural network-based physical system trajectory prediction method according to claim 1, wherein, The state data calculation process of the virtual node is: Based on the four-point positioning principle, the edge features and distances between any two real fluid particle nodes are calculated, and the multi-layer perception is passed through The edge features are encoded, and the multi-layer perception is passed through And The virtual node initialization features are calculated, and finally the aggregate information of all neighbors is calculated for each real fluid particle node to obtain the coordinates of the virtual node.

3. The isometric graph neural network-based physical system trajectory prediction method according to claim 1, wherein, The state data calculation formula of the virtual node comprises: wherein, denotes the encoded edge feature, , and denotes a multi-layer perceptron operation, table node i feature representation, denotes the feature of a node j , denotes the edge feature, denotes the distance between two nodes, denotes the feature shared by virtual nodes, denotes the coordinates of a virtual node, denotes the all-ones vector representation, denotes the coordinates of a real node, denotes the neighborhood of a node i , α i denotes a normalization coefficient, φ Z denotes a multi-layer perceptron computing the coordinate difference weight.

4. The isometric graph neural network-based physical system trajectory prediction method according to claim 1, wherein, The process of updating the state data of the real fluid particle node is specifically represented as: in, This represents the encoded edge message. and This represents the multilayer perceptron operation. Table Node i Features shown, Represents a node j Features Indicates the characteristics of the connected edges. Indicates the distance between two nodes. α i Represents the normalization coefficient. Represents a node i The neighborhood, Vector messages representing connected edges This represents a multilayer perceptron for calculating vector feature weights. This represents the aggregated scalar message. This represents the aggregated vector message. Represents the coordinates of the node.

5. The isometric graph neural network-based physical system trajectory prediction method according to claim 1, wherein, The state data of the virtual node is updated according to the updated state data, and the process is specifically: According to the updated state data, a DeepSet is constructed equivalently, the coordinate difference between the virtual node and the real fluid particle node is calculated, and a brand-new multi-layer perception is introduced Construct a complete scalar information Finally, the node features and coordinates are updated in turn.

6. The isometric graph neural network-based physical system trajectory prediction method according to claim 1, wherein, The process of updating the state data of the virtual node is specifically represented as: wherein, represents the coordinate difference between virtual and real nodes, represents the all-ones vector representation, represents the coordinates of a virtual node, represents the scalar information, represents the features shared by virtual nodes, represents the features of a node j , represents the features of a node i , α i represents the normalization coefficient, represents the neighborhood of a node i , represents the coordinates of a neighbor node, represents the complete multilayer perceptron for edge message computation, represents the complete multilayer perceptron for real node scalar feature update, represents the complete multilayer perceptron for virtual node scalar feature update, represents the coordinates of a real node, (v) represents the multilayer perceptron for weights from virtual node information and for updating real node coordinates, (v) represents the multilayer perceptron for weights from virtual node information and for updating virtual node coordinates.

7. An isometric graph neural network-based physical system trajectory prediction system, comprising: The method comprises the following steps: A model construction unit is configured to construct a virtual node corresponding to a real fluid particle node according to a target state at a given time, and to construct a trajectory prediction model based on an equivariant graph neural network according to the virtual node; the target state comprises the characteristics and coordinates of a target fluid particle at a given time; A trajectory prediction unit is configured to first update the state data of the real fluid particle node based on the trajectory prediction model, and then to update the state data of the virtual node according to the updated state data.

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