Particle trajectory prediction method and device based on symmetric coding, medium and product

Abstract

The invention discloses a particle trajectory prediction method and device based on symmetric coding, a medium and a product, and relates to the technical field of civil engineering geotechnical mechanics analysis and machine learning, and the method comprises the steps: obtaining the attribute information of geotechnical particles; constructing a rock-soil particle undirected graph according to the attribute information; constructing node features and edge features of the graph neural network model according to the rock-soil particle undirected graph; according to the method, when particles are coded, the radius of the particles serves as an important feature to be added into a particle feature vector, so that the model can process the particles of different sizes, then an orthogonal decomposition method in mechanics is introduced into the model, tangential force and normal phase force are learned respectively by constructing two networks of similar structures, and the method is used for solving the problem. Therefore, the model does not need to learn vector operation. According to the invention, systems with different particle sizes can be simulated, and vector learning operation is not needed.

Description

Technical Field

[0001] The present application relates to the field of geotechnical analysis and machine learning technology in civil engineering, and in particular to a particle trajectory prediction method, device, medium and product based on symmetric coding. Background Art

[0002] Solid physics systems appear relatively continuous from a macroscopic perspective, but from a microscopic perspective, they are composed of a large number of particles. Traditional solid dynamics uses discrete systems to simulate particle contacts and fit macroscopic behaviors. This method has advantages in solving problems such as particle stability and deformation and is widely used in practical engineering, including material design, structural optimization, and geological disaster prevention. However, with the increasing complexity of contact models and the growth of the number of particles, the development of traditional simulators is limited by computing power.

[0003] In recent years, with the rapid development of deep learning, researchers have begun to use deep models to replace traditional physical simulation processes to improve simulation efficiency. This approach has also been applied to particle-based dynamic simulations. In the past two years, simulation models based on graph neural networks (GNNs) have been widely used because of their high consistency with the topological structure of particle systems, including simulations related to fluid dynamics, articulated rigid body dynamics, and molecular dynamics.

[0004] Subsequently, recent studies have incorporated conservation laws or equivariance into models to further improve prediction accuracy. Equivariance is a property of an object that remains unchanged after a transformation. For example, a system of particles should remain symmetrical after being flipped horizontally. Models such as EGNN, GMN, and ESTAG have incorporated equivariance and performed well on microscopic datasets such as molecules and proteins.

[0005] However, existing methods can only simulate systems with consistent particle sizes. Moreover, these existing models require learning vector operations, which increases the difficulty of learning the models. Summary of the invention

[0006] The purpose of this application is to provide a particle trajectory prediction method, device, medium and product based on symmetric coding, which can simulate systems with different particle sizes and does not require learning vector operations.

[0007] To achieve the above objectives, this application provides the following solutions:

[0008] In a first aspect, the present application provides a particle trajectory prediction method based on symmetric coding, and the particle trajectory prediction method based on symmetric coding includes:

[0009] Acquire attribute information of rock and soil particles; the attribute information includes: type information of rock and soil particles, size information of rock and soil particles, velocity information of rock and soil particles, direction information of rock and soil particles, distance relationship between rock and soil particles, and mechanical relationship between rock and soil particles;

[0010] Constructing an undirected graph of rock and soil particles according to the attribute information; the nodes in the undirected graph of rock and soil particles correspond to rock and soil particles, and the edges in the undirected graph of rock and soil particles correspond to the mechanical relationships between the rock and soil particle nodes;

[0011] A graph neural network model is constructed according to the rock and soil particle undirected graph; the graph neural network model includes node features and edge features; the node features include: particle radius features, particle type features, and distance features between particles and set boundaries; the edge features include: distance features between particles;

[0012] Acquire the direction information of the node feature based on the rock and soil particle undirected graph; the direction information includes the direction information of speed and the direction information of distance;

[0013] Symmetrically encode the node feature based on the direction information to obtain a node code;

[0014] Based on the undirected graph of rock and soil particles, the mechanical relationship between the node features is decomposed into a normal component and a tangential component, and the normal component and the tangential component are encoded respectively to obtain a normal embedding function and a tangential embedding function, and then the damping effect of each node is encoded in the form of a damping component to obtain a damping embedding function;

[0015] The graph neural network model is used to associate the node coding with the edge coding to obtain a rock and soil particle graph neural network; the edge coding includes: a normal embedding function, a tangential embedding function and a damping embedding function;

[0016] The rock and soil particle graph neural network is used to predict rock and soil particle trajectories.

[0017] Optionally, constructing a graph neural network model according to the rock and soil particle undirected graph specifically includes:

[0018] The information in the undirected graph of rock and soil particles is encoded into numerical features through an embedding function to obtain a graph neural network model.

[0019] Optionally, the node feature in the graph neural network model is: n' i = {v i ,∈ k (k i ),r i ,B i};

[0020] Among them, v i represents the particle velocity, ∈ k (·) represents the embedding function, k i Indicates the particle type, r i represents the particle radius, B i Indicates the distance information between the particle corresponding to the i-th node and the set boundary.

[0021] Optionally, the edge feature in the graph neural network model is: e' ij ={dist ij ,∈ T (T ij )};

[0022] Among them, dist ij represents the distance between two particles, T ij is the edge type encoded by the particle types at both ends, ∈ T (·) is the edge type embedding function.

[0023] Optionally, the formula for the symmetric encoding is: {ij} =|d(v {x,j} )·3 2 +d(v {x,i} )·3 1 +d(dist {x,ij} )·3 0 |;

[0024] Among them, d(·) is the direction extraction function, v {x,i} is the horizontal velocity of the node.

[0025] Optionally, the graph structure of the rock particle graph neural network is: G0=(N,(E f ,E g ,E d ));

[0026] Where N represents the node set, E f 、E g 、E d The edge sets representing normal force, tangential force, and damping force respectively.

[0027] Optionally, the using the rock particle graph neural network to predict rock particle trajectories specifically includes:

[0028] Iteratively updating the rock and soil particle graph neural network through a message passing mechanism;

[0029] Obtain the motion trajectories of rock and soil particles in the updated rock and soil particle graph neural network.

[0030] In a second aspect, the present application provides a computer device, comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement any of the above-described particle trajectory prediction methods based on symmetric coding.

[0031] In a third aspect, the present application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements any of the above-mentioned particle trajectory prediction methods based on symmetric coding.

[0032] In a fourth aspect, the present application provides a computer program product, including a computer program, which, when executed by a processor, implements any of the above-mentioned particle trajectory prediction methods based on symmetric coding.

[0033] According to the specific embodiments provided in this application, this application discloses the following technical effects:

[0034] The present application provides a particle trajectory prediction method, device, medium and product based on symmetric coding, the method comprising: obtaining attribute information of rock and soil particles; the attribute information comprising: type information of rock and soil particles, size information of rock and soil particles, speed information of rock and soil particles, direction information of rock and soil particles, distance relationship between rock and soil particles and mechanical relationship between rock and soil particles; constructing an undirected graph of rock and soil particles according to the attribute information; the nodes in the undirected graph of rock and soil particles correspond to rock and soil particles, and the edges in the undirected graph of rock and soil particles correspond to the mechanical relationship between rock and soil particle nodes; constructing node features and edge features of a graph neural network model according to the undirected graph of rock and soil particles; the node features comprising: particle radius features, particle type features and distance features between particles and set boundaries; the edge features comprising: distance features between particles; the present application adds particle radius as an important feature to the particle feature vector when encoding particles, so that the model can handle undesired particles. Particles of the same size; based on the undirected graph of rock and soil particles, the direction information of the node features is obtained; the direction information includes the direction information of the speed and the direction information of the distance; based on the direction information, the node features are symmetrically encoded to obtain the node code; based on the undirected graph of rock and soil particles, the mechanical relationship between the node features is decomposed into normal components and tangential components for separate encoding, and the damping effect of each node is encoded in the form of damping components to obtain edge coding; the edge coding includes: normal embedding function, tangential embedding function and damping embedding function; in terms of particle force processing, the present application introduces the orthogonal decomposition method in mechanics into the model, and learns the tangential force and normal force respectively by constructing two networks with similar structures, so that the model does not need to learn vector operations; the graph neural network model is used to associate the node code with the edge code to obtain the rock and soil particle graph neural network; the rock and soil particle graph neural network is used to predict the trajectory of rock and soil particles. The present application can simulate systems with different particle sizes without the need to learn vector operations. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0036] Figure 1 This is an application environment diagram of a particle trajectory prediction method based on symmetric coding in an embodiment of the present application;

[0037] Figure 2 A schematic diagram of a flow chart of a particle trajectory prediction method based on symmetric coding provided in an embodiment of the present application;

[0038] Figure 3 A schematic diagram of a graph structure construction process provided in an embodiment of the present application;

[0039] Figure 4 A schematic diagram of a flow chart of a particle trajectory prediction method based on symmetric coding provided in an embodiment of the present application;

[0040] Figure 5 A schematic diagram of the structure of a computer device provided in one embodiment of the present application. DETAILED DESCRIPTION

[0041] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0042] In terms of particle force processing, this application introduces the orthogonal decomposition method in mechanics into the model, and builds two networks with similar structures to learn the tangential force and normal force respectively. Finally, for particles of different sizes, similar to the way gravity is handled, the particle radius is added to the particle feature vector as an important feature when encoding the particles. This allows the model to handle particles of different sizes.

[0043] In order to make the above-mentioned objects, features and advantages of the present application more obvious and easy to understand, the present application is further described in detail below with reference to the accompanying drawings and specific implementation methods.

[0044] The particle trajectory prediction method based on symmetric coding provided in the embodiment of the present application can be applied to Figure 1In the application environment shown. Among them, the terminal 102 communicates with the server 104 through the network. The data storage system can store the data that the server 104 needs to process. The data storage system can be set up separately, integrated on the server 104, or placed on the cloud or other servers. The terminal 102 can send the attribute information of the rock and soil particles to be processed to the server 104. After the server 104 receives the attribute information of the rock and soil particles to be processed, it constructs an undirected graph of rock and soil particles according to the attribute information; the nodes in the undirected graph of rock and soil particles correspond to rock and soil particles, and the edges in the undirected graph of rock and soil particles correspond to the mechanical relationship between rock and soil particle nodes; the node features and edge features of the graph neural network model are constructed according to the undirected graph of rock and soil particles; the node features include: particle radius features, particle type features, and distance features between particles and set boundaries; the edge features include: distance features between particles; the node features are obtained based on the undirected graph of rock and soil particles. The direction information of the feature; the direction information includes the direction information of the speed and the direction information of the distance; the node feature is symmetrically encoded based on the direction information to obtain the node code; based on the undirected graph of the rock and soil particles, the mechanical relationship between the node features is decomposed into normal components and tangential components for encoding respectively, and the damping effect of each node is encoded by the damping component to obtain the edge code; the edge code includes: normal embedding function, tangential embedding function and damping embedding function; the node code is associated with the edge code by using the graph neural network model to obtain the rock and soil particle graph neural network; the rock and soil particle graph neural network is used to predict the trajectory of the rock and soil particles. The server 104 can feed back the obtained trajectory prediction result to the terminal 102. In addition, in some embodiments, the particle trajectory prediction method based on symmetric coding can also be implemented by the server 104 or the terminal 102 alone, such as the terminal 102 can directly process the attribute information of the rock and soil particles to be processed, or the server 104 can obtain the attribute information of the rock and soil particles to be processed from the data storage system and process it.

[0045] The terminal 102 may be, but is not limited to, various desktop computers, laptop computers, smart phones, tablet computers, IoT devices, and portable wearable devices. The IoT devices may be smart speakers, smart TVs, smart air conditioners, smart vehicle-mounted devices, etc. The portable wearable devices may be smart watches, smart bracelets, head-mounted devices, etc. The server 104 may be implemented as an independent server or a server cluster consisting of multiple servers, or may be a cloud server.

[0046] In an exemplary embodiment, Figure 2As shown, a particle trajectory prediction method based on symmetric coding is provided. The method is executed by a computer device, and can be executed by a computer device such as a terminal or a server alone, or by a terminal and a server together. In the embodiment of the present application, the method is applied to Figure 1 The server 104 in the example is used as an example to illustrate the method, which includes the following steps S1 to S8. Among them:

[0047] S1. Obtaining attribute information of rock and soil particles; the attribute information includes: type information of rock and soil particles, size information of rock and soil particles, velocity information of rock and soil particles, direction information of rock and soil particles, distance relationship between rock and soil particles, and mechanical relationship between rock and soil particles.

[0048] S2. Construct an undirected graph of rock and soil particles according to the attribute information; the nodes in the undirected graph of rock and soil particles correspond to rock and soil particles, and the edges in the undirected graph of rock and soil particles correspond to the mechanical relationships between the rock and soil particle nodes.

[0049] S3. Construct a graph neural network model based on the rock and soil particle undirected graph; the graph neural network model includes node features and edge features; the node features include: particle radius features, particle type features and distance features between particles and set boundaries; the edge features include: distance features between particles.

[0050] A graph structure is constructed, where each node represents a particle, and node features include the particle's speed, type, radius, and the distance between the particle and the boundary. The particle's speed is a key dynamic variable in the simulation process, which determines the particle's motion trajectory and the results of its interaction. The particle type is encoded as a numerical feature through an embedding function, allowing the model to distinguish between different types of particles and their different physical behaviors. The radius of the particles affects their contact and collision behavior, and particles of different radii may differ in the way they stack and move. The distance between the particle and the boundary of the system is also an important consideration, especially when simulating the movement of particles in a limited space, the boundary may have an important impact on the behavior of the particles, so this is also included in the node features.

[0051] The initialization of edge features (or edge features) mainly considers the distance between particles and the type of edge. The distance between particles is a key variable because the interaction force is usually a function of distance. Calculating and updating the distance between particles helps determine the magnitude and direction of the interaction force. In addition, the type of edge is determined by the type of particle, and different types of particles may have different interaction mechanisms. The type of edge is encoded as a numerical feature through the embedding function, allowing the model to handle these complex interactions.

[0052] In the process of constructing the graph structure, the nodes and edges in the graph are first defined based on the positions of the particles and the initialized features. Each particle corresponds to a node, and each pair of interacting particles corresponds to an edge. Then the connection rules between particles are determined. Usually, only particles within a certain distance range will be connected to simulate their interaction. This distance threshold is determined according to the specific physical scene and simulation requirements. In addition to the interaction between particles, the self-influence of particles, that is, the effect of particles on themselves, needs to be considered. This can be achieved by adding a self-edge to each node in the graph. The characteristics of the self-edge usually contain the particle's own properties, such as speed and type.

[0053] S4. Acquire directional information of the node feature based on the rock and soil particle undirected graph; the directional information includes directional information of speed and directional information of distance.

[0054] S5. Symmetrically encode the node features based on the direction information to obtain a node code.

[0055] S6. Based on the undirected graph of rock and soil particles, the mechanical relationship between the node features is decomposed into a normal component and a tangential component, and the normal component and the tangential component are encoded respectively to obtain a normal embedding function and a tangential embedding function, and then the damping effect of each node is encoded in the form of a damping component to obtain a damping embedding function.

[0056] In the symmetric interactive direction encoding part of this embodiment, the direction attribute of the particle is first eliminated by absolute value conversion, and the symmetric interactive direction encoding is introduced to uniquely represent the relative motion relationship between the particle pairs. In this process, the direction extraction function is first used to extract the direction information of the particle. Specifically, through absolute value conversion, the direction of the particle velocity and the distance between the particles can be converted into scalars, thereby eliminating their direction attributes.

[0057] Next, symmetric interaction direction encoding is used to ensure the flip symmetry of the system. First, the direction information is extracted from the horizontal velocity of the particles and the distance between the particles, and then normalized by the direction extraction function. This direction information includes the horizontal velocity of the particles and the direction of the distance between the particles. Then, the interaction direction type between the particle pairs is determined by querying the symmetric interaction direction table. This interaction direction type is used to uniquely represent the relative motion relationship of the particle pairs and is embedded in the edge features.

[0058] To ensure flip symmetry, the symmetric interaction direction encoding encodes the direction information as scalars and embeds these scalar values ​​into the edge features. In this way, the model is able to ensure the symmetry of the system after flipping operations.

[0059] Based on the above graph structure construction and symmetric information encoding, the next step is to update the graph structure through the message passing mechanism to simulate the normal and tangential interactions, as well as the self-interaction of particles. First, the contact model decomposes the contact force into normal force and tangential force, and considers the damping effect of the particle itself. Specifically, the normal force and tangential force are the main components of the interaction between particles, while the damping force is an intrinsic effect of the particle itself, which is used to simulate the energy dissipation of the particle.

[0060] S7. Use the graph neural network model to associate the node coding with the edge coding to obtain a rock and soil particle graph neural network; the edge coding includes: a normal embedding function, a tangential embedding function and a damping embedding function.

[0061] S8. Predict rock and soil particle trajectories using the rock and soil particle graph neural network.

[0062] This embodiment updates the graph structure through a message passing mechanism to capture the complex interactions between particles. The message passing mechanism includes multiple iterative steps, in each step, the characteristics of the particle are updated according to the characteristics of the neighboring particles and the characteristics of the edge. In each iteration, the edge characteristics are updated according to the current node characteristics, thereby simulating the normal and tangential forces between particles. The update of the normal force takes into account the overlapping distance and direction of the particles, while the update of the tangential force takes into account the relative motion direction of the particles. The update of the damping force is mainly based on the speed and type of the particles.

[0063] In each iteration, the normal force, tangential force, and damping force are updated separately, and then the updated results are combined to adjust the characteristics of the particles. This process ensures accurate update of particle characteristics through multiple iterative steps to capture the complex interactions between particles. The number of iterations of the message passing mechanism is usually set to a large value to ensure that the system can converge stably.

[0064] Finally, after multiple iterations, the acceleration of the particles is calculated based on the updated features. This process ensures that the model can accurately simulate the interactions between particles and the trajectory of the particles. Through this detailed contact modeling, the model can effectively capture the complex interactions between solid particles and provide high-precision dynamic simulations in different physical scenarios. This modeling approach not only improves the accuracy of the simulation, but also enhances the versatility and robustness of the model when dealing with particles of different types and sizes.

[0065] Specifically, in this embodiment, the rock and soil particle system is first represented as an undirected graph, in which the nodes correspond to the rock and soil particles, and the edges correspond to the complex mechanical relationships between the rock and soil particle nodes. Taking the most basic linear elastic model in discrete element simulation as an example, the edges in the undirected graph correspond to the linear elastic interaction forces between particles.

[0066] Subsequently, the undirected graph structure is input into the graph neural network. This process includes four steps: expansion of node and edge features, fitting the interaction relationship between nodes using edge connections, synthesizing the action relationships in different directions, and decoding the resultant force to obtain the acceleration at the next moment. In these calculation steps, there may be linear or nonlinear relationships. For example, the interaction force between discrete element particles can show both linear and nonlinear relationships. The model effect is evaluated by calculating the gap between the model prediction results and the actual values. After reasonably selecting the model and parameters, this method can efficiently and accurately predict the motion trajectory of discrete element particles.

[0067] like Figure 3 As shown, based on the given definition and the established graph structure, node and edge features are first constructed. The constructed i-th node feature n' i As shown below:

[0068] n′ i = {v i ,∈ k (k i ),r i ,B i};

[0069] Among them, the characteristics involve the particle velocity v i , by embedding function ∈ k (·) The type k obtained i and radius r i , the distance information B between the particle corresponding to the i-th graph node and the set boundary i . The distance information is calculated by coordinates, which are two-dimensional coordinates defined in the software. Among them, the particle type represents the different soil types of the particles. In addition, since the deep learning training data of this embodiment is simulation data obtained through simulation software, the above parameters are set and exported through the simulation software. Similarly, construct the edge feature vector:

[0070] e′ ij ={dist ij ,∈ T (T ij )};

[0071] where dist ij Represents the distance between two particles, which is obtained by calculating the Euclidean distance through the coordinates of the particles at both ends. ij is the edge type encoded by the particle types at both ends. The edge type is obtained by permutation and combination of the particle types at both ends. Each edge type corresponds to a particle pair type combination. ∈ T (·) is the edge type embedding function.

[0072] In order to make the model flip symmetric, first, use absolute value transformation to eliminate the direction attributes in the node and edge features, and then extract the direction information of speed and distance. Based on this direction information, a unique code is generated to represent the relative motion relationship between the particle pairs. The symmetric encoding method is as follows:

[0073] D {ij} =|d(v {x,j} )·3 2 +d(v {x,i} )·3 1 +d(dist {x,ij} )·3 0 |;

[0074] Where d(·) is the direction extraction function, v {x,i} 、v {x,j} are the horizontal speeds of nodes i and j, respectively, dist {x,ij} is the horizontal distance between the two nodes. Using the hash coding idea, by multiplying the three types of information by different powers of 3, it is ensured that the particle pairs with different information get different codes. The generated symmetric code is embedded into the edge feature e' ij In the above, the updated node and edge features include the elimination of the value of the direction attribute and the embedding encoding. Through these steps, it is ensured that the particle system can still maintain the same behavior after flipping. This method effectively maintains the symmetry of the system through symmetric interaction direction encoding while reducing the computational cost.

[0075] Since the contact is decomposed into tangential and normal directions, as well as the damping effect of the particle itself, the modeling of the effect acting on the particle is divided into three parts. For each pair of interactions (mechanical relationships), the effect is simulated by decomposing it into normal and tangential components. In addition, for each individual particle, the damping effect is simulated by the damping component. The final particle features and 3 types of edge features are as follows:

[0076] n i =∈ n (n′ i ,|v i |);

[0077]

[0078] where ∈ n ,∈ f ,∈ g ,∈ d are the corresponding node, normal, tangential and damping embedding functions, v i is the particle velocity, h is the overlap distance between particles, θ i and θ j is the angle between the velocity of particle i and particle j and the line connecting the particles.i is the final node feature of node i. are the final normal and tangent features of the edge connecting nodes i and j. ii is the edge feature of the “self-edge” between node i and itself, is the final damping characteristic of the “self-edge” of node i.

[0079] After the above process, we finally get the graph G0=(N,(E f ,E g ,E d )), where N is the node set, E f 、E g 、E d are the edge sets representing normal force, tangential force, and damping force respectively,

[0080] Then, using graph neural networks, we associate node features with edge features in three dimensions: normal, tangent, and damping. For example, the edge feature and the node feature n at both ends i With n j Perform association to obtain normal feature association Similarly, we get the tangential feature association Associated with Damping Features The damping feature association only involves nodes and themselves.

[0081] According to the message aggregation method of graph neural network, edge features and node features are updated L times through L-layer network aggregation. When node features are updated, all neighboring nodes and edge features connected to them are aggregated as a fit to the resultant force on the particle. Taking the lth update as an example, the specific update method of the edge feature is as follows:

[0082]

[0083]

[0084] in, is the normal feature update function of the lth layer of the graph neural network, They represent the edge normal features of the l+1th layer and the lth layer in the update process, n i,l ,n j,l Then it is the node feature of the lth layer of nodes i and j. is the change in the edge normal characteristic of the l+1th layer, and similarly, the change in the edge tangential characteristic and the change in the damping characteristic of the l+1th layer are obtained. Based on the updated edge features, the aggregation is as follows:

[0085]

[0086] Among them, N J Represents node n j The set of neighbor nodes. is the node feature update function of the lth layer of the graph neural network. j,l+1 、n j,l They represent the node features of the l+1th layer and the lth layer during the update process respectively. They respectively represent the normal feature change and tangential feature change of the edge connecting neighbor node k and node j.

[0087] According to the node feature n updated by L layers j,L Generate acceleration a j The generation process is as follows:

[0088] a j =μ a (n j,L );

[0089] Among them, μ a is the acceleration mapping function.

[0090] Finally, the particle position is updated using the laws of motion of basic physics based on the predicted particle acceleration.

[0091] This embodiment provides a particle trajectory prediction method based on symmetric coding. The method constructs a graph neural network model by introducing a symmetric interactive coding system and a message passing mechanism, thereby achieving efficient and accurate solid dynamics simulation. The method represents the rock and soil particle system as an undirected graph, in which nodes represent particles and edges represent interactions between particles. Through absolute value conversion and symmetric interactive direction encoding, the particle direction attribute is eliminated to ensure the flipping symmetry of the system. Then, the graph structure is updated using a message passing mechanism to capture the complex normal and tangential forces and damping forces between particles, and finally an accurate particle acceleration prediction result is obtained. The graph neural network model of the present invention has high accuracy and robustness when processing particles of different types and sizes, and is suitable for practical engineering applications such as material design, structural optimization, and geological disaster prevention.

[0092] In an exemplary embodiment, see Figure 4 , a flow chart of a particle trajectory prediction method based on symmetric coding is provided, including:

[0093] The rock-soil particle system is represented as an undirected graph, wherein the nodes of the undirected graph correspond to the rock-soil particles, and the edges correspond to the interactions between the rock-soil particles; the node features are encoded, including the velocity, type, radius and distance from the boundary of the particles; the edge features are initialized, including the distance between particles and the type of edges; the direction attribute of the particles is eliminated by absolute value conversion, and the relative motion relationship between the particle pairs is uniquely represented by symmetric interaction direction encoding; the graph structure is updated based on a message passing mechanism to simulate normal and tangential interactions, as well as the self-interaction of particles; the acceleration of the particles is calculated and updated to predict their motion trajectories.

[0094] The encoding of the node features converts the particle's speed, type, radius and distance from the boundary into numerical features through an embedding function.

[0095] The initialization of the edge features includes calculating the distance between particles and encoding the edge type into a numerical feature through an embedding function.

[0096] The symmetric interactive direction encoding extracts the direction information of the horizontal velocity of the particles and the distance between the particles through the direction extraction function, and eliminates the direction attribute through absolute value conversion.

[0097] The message passing mechanism includes multiple iterative steps, in each of which node features are updated according to features of neighbor particles and features of edges.

[0098] The number of iterations of the message passing mechanism is set to a larger value to ensure stable convergence of the system.

[0099] The updating of the normal and tangential interaction forces takes into account the overlap distance and direction of the particles, as well as the relative motion direction.

[0100] The damping force is updated based on the velocity and type of the particle, encoded via an embedded function.

[0101] In an exemplary embodiment, a computer device is provided. The computer device may be a server or a terminal. The internal structure diagram thereof may be as follows: Figure 5As shown. The computer device includes a processor, a memory, an input / output interface (Input / Output, referred to as I / O) and a communication interface. The processor, the memory and the input / output interface are connected through a system bus, and the communication interface is connected to the system bus through the input / output interface. The processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program and a database. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The input / output interface of the computer device is used to exchange information between the processor and an external device. The communication interface of the computer device is used to communicate with an external terminal through a network connection. When the computer program is executed by the processor, a particle trajectory prediction method based on symmetric coding is implemented.

[0102] Those skilled in the art will understand that Figure 5 The structure shown in the figure is only a block diagram of a part of the structure related to the solution of the present application, and does not constitute a limitation on the computer device to which the solution of the present application is applied. The specific computer device may include more or fewer components than those shown in the figure, or combine certain components, or have a different arrangement of components.

[0103] In an exemplary embodiment, a computer device is further provided, including a memory and a processor, wherein a computer program is stored in the memory, and the processor implements the steps in the above-mentioned method embodiments when executing the computer program.

[0104] In an exemplary embodiment, a computer-readable storage medium is provided, storing a computer program, and when the computer program is executed by a processor, the steps in the above method embodiments are implemented.

[0105] In an exemplary embodiment, a computer program product is provided, including a computer program, and when the computer program is executed by a processor, the steps in the above method embodiments are implemented.

[0106] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, stored data, displayed data, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of relevant data must comply with relevant regulations.

[0107] Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to the memory, database or other medium used in the embodiments provided in the present application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetoresistive random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM may be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM).

[0108] The database involved in each embodiment provided in this application may include at least one of a relational database and a non-relational database. The non-relational database may include a distributed database based on blockchain, etc., but is not limited thereto. The processor involved in each embodiment provided in this application may be a general-purpose processor, a central processing unit, a graphics processor, a digital signal processor, a programmable logic device, a data processing logic device based on quantum computing, etc., but is not limited thereto.

[0109] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0110] This article uses specific examples to illustrate the principles and implementation methods of this application. The description of the above embodiments is only used to help understand the method and core ideas of this application. At the same time, for those skilled in the art, according to the ideas of this application, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting this application.

Claims

1. A particle trajectory prediction method based on symmetric coding, characterized in that: The particle trajectory prediction method based on symmetric coding includes: Acquire attribute information of rock and soil particles; the attribute information includes: type information of rock and soil particles, size information of rock and soil particles, velocity information of rock and soil particles, direction information of rock and soil particles, distance relationship between rock and soil particles, and mechanical relationship between rock and soil particles; Constructing an undirected graph of rock and soil particles according to the attribute information; the nodes in the undirected graph of rock and soil particles correspond to rock and soil particles, and the edges in the undirected graph of rock and soil particles correspond to the mechanical relationships between the rock and soil particle nodes; A graph neural network model is constructed according to the rock and soil particle undirected graph; the graph neural network model includes node features and edge features; the node features include: particle radius features, particle type features, and distance features between particles and set boundaries; the edge features include: distance features between particles; Acquire the direction information of the node feature based on the rock and soil particle undirected graph; the direction information includes the direction information of speed and the direction information of distance; Symmetrically encode the node feature based on the direction information to obtain a node code; Based on the undirected graph of rock and soil particles, the mechanical relationship between the node features is decomposed into a normal component and a tangential component, and the normal component and the tangential component are encoded respectively to obtain a normal embedding function and a tangential embedding function, and then the damping effect of each node is encoded in the form of a damping component to obtain a damping embedding function; The graph neural network model is used to associate the node coding with the edge coding to obtain a rock and soil particle graph neural network; the edge coding includes: a normal embedding function, a tangential embedding function and a damping embedding function; The rock and soil particle graph neural network is used to predict rock and soil particle trajectories.

2. The particle trajectory prediction method based on symmetric coding according to claim 1 is characterized in that: Constructing a graph neural network model according to the rock and soil particle undirected graph specifically includes: The information in the undirected graph of rock and soil particles is encoded into numerical features through an embedding function to obtain a graph neural network model.

3. The particle trajectory prediction method based on symmetric coding according to claim 1 is characterized in that: The node features in the graph neural network model are: n' i = {v i ,∈ k (k i ),r i ,B i }; Among them, v i represents the particle velocity, ∈ k (·) represents the embedding function, k i Indicates the particle type, r i represents the particle radius, B i Indicates the distance information between the particle corresponding to the i-th node and the set boundary.

4. The particle trajectory prediction method based on symmetric coding according to claim 1 is characterized in that: The edge feature in the graph neural network model is: e' ij ={dist ij ,∈ T (T ij )}; Among them, dist ij represents the distance between two particles, T ij is the edge type encoded by the particle types at both ends, ∈ T (·) is the edge type embedding function.

5. The particle trajectory prediction method based on symmetric coding according to claim 1, characterized in that: The formula for the symmetric encoding is: {ij} =|d(v {x,j} )·3 2 +d(v {x,i} )·3 1 +d(dist {x,ij} )·3 0 |; Among them, d(·) is the direction extraction function, v {x,i} 、v {x,j} are the horizontal speeds of nodes i and j, respectively, dist {x,ij} is the horizontal distance between two nodes.

6. The particle trajectory prediction method based on symmetric coding according to claim 1, characterized in that: The graph structure of the rock particle graph neural network is: G0 = (N, (E f ,E g ,E d )); Where N represents the node set, E f 、E g 、E d The edge sets representing normal force, tangential force, and damping force respectively.

7. The particle trajectory prediction method based on symmetric coding according to claim 1 is characterized in that: The method of using the rock particle graph neural network to predict rock particle trajectories specifically includes: Iteratively updating the rock and soil particle graph neural network through a message passing mechanism; Obtain the motion trajectories of rock and soil particles in the updated rock and soil particle graph neural network.

8. A computer device comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the particle trajectory prediction method based on symmetric coding according to any one of claims 1 to 7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the particle trajectory prediction method based on symmetric coding described in any one of claims 1 to 7 is implemented.

10. A computer program product, comprising a computer program, characterized in that When the computer program is executed by a processor, the particle trajectory prediction method based on symmetric coding described in any one of claims 1 to 7 is implemented.

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