Self-adaptive physical simulation method and system based on hierarchical graph evolution

Abstract

The invention provides a self-adaptive physical simulation method and system based on hierarchical graph evolution, and the method comprises the steps: introducing an anisotropic message passing mechanism, carrying out the directional aggregation of the features of an ith layer of nodes through a learnable weight parameter, and obtaining the ith layer of message passing features; carrying out differentiable multi-scale graph construction, and determining an (i + 1) th layer of nodes; carrying out downsampling on the ith layer of message passing characteristics to obtain the characteristics of the (i + 1) th layer of nodes; performing up-sampling on the jth layer of message passing features, and fusing the jth layer of message passing features with the (j-1) th layer of message passing features to obtain the (j-1) th layer of fusion features, j being from N to 2; and taking the final fusion feature of the first layer as the predicted physical quantity at the t + 1 moment. According to the method, a multi-scale graph structure is dynamically generated depending on a given structure and physical quantity information, and dynamic characteristics and long-distance dependency relationships in a physical system are adaptively captured in combination with an anisotropic message passing mechanism, so that efficient and accurate physical simulation is realized.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of computer simulation, in particular, to an adaptive physical simulation method and system based on hierarchical graph evolution. BACKGROUND

[0002] Physical simulation is an important research direction in the field of computer science and engineering, aiming to simulate physical phenomena in the real world through mathematical models and computational methods. Its application range is wide, including fluid dynamics, structural mechanics, heat conduction, aerodynamics, etc. Traditional physical simulation methods are usually based on numerical solution of partial differential equations (PDEs), such as Navier-Stokes equation, heat conduction equation and elastic mechanics equation. Although these methods have high precision, they have high computational complexity and are difficult to meet the needs of large-scale real-time simulation. With the rapid development of deep learning technology, physical simulation methods based on neural networks have gradually become a research hotspot. These methods can achieve efficient simulation with lower computational cost by learning the dynamic behavior of physical systems. Among them, graph neural networks (GNNs) have shown significant advantages in grid-based physical simulation due to their powerful modeling ability for data.

[0003] Graph neural networks can effectively capture the interaction relationships between nodes by modeling physical systems as graph structures. In grid-based physical simulation, nodes represent spatial discrete points, and edges represent the physical connection relationships between nodes. GNNs propagate physical quantities (such as velocity, pressure, temperature, etc.) between nodes through a message passing mechanism, thereby simulating the dynamic behavior of the system. However, traditional GNNs face two major challenges when dealing with large-scale physical systems: one is the long-distance dependence problem, the interaction between nodes in a physical system may span a long spatial distance, and traditional GNNs through local message passing are difficult to effectively capture these long-distance dependence relationships; the second is the problem of computational efficiency, as the grid size increases, the computational complexity of GNNs increases significantly, making it difficult to meet the needs of real-time simulation.

[0004] To solve the above problems, researchers have proposed physical simulation methods based on hierarchical graph structures. These methods capture the interaction relationships between nodes at different resolutions by constructing multi-scale graph structures, thereby improving the modeling ability and computational efficiency of long-range dependencies. Specifically, hierarchical graph structures convert fine-grained graphs to coarse-grained graphs through downsampling and upsampling operations, and propagate information between different levels. However, existing methods usually use predefined graph structures, which cannot dynamically adjust the hierarchical graph according to the physical input, resulting in limited simulation accuracy. In addition, existing methods usually use isotropic aggregation methods during feature propagation, which cannot effectively capture the directional features in physical systems. Therefore, existing methods cannot adaptively adjust the graph structure according to the dynamic changes of the physical system, making it difficult to cope with uncertainties in complex physical environments.

[0005] According to the search, the application number 202311072802.9 discloses a physical field data prediction method based on a neural network model, which first acquires physical field data of a mixture state at a first time, then splits a block slice with a specified position as a splitting point for each spatial dimension of the data space, determines sparse values according to the data boundaries of the slice in other spatial dimensions, adjusts the splitting point by comparing the sparse values with a preset threshold, and further divides the block data. Then calculate the comprehensive benefit value of each spatial dimension under the block data prediction, select the block data under the spatial dimension with the highest comprehensive benefit value, input the boundary supplemented block data into the prediction model to obtain the physical field data at the second time. However, it does not involve the processing of directional features and multi-scale hierarchical information interaction in the physical system, and there is a lack of accuracy in complex physical system simulation. SUMMARY

[0006] In view of the defects in the prior art, the purpose of the present application is to provide a self-adaptive physical simulation method and system based on hierarchical graph evolution.

[0007] According to one aspect of the present application, a self-adaptive physical simulation method based on hierarchical graph evolution is provided, which includes a forward cycle and a reverse cycle in sequence;

[0008] The forward cycle includes:

[0009] The physical quantity information of the physical system at time t is taken as the nodes and features of the first layer;

[0010] An anisotropic message passing mechanism is introduced, and the nodes and features of the i-th layer are directionally aggregated through learnable weight parameters to obtain the i-th layer message passing features; i is a natural number greater than or equal to 1;

[0011] A differentiable multi-scale graph is constructed for the i-th layer message passing features to determine the nodes of the i+1-th layer;

[0012] downsample the i-th layer message passing feature, pass inter-layer feature, and obtain a feature of a node of an i+1-th layer;

[0013] repeat the anisotropic message passing, the differentiable multi-scale construction, and the down-sampling process, and i increases from 1 to N-1, N is a natural number greater than or equal to 2, until a feature of a node of an N-th layer is obtained;

[0014] the inverse cycle comprises:

[0015] directionally aggregate the feature of the node of the N-th layer to obtain an N-th layer message passing feature as an N-th layer fusion feature;

[0016] up-sample the j-th layer fusion feature, pass inter-layer feature, and merge and directionally aggregate the j-th layer fusion feature with the (j-1)-th layer message passing feature in the forward cycle to obtain a (j-1)-th layer fusion feature;

[0017] repeat the up-sampling, the merging, and the aggregating process, and j decreases from N to 2, until a first layer fusion feature is obtained by backtracking;

[0018] use the first layer fusion feature as a predicted physical quantity at a t+1 time.

[0019] Optionally, the anisotropic message passing mechanism is introduced to directionally aggregate the node and the feature of the i-th layer by using a learnable weight parameter to obtain the i-th layer message passing feature, which comprises:

[0020] for a node of the i-th layer, calculate a feature weight between the node and a neighbor node;

[0021] normalize the feature weight between the node and all neighbor nodes to obtain a normalized weight;

[0022] use the normalized weight to weight-aggregate the features of the neighbor nodes of the node to update the feature of the node to obtain a message passing feature of the node;

[0023] the message passing features of all nodes of the i-th layer constitute the i-th layer message passing feature.

[0024] Optionally, the differentiable multi-scale graph construction on the i-th layer message passing feature is used to determine a node of an i+1-th layer, which comprises:

[0025] for a node of the i-th layer, calculate a probability value of the node being reserved in the i+1-th layer;

[0026] use a sampling method to change the probability value into a binary variable to determine whether the node is reserved in the i+1-th layer;

[0027] Based on the reservation results of all nodes of the i-th layer, a node set of the i+1-th layer is obtained.

[0028] Optionally, after obtaining the node set of the i+1-th layer, connectivity of the K-hop edge augmented graph is enhanced.

[0029] Optionally, the message passing feature of the i-th layer is down-sampled, and inter-layer features are passed to obtain the feature of the i+1-th layer node.

[0030] The message passing feature of the i-th layer node corresponding to the determined i+1-th layer node is aggregated into the i+1-th layer by using the normalized weight of the i-th layer, to obtain the feature of the i+1-th layer node.

[0031] Optionally, the j-th layer fusion feature is up-sampled, and inter-layer features are passed, and the j-1-th layer message passing feature is merged and directionally aggregated to obtain the j-1-th layer fusion feature.

[0032] The j-th layer fusion feature is re-distributed into the j-1-th layer by using the normalized weight of the j-1-th layer;

[0033] The re-distributed feature of the j-1-th layer is fused with the message passing feature of the j-1-th layer to obtain a fusion function of the j-1-th layer;

[0034] The fusion function of the j-1-th layer is further directionally aggregated to obtain the j-1-th layer fusion feature.

[0035] Optionally, the learnable weight parameter is optimized by minimizing the mean square error between the predicted physical quantity at t+1 time and the true value.

[0036] In a second aspect, the application provides an adaptive physical simulation system based on hierarchical graph evolution, which comprises a forward cycle module and a reverse cycle module running in sequence.

[0037] The forward cycle module comprises:

[0038] A forward cycle initial information submodule: taking the physical quantity information of the physical system at t time as the node and feature of the first layer;

[0039] An anisotropic message passing submodule: introducing an anisotropic message passing mechanism, and directionally aggregating the node and feature of the i-th layer by using a learnable weight parameter to obtain the i-th layer message passing feature; i is a natural number greater than or equal to 1;

[0040] A differentiable multi-scale construction submodule: performing differentiable multi-scale graph construction on the i-th layer message passing feature to determine the i+1-th layer node; and down-sampling the i-th layer message passing feature to pass inter-layer features to obtain the feature of the i+1-th layer node.

[0041] repeating the anisotropic message passing, the differentiable multiscale construction and the down-sampling process, i increases from 1 to N-1, N is a natural number greater than or equal to 2, until the feature of the Nth layer node is obtained;

[0042] The inverse cycle module comprises:

[0043] The inverse cycle initial information submodule aggregates the feature of the Nth layer node directionally to obtain the Nth layer message passing feature as the Nth layer fusion feature;

[0044] The hierarchical information interaction submodule up-samples the jth layer fusion feature, transmits the interlayer feature, and merges and directionally aggregates the j-1th layer message passing feature in the positive cycle to obtain the j-1th layer fusion feature;

[0045] The up-sampling, merging and aggregating process is repeated, j decreases from N to 2, until the first layer fusion feature is obtained by backtracking;

[0046] The prediction information submodule takes the first layer fusion feature as the predicted physical quantity at t+1.

[0047] In a third aspect, the application provides a simulation method of a cylinder flow physical system, comprising:

[0048] Obtaining initial physical quantity information of the cylinder flow physical system at t, including grid structure and fluid velocity, pressure, local Reynolds number of nodes;

[0049] Using the adaptive physical simulation method based on hierarchical graph evolution, the physical quantity information of the cylinder flow physical system at t+1 is predicted and obtained based on the initial physical quantity information, and is taken as the initial physical quantity information at the next time;

[0050] The above process is repeated until the simulation time is set, and a simulation video of the cylinder flow physical system is obtained.

[0051] In a fourth aspect, the application provides a terminal comprising a memory, a processor and a computer program stored in the memory and executable on the processor, wherein the processor can be used to execute the method or run the system when executing the program.

[0052] Compared with the prior art, the embodiments of the application have at least one of the following beneficial effects:

[0053] The adaptive physical simulation method based on hierarchical graph evolution in the embodiment of the application uses anisotropic message passing mechanism, differentiable node selection mechanism and inter-layer feature interaction, adaptively captures multi-level dynamic features in a physical system and long-distance dependence between nodes, and thus realizes efficient and accurate physical simulation. BRIEF DESCRIPTION OF DRAWINGS

[0054] Other features, objects, and advantages of the application will become more apparent from the following detailed description of non-limiting embodiments thereof, read in conjunction with the accompanying drawings:

[0055] Figure 1 A flowchart of the adaptive physical simulation method based on hierarchical graph evolution in an embodiment of the application;

[0056] Figure 2 A framework diagram of the adaptive physical simulation method based on hierarchical graph evolution in an embodiment of the application; (a) is a flowchart of the adaptive physical simulation method based on hierarchical graph evolution; (b) is a schematic diagram of an anisotropic message passing mechanism; and (c) is a schematic diagram of differentiable multi-scale graph construction;

[0057] Figure 3 A structural diagram of the adaptive physical simulation system based on hierarchical graph evolution in an embodiment of the application;

[0058] Figure 4 A comparison diagram of prediction results of a cylindrical flow system in an embodiment of the application after applying the method of the application and a traditional method. DETAILED DESCRIPTION

[0059] The application will be described in detail below with reference to specific embodiments. The following embodiments will help those skilled in the art to further understand the application, but do not limit the application in any form. It should be noted that, for those skilled in the art, without departing from the concept of the application, a number of modifications and improvements can be made. These all belong to the protection scope of the application.

[0060] In an embodiment of the application, an adaptive physical simulation method based on hierarchical graph evolution is provided, as shown in (a) of FIG. 1, which includes forward and reverse cycles performed in sequence. Figure 1 and Figure 2 The forward cycle includes:

[0061] The forward cycle includes:

[0062] Step 1, taking physical quantity information of a physical system at time t as nodes and features of the first layer;

[0063] Specifically, the physical system is an object or combination of objects in reality that follows physical laws in motion and changes. The physical quantity information is "data" describing the state or changes of the physical system, which can reflect the physical properties, motion state, interaction, etc. of the object.

[0064] Step 2, introducing an anisotropic message passing mechanism, directionally aggregating the nodes and features of the i-th layer through learnable weight parameters to obtain the i-th layer message passing feature;

[0065] Step 3, differentiable multi-scale graph construction is performed on the i-th layer message passing feature to determine the i+1-th layer node;

[0066] Step 4, down-sampling the i-th layer message passing feature to pass the inter-layer feature and obtain the feature of the i+1-th layer node;

[0067] The anisotropic message passing of step 2, the differentiable multi-scale construction of step 3, and the down-sampling process of step 4 are repeated, i increases from 1 to N-1, N is a natural number greater than or equal to 2, until the feature of the N-th layer node is obtained;

[0068] The reverse cycle includes:

[0069] Step 5, directionally aggregating the features of the N-th layer node to obtain the N-th layer message passing feature as the N-th layer fusion feature;

[0070] Step 6, up-sampling the j-th layer fusion feature to pass the inter-layer feature, merging and directionally aggregating with the j-1-th layer message passing feature to obtain the j-1-th layer fusion feature;

[0071] The up-sampling, merging and aggregation process of step 6 is repeated, j decreases from N to 2, until the first layer fusion feature is obtained by backtracking;

[0072] Step 7, taking the first layer fusion feature as the predicted physical quantity at time t+1.

[0073] Specifically, the adaptation refers to the dynamic adjustment of the graph evolution process according to the physical quantity information and its features of the physical system at different times t in steps 1-7 above. This method automatically generates the corresponding hierarchical graph evolution structure according to the physical state information at time t. This feature of automatically adjusting with the change of the physical system state is called adaptation.

[0074] In the above embodiments, the multi-scale graph structure adaptive to physical input can be dynamically generated through the positive cycle step. By using an anisotropic message passing mechanism, directional feature propagation is achieved. Here, directional feature propagation refers to the process of directional aggregation and transmission of directional physical laws (such as vortex rotation and pressure distribution direction difference) in the simulation of a physical system (such as cylinder flow), in which different weights are assigned according to the directional relationship between nodes (such as fluid motion direction and relative position direction) when features are transmitted. The down-sampling graph structure generated by the differentiable node selection mechanism connects remote nodes, thereby improving long-distance dependency. The number of nodes and edges of the graph structure generated by the positive cycle down-sampling is much smaller than that of the original input graph structure, and the time cost of message passing and feature aggregation at each layer is much smaller than that on the original graph structure, which can greatly improve the computational efficiency.

[0075] Traditional message passing neural networks usually use non-parametric aggregation functions (such as summation) to update node features, which can easily lead to feature over-smoothing and cannot capture directional features in physical systems. For example, in the case of cylinder flow, the direction of fluid velocity on different nodes cannot effectively model the change in fluid flow direction in the neighborhood. To solve this problem, a preferred embodiment implements step 2 and introduces an anisotropic message passing (AMP) mechanism to achieve directional aggregation of features between nodes through learnable weight parameters. The following steps S2.1-S2.4 can be used.

[0076] S2.1: For each node v i , calculate the feature weight w ij between it and the neighbor node v j ;

[0077] w ij =φ w (e ij ,v i ,v j )

[0078] φ w is a learnable weight calculation function, e ij is an edge feature, v i and v j are the features of nodes v i and v j , respectively;

[0079] S2.2: Normalize the feature weight obtained in S2.1 by using the Softmax function:

[0080]

[0081] is a neighbor set of node v i .

[0082] S2.3, calculating the updated variable feature

[0083] where φ e is an edge update function

[0084] S2.4, the normalized weight α ij is used to aggregate the features of the neighbor nodes, and update the features of the current node:

[0085]

[0086] where φ v is a node update function realized by a two-layer multi-layer perception, is the updated edge feature, represents the neighbor node set of the current node.

[0087] It should be noted that the S2.1 step involves calculating the feature weight between nodes, the S2.2 step normalizes the feature weight, and the S2.3 step updates the features of the current node using the normalized weight. These steps together constitute the implementation process of AMP.

[0088] In a specific embodiment, as shown in the b figure of Figure 2 , the arrows point from the neighbor nodes to the center node v i , indicating the influence of the neighbor nodes on the center node. Different numbers (4 / 14, 3 / 14) represent the importance of each neighbor node to the feature of v i .

[0089] The anisotropic message passing (AMP) of the above embodiment realizes the directional aggregation of the features between nodes by introducing a learnable weight parameter, thereby capturing the dynamic characteristics in the physical system.

[0090] In a preferred embodiment, step 3 is implemented by an anisotropic message passing mechanism to calculate the probability of each node being retained in the next level graph, and using the Gumbel-Softmax sampling method to generate the node set of the next level graph. The following steps can be used:

[0091] S3.1, for each node v i , calculate the probability p i of being retained in the next level graph:

[0092]

[0093] The superscript 'l' represents the depth label of the current layer. For example, if the current layer is the second downsampled layer, then l = 2.

[0094] This represents a two-layer Multilayer Perceptron (MLP) neural network, with the input in parentheses. This two-layer MLP neural network simultaneously predicts two parts: the updated features of the nodes. The probability that a node is retained Represents the set of neighboring nodes of the current node. α ij Represents node v i With neighbor node v j The normalized feature weights between them.

[0095] like Figure 2 As shown in Figure (c), v* represents the updated features of the nodes, and the normalized feature weights between adjacent nodes 3 / 14 and 4 / 14 in the figure.

[0096] S3.2, Use the Gumbel-Softmax downsampling method to generate binary variables. (Keep or discard), indicating node v i Whether to retain:

[0097]

[0098] After sampling using Gumbel-Softmax, the number of nodes retained at the current scale is greatly reduced. This reduces the amount of data that needs to be processed for message passing at each level of the physical system, thus significantly improving the model's running speed and performance.

[0099] S3.3, based on S3.2, obtains the retained results of all nodes in the i-th layer, thus obtaining the node set of the (i+1)-th layer.

[0100] The embodiments described above in this application utilize anisotropic message passing and MLP to accurately calculate the node retention probability, and then use Gumbel-Softmax to generate binary retention results, providing a reliable basis for node selection and adapting to the needs of the physical scene. Through Gumbel-Softmax sampling, the number of retained nodes at the current scale is significantly reduced, decreasing the data processing volume of message passing at each level, significantly accelerating model operation and improving performance. A multi-scale graph structure is constructed based on the node retention results, and the selection mechanism is differentiable, enabling dynamic adaptation to physical input, helping the model better capture long-distance dependencies, and enhancing the modeling capability of the physical system.

[0101] During the evolution of the hierarchy, the direct dependency of the preserved nodes and edges on the original graph can lead to discrete parts in the next level of the graph (i.e., the graph is split into multiple unconnected subgraphs). This discretization can destroy the overall structure of the graph, affecting the information transmission and the accuracy of the physical simulation. Therefore, in some preferred embodiments, the process of steps S3.1-S3.3 above is used to dynamically generate the node set of the next level of the graph Enhancing the connectivity of the graph by K-hop edges:

[0102]

[0103] wherein, denotes the enhanced edge set of the l+1 level, is the enhanced edge set of the l level, containing K-hop edges.

[0104] This embodiment uses K-hop edge technology to enhance the connectivity of the graph, which can connect nodes that are not originally connected, reduce the possibility of discrete parts in the next level of the graph, and ensure the integrity of the graph. After the connectivity is improved, the information transmission between nodes can be carried out through more paths, thereby enhancing the model's ability to capture global information.

[0105] In a physical system, features of different scales between levels need to interact. In a preferred embodiment, step 4 is implemented to aggregate the message passing features of the i-th level nodes corresponding to the determined i+1-th level nodes into the i+1-th level using the normalized weights of the i-th level, to obtain the features of the i+1-th level nodes. That is, in the down-sampling process, the features of the fine-grained graph (i-th level graph) are aggregated into the coarse-grained graph (i+1-th level graph) using the weights of anisotropic message passing:

[0106]

[0107] wherein the superscript l denotes the depth label of the current graph level, denotes the normalized weight of anisotropic message passing of the current graph level, the updated feature of the node, is the neighbor set of the node v i .

[0108] In another preferred embodiment, step 6 is implemented to first redistribute the j-th level fusion features into the j-1-th level using the normalized weights of the j-1-th level, and then fuse and directionally aggregate the redistributed j-1-th level features with the message passing features of the j-1-th level to obtain the j-1-th level fusion features. That is, in the up-sampling process, the features of the coarse-grained graph are redistributed into the fine-grained graph, and are fused with the message passing results of the fine-grained graph through a feature mixing mechanism:

[0109]

[0110] In the foregoing embodiments, the anisotropic message passing mechanism and the hierarchical information interaction are utilized to realize efficient propagation of features between layers and ensure accurate transmission of information between different scale graph structures.

[0111] It should be noted that there is a difference between the fusion features of other layers. In the Nth layer, the Nth layer feature obtained through the forward cycle is directionally aggregated to form the Nth layer message passing feature. This feature is defined as the fusion feature of the Nth layer and serves as the starting feature of the aforementioned backward cycle tracing process.

[0112] In a preferred embodiment, a one-step supervised training method is adopted to optimize the model parameters by minimizing the L2 error between the predicted value and the true value. Specifically, the training target is:

[0113]

[0114] where y pred is the model predicted value, and y true is the true value.

[0115] As in the foregoing description, "forward" refers to the calculation process of the neural network from input to output, and "gradient" refers to the process of error backpropagation from the output layer to the input layer to update the model parameters. Figure 2

[0116] Based on the same inventive concept, other embodiments of the present application provide an adaptive physical simulation system 100 based on hierarchical graph evolution, as shown in Figure 3 which includes a forward cycle module and a backward cycle module running in sequence.

[0117] The forward cycle module includes:

[0118] A forward cycle initial information submodule 110: taking the physical quantity information of the physical system at time t as the nodes and features of the first layer;

[0119] An anisotropic message passing submodule 120: introducing an anisotropic message passing mechanism, directionally aggregating the nodes and features of the ith layer through learnable weight parameters to obtain the ith layer message passing feature; i is a natural number greater than or equal to 1;

[0120] A differentiable multi-scale construction submodule 130: performing differentiable multi-scale graph construction on the ith layer message passing feature to determine the nodes of the (i+1)th layer; downsampling the ith layer message passing feature to transmit the inter-layer feature and obtain the features of the nodes of the (i+1)th layer;

[0121] ​The anisotropic message passing, the differentiable multi-scale construction and the down-sampling process are repeated, i is increased from 1 to N-1, N is a natural number greater than or equal to 2, until the feature of the Nth layer node is obtained;

[0122] The inverse cycle module comprises:

[0123] The inverse cycle initial information submodule 140: the features of the Nth layer nodes are directionally aggregated to obtain the Nth layer message passing feature as the Nth layer fusion feature;

[0124] The hierarchical information interaction submodule 150: the jth layer fusion feature is up-sampled, the interlayer feature is transmitted, and the j-1th layer message passing feature in the positive cycle is merged and directionally aggregated to obtain the j-1th layer fusion feature;

[0125] The up-sampling, merging and aggregation process is repeated, j is decreased from N to 2, until the first layer fusion feature is obtained by backtracking;

[0126] The prediction information submodule 160: the first layer fusion feature is used as the predicted physical quantity at t+1.

[0127] The modules / units in the above examples can refer to the implementation techniques of the corresponding steps of the adaptive physical simulation method based on hierarchical graph evolution in the above embodiments, and will not be described here.

[0128] The application will be further described below in combination with specific application examples / contrastive examples, so that the above technical solutions of the application can be better understood. It should be understood that the following are only some examples and do not limit the application.

[0129] In a specific embodiment, the method or system in the above embodiment is applied to a cylinder flow physical system. A simulation method of a cylinder flow physical system comprises:

[0130] Obtaining initial physical quantity information of the cylinder flow physical system at t, including grid structure and fluid velocity, pressure, local Reynolds number of nodes;

[0131] Using the adaptive physical simulation method based on hierarchical graph evolution, the physical quantity information of the cylinder flow physical system at t+1 is predicted and obtained based on the initial physical quantity information, and is used as the initial physical quantity information at the next time;

[0132] The above process is repeated until the simulation time is set, and a simulation video of the cylinder flow physical system is obtained.

[0133] Specifically, as Figure 2As shown, for the physical system of cylinder flow, using its grid structure (containing 2D hybrid grid, unstructured triangular elements around the cylinder, structured rectangular grid in the far field, about 10 4 -10 5 ) and node physical quantities (fluid velocity, pressure, local Reynolds number, etc.), an adaptive physical simulation method is used to dynamically construct a multi-scale graph structure, and through the encoding-transmission-decoding mode, the accurate prediction of the physical quantity at the next moment is realized.

[0134] Specifically, in the encoding stage, the cylinder flow system and the node physical quantity are input into the encoder to generate high-dimensional space features, and the abstract representation of physical information is completed.

[0135] In the transmission and aggregation stage, the adaptive physical simulation method based on hierarchical graph evolution in the above embodiment is used to realize the directional aggregation of features between nodes relying on the anisotropic message passing mechanism, adapt to the flow direction characteristics of the cylinder flow; combined with the differentiable adaptive multi-scale graph construction mechanism, the multi-scale graph structure matching the physical input is dynamically generated (key nodes are selected by downsampling, and details are supplemented by upsampling), and the multi-scale information is aggregated and the learnable hierarchical interaction is carried out to strengthen the modeling of long-distance dependence.

[0136] In the decoding stage, the aggregated multi-scale features are decoded, and the prediction result of the physical quantity of the cylinder flow system at the next moment is output.

[0137] Figure 4 Comparing the prediction performance of the method of the embodiment of the present application with the prior art, the results show that the method of the embodiment of the present application has more advantages in prediction error control, can more accurately capture the fluid dynamic changes of the cylinder flow, and verifies the effectiveness of the multi-scale graph structure and the anisotropic message passing mechanism.

[0138] The above embodiment is directed to the cylinder flow scene, uses the multi-scale graph structure as the carrier, and realizes more optimal physical quantity prediction through the encoding-transmission (anisotropic + adaptive multi-scale)-decoding process, providing an efficient and accurate new scheme for fluid dynamics simulation. The embodiment is mainly applied to the field of fluid dynamics, but its application range can also be extended to the prediction of physical systems such as structural mechanics, heat conduction, and aerodynamics. Through comparison with the prior art in multiple different application industries, such as cylinder flow simulation, structural mechanics simulation, aerodynamics simulation, and cloth simulation, the embodiment of the present application shows significant performance improvement, with an average improvement of 22.7%.

[0139] Based on the same inventive concept, in other embodiments of the present application, a terminal is provided, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the program, is configured to perform the method described above, or run the system described above.

[0140] Optionally, the memory is configured to store the program; the memory can comprise volatile memory (e.g., random-access memory (RAM), such as static random-access memory (SRAM), Double Data Rate Synchronous Dynamic Random Access Memory (DDR SDRAM), etc.), or non-volatile memory (e.g., flash memory). The memory is configured to store computer programs (e.g., application programs, functional modules, etc. for implementing the method described above), computer instructions, etc. The computer programs, computer instructions, etc. described above can be stored in one or more memories in a partitioned manner.

[0141] The processor is configured to execute the computer program stored in the memory, so as to implement each step in the method described above. For details, refer to the related description in the method embodiments above.

[0142] The processor and the memory can be independent structures, or can be integrated into an integrated structure. When the processor and the memory are independent structures, the memory and the processor can be coupled and connected through a bus.

[0143] Obviously, those skilled in the art can make various modifications and variations to the present application without departing from the spirit and scope of the present application. Thus, if these modifications and variations of the present application fall within the scope of the claims of the present application and their equivalent technologies, the present application is also intended to include these modifications and variations.

Claims

1. A self-adapting physical simulation method based on hierarchical graph evolution, characterized in that, The forward cycle and the reverse cycle are sequentially performed; The forward cycle comprises: Physical quantity information of a physical system at time t is taken as a node and a feature of a first layer; An anisotropic message passing mechanism is introduced, and a feature of an i-th layer is directionally aggregated by using a learnable weight parameter, to obtain a message passing feature of the i-th layer; i is a natural number greater than or equal to 1; A differentiable multi-scale graph is constructed for the message passing feature of the i-th layer, to determine a node of an (i+1)-th layer; The message passing feature of the i-th layer is down-sampled, and an inter-layer feature is transmitted, to obtain a feature of the node of the (i+1)-th layer; The anisotropic message passing, the differentiable multi-scale construction, and the down-sampling process are repeated, i is sequentially increased from 1 to N-1, N is a natural number greater than or equal to 2, until a feature of a node of an N-th layer is obtained; The reverse cycle comprises: The feature of the node of the N-th layer is directionally aggregated, to obtain a message passing feature of the N-th layer as a fusion feature of the N-th layer; A fusion feature of a j-th layer is up-sampled, an inter-layer feature is transmitted, and the fusion feature of the j-th layer is merged and directionally aggregated with a message passing feature of a (j-1)-th layer in the forward cycle, to obtain a fusion feature of the (j-1)-th layer; The up-sampling, the merging, and the aggregating process are repeated, j is sequentially decreased from N to 2, until a fusion feature of a first layer is backtracked to obtain; The fusion feature of the first layer is taken as a predicted physical quantity at time t+1.

2. The self-adaptive physical simulation method based on hierarchical graph evolution according to claim 1, characterized in that, The anisotropic message passing mechanism comprises: For a node of the i-th layer, a feature weight between the node and a neighbor node is calculated; The feature weight of the node and all neighbor nodes is normalized to obtain a normalized weight; The feature of the neighbor node of the node is weighted and aggregated by using the normalized weight, the feature of the node is updated, and a message passing feature of the node is obtained; The message passing features of all nodes of the i-th layer constitute a message passing feature of the i-th layer.

3. The self-adaptive physical simulation method based on hierarchical graph evolution of claim 1, wherein, The differentiable multi-scale graph construction for the message passing feature of the i-th layer comprises: For a node of the i-th layer, a probability value of the node being reserved in an (i+1)-th layer is calculated; The probability value is changed into a binary variable by using a sampling method, to determine whether the node is reserved in the (i+1)-th layer; Based on the reservation results of all nodes of the i-th layer, a node set of the (i+1)-th layer is obtained.

4. The self-adaptive physical simulation method based on hierarchical graph evolution according to claim 3, characterized in that, After the node set of the (i+1)-th layer is obtained, the connectivity of a K-hop edge-enhanced graph is enhanced.

5. The self-adaptive physical simulation method based on hierarchical graph evolution of claim 2, wherein, The down-sampling of the message passing feature of the i-th layer, the transmission of the inter-layer feature, and the obtaining of the feature of the node of the (i+1)-th layer comprise: The message passing feature of the node of the i-th layer corresponding to the determined node of the (i+1)-th layer is aggregated into the (i+1)-th layer by using the normalized weight of the i-th layer, to obtain the feature of the node of the (i+1)-th layer.

6. The self-adaptive physical simulation method based on hierarchical graph evolution of claim 2, wherein, The up-sampling of the fusion feature of the j-th layer, the transmission of the inter-layer feature, and the merging and directional aggregation of the fusion feature of the j-th layer with the message passing feature of the (j-1)-th layer comprise: The fusion feature of the j-th layer is re-distributed into the (j-1)-th layer by using the normalized weight of the (j-1)-th layer; The feature of the j-1th layer after the re-allocation is fused with the message passing feature of the j-1th layer to obtain a fusion function of the j-1th layer; The fusion function of the j-1th layer is further directionally aggregated to obtain a fusion feature of the j-1th layer.

7. The self-adaptive physical simulation method based on hierarchical graph evolution of claim 1, wherein, The learnable weight parameter is optimized by minimizing the mean square error between the predicted physical quantity at the t+1 time and the true value.

8. An adaptive physical simulation system based on hierarchical graph evolution, characterized in that, The method comprises a forward circulation module and a reverse circulation module which are sequentially operated. The forward circulation module comprises: A forward circulation initial information submodule: taking the physical quantity information of the physical system at the t time as the nodes and features of the 1st layer; An anisotropic message passing submodule: introducing an anisotropic message passing mechanism, and directionally aggregating the nodes and features of the i-th layer through a learnable weight parameter to obtain message passing features of the i-th layer; i is a natural number greater than or equal to 1; A differentiable multi-scale construction submodule: performing differentiable multi-scale graph construction on the message passing features of the i-th layer to determine nodes of the i+1th layer; and down-sampling the message passing features of the i-th layer to pass the inter-layer features and obtain features of the nodes of the i+1th layer; The anisotropic message passing, differentiable multi-scale construction, and down-sampling processes are repeated, i is increased from 1 to N-1, N is a natural number greater than or equal to 2, until the features of the nodes of the Nth layer are obtained; The reverse circulation module comprises: A reverse circulation initial information submodule: directionally aggregating the features of the nodes of the Nth layer to obtain message passing features of the Nth layer as fusion features of the Nth layer; A hierarchical information interaction submodule: up-sampling the fusion features of the jth layer, passing the inter-layer features, merging and directionally aggregating the message passing features of the j-1th layer in the forward circulation to obtain fusion features of the j-1th layer; The up-sampling, merging, and aggregating processes are repeated, j is decreased from N to 2, until the fusion features of the 1st layer are obtained by backtracking; A prediction information submodule: taking the fusion features of the 1st layer as the predicted physical quantity at the t+1 time.

9. A method of simulating a physical system of a cylinder in a flow, characterized by, The method comprises: Obtaining initial physical quantity information of a cylindrical flow physical system at the t time, including the grid structure and the fluid velocity, pressure, and local Reynolds of the nodes; Using the adaptive physical simulation method based on hierarchical graph evolution in any one of claims 1-7, based on the initial physical quantity information, predicting and obtaining the physical quantity information of the cylindrical flow physical system at the t+1 time, and taking it as the initial physical quantity information of the next time; Repeating the above process until the simulation time is set to obtain a simulation video of the cylindrical flow physical system.

10. A terminal comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, The processor executes the program to execute the method in any one of claims 1-7, or runs the system in claim 8.

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