Seismic simulation method and system fusing implicit iterative graph network and spectral element method

Abstract

The invention discloses a seismic simulation method and system fusing an implicit iterative graph network and a spectral element method. The method comprises the following steps: acquiring acceleration data of a small time step node; performing grid sparse division and interpolation mapping processing, and projecting to a low-dimensional manifold to obtain large-time-step node acceleration data and a low-order unit calculation force matrix of the current frame; obtaining a physical relation sparse matrix I, a physical relation sparse matrix II and sparse matrix topological relation information of the physical relation sparse matrix I and the physical relation sparse matrix II through a processing method of Jacobian iteration and projection to a low-dimensional manifold; obtaining a seismic simulated diagram neural network model; and predicting by using the seismic simulation diagram neural network model, and predicting the acceleration by using the large time step of the sparse unit nodes projected back to the target area by using the projection matrix. According to the method provided by the invention, the mapping between the high-order unit small time step and the low-order unit large time step is established through the fitting capability of the neural network, so that the calculation time is greatly shortened, and the earthquake simulation is quickly carried out.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of earthquake engineering, and in particular to a seismic simulation method and system fusing an implicit iterative graph network and a spectral element method. BACKGROUND

[0002] As a key scientific research means, seismic simulation has important significance for the prevention, prediction and coping strategy of earthquake disasters. However, the existing seismic simulation process faces many severe challenges, which seriously restrict its development and application: on the one hand, the calculation amount of seismic simulation is extremely large, each calculation needs to consume a large amount of computing resources, and the calculation process is time-consuming, and once a new working condition (new seismic source / new earthquake level) appears, it must be calculated again, and the previous calculation data is often difficult to be effectively utilized, resulting in great waste of resources and low efficiency; on the other hand, the spectral element method generally uses explicit method for calculation, in order to meet the stability requirement, the calculation time step (usually 0.001 seconds to 0.0001 seconds) of seismic simulation must be very small, which further prolongs the calculation time; at the same time, in order to achieve the required accuracy, the spectral element method usually needs to be based on at least 6-order integral calculation, which makes the calculation scale grow exponentially, and puts forward very high requirements on the hardware performance of the computer, greatly limiting the feasibility of large-scale seismic simulation. The traditional calculation method based on high-order unit (greater than or equal to 6-order) and small time step (0.001 seconds to 0.0001 seconds) spectral element method is difficult to meet the requirement of rapid seismic simulation.

[0003] In view of this, it is necessary to provide a seismic simulation method and system fusing an implicit iterative graph network and a spectral element method to solve or at least partially solve the above technical problems, and then to realize rapid seismic simulation in new working conditions after studying the internal physical relationship of historical seismic simulation data of certain working conditions based on spectral element method calculation. SUMMARY

[0004] The main purpose of the present application is to provide a seismic simulation method and system fusing an implicit iterative graph network and a spectral element method, which aims to solve the technical problems that the spectral element method based on high-order unit and small time step is used for real-time calculation in the prior art, the high-order unit grid quantity is dense, resulting in large calculation scale and many small time step calculations, and the repeated calculation operation is needed for similar regions or the same region in different working conditions, which is time-consuming and requires high computer requirements, and limits the feasibility of large-scale seismic simulation.

[0005] To achieve the above purpose, the present application provides a seismic simulation method fusing an implicit iterative graph network and a spectral element method, comprising the following steps: S10 uses the spectral element method to perform seismic simulation calculations in the target area and obtains the nodal acceleration data of high-order elements and small time steps at small time steps. S20 performs sparse mesh generation and interpolation mapping, and projects the mesh onto a low-dimensional manifold, generating sparse physical constraint information for the region during sparse mesh generation. The small-time-step node acceleration data is mapped to low-order units by point location and then processed by frame extraction according to a preset time step. Based on the projection matrix, it is projected onto a low-dimensional manifold to obtain the large-time-step node acceleration data and the low-order unit computational force matrix of the current frame. ; S30, based on regional sparse physical constraint information Low-order element calculation force matrix The solution is obtained by combining undamped and implicit methods, utilizing the sparse physical constraint information of the region. and low-order unit calculation force matrix The physical relation sparse matrix I and the physical relation sparse matrix II are obtained by using Jacobi iteration and projection onto a low-dimensional manifold. And the physical relation sparse matrix B and the physical relation sparse matrix B. Sparse matrix topological relationship information; S40 employs a graph neural network architecture that combines implicit physical laws, utilizing the normalized physical relation sparse matrix B and the physical relation sparse matrix C. The model is trained using large-time-step node acceleration data to achieve convergence, resulting in a neural network model for the earthquake simulation graph. During training, the normalized sparse time-step node acceleration data from the large-time-step node acceleration data is used as the node feature, along with the normalized sparse physical relation matrix B and the sparse physical relation matrix B. The implicit method iterative matrix elements are formed as edge features, and the sparse matrix topological relationship information is used as topological information. The iterative process of the implicit method is simulated through residual connection. S50, based on the current force matrix information and using the earthquake simulation graph neural network model, perform working condition generalization prediction on the target area, and use the projection matrix to perform inverse projection mapping to obtain the large time step predicted acceleration of the sparse unit nodes of the target area.

[0006] Furthermore, using the formula Processing is performed by Jacobi iteration and projection onto a low-dimensional manifold based on the projection matrix. We obtain the first sparse matrix B of physical relations and the second sparse matrix B of physical relations. And the physical relation sparse matrix B and the physical relation sparse matrix B. The sparse matrix topological relationship information, where, Represents sparse physical constraint information of the region. This represents the low-order unit computational force matrix of the current frame. Indicates the previous moment in a large time step. Indicates the current moment within a large time step. This indicates the time step size corresponding to the larger time step. For acceleration data of large time step nodes, the acceleration metric of the previous frame is used. It is the acceleration metric for the current frame in the large time step node acceleration data.

[0007] Furthermore, snapshots are constructed based on data at large time steps, and singular value decomposition is performed to construct a projection matrix; Sparse physical constraint information for the region and the low-order unit computational force matrix The feature is obtained by using Jacobi iteration and projecting the projection matrix onto the low-dimensional manifold. Construct a sparse matrix based on physical relations, B1 and B2. The graph network structure topology.

[0008] Furthermore, the computational principle of Jacobi iteration in the implicit method is as follows: D represents the main diagonal elements of the assembly implicit method, L and U are the upper and lower diagonal matrix elements of the assembly implicit method, respectively, and the projection matrix is ​​obtained using singular value decomposition. `data` represents the large-time-step node acceleration data, and `W`, `S`, and `V` represent the left singular vector, eigenvalue, and right singular vector, respectively. The first m vectors form the projection matrix, and the projection process is as follows: .

[0009] Furthermore, the regional sparse physical matrix information includes the regional sparse stiffness matrix. , region sparse quality matrix and regional sparse damping matrix ; Using formula , Calculate and obtain regional sparse physical constraint information. and low-order unit calculation force matrix , Represented as the sparse element node force matrix of the current frame. and These represent the displacement and velocity of the previous frame at a large time step, respectively. ∈[0.2,0.35].

[0010] Furthermore, in step S10, the regional dense physical matrix information of the target region under the higher-order unit is obtained. And the force matrix of dense unit nodes, based on the regional dense physical matrix information Small-time-step node acceleration data are obtained by calculating the force matrix of dense unit nodes.

[0011] Furthermore, the time step size for the small time step is 0.001 seconds, and the time step size for the large time step is 0.1 seconds.

[0012] Furthermore, step S50 also includes, Using formula and formula Perform calculations to obtain the predicted displacements of sparse nodes in the target region within the current frame. and prediction speed , To predict acceleration for large time steps, , , These represent the predicted velocity, predicted acceleration, and predicted displacement of the sparse nodes in the target region in the previous frame. , .

[0013] Furthermore, in step S40, The topological relationship information of sparse matrices is divided into source nodes and target nodes. The graph neural network architecture simulates the architectural relationship of Jacobi iteration by multiple message passing and residual connection networks.

[0014] The present invention also provides an earthquake simulation system that integrates implicit iterative graph networks and spectral element method, including a processing unit for implementing the earthquake simulation method integrating implicit iterative graph networks and spectral element method as described above.

[0015] Beneficial effects: The earthquake simulation method of this application, which integrates implicit iterative graph networks and the spectral element method, first uses the spectral element method to perform earthquake simulation calculations on the target area, obtaining small-time-step node acceleration data at high-order elements and small time steps. The small-time-step node acceleration data includes the acceleration information of dense physical element nodes at small time steps. Then, it performs processing from high-order elements to low-order elements, from small time steps to large time steps, and projects onto a low-dimensional manifold to obtain large-time-step node acceleration data. Simultaneously, it generates regional sparse physical constraint information during sparse mesh generation. The large-time-step node acceleration data includes acceleration information of sparse physical unit nodes at large time-step points; then, a database is built based on the regional sparse physical matrix information. and the low-order unit computational force matrix Based on the data projected onto the low-dimensional manifold, the physical relation sparse matrix B and the physical relation sparse matrix B are obtained by using an undamped method combined with an implicit method, followed by Jacobi iteration and projection onto the low-dimensional manifold. And the physical relation sparse matrix B and the physical relation sparse matrix B The database also includes sparse matrix topological relationship information, and includes large-time-step node acceleration data projected onto a low-dimensional manifold; then, it examines the physical relation sparse matrix B and the physical relation sparse matrix B. The large-time-step node acceleration data is normalized, and the normalized data is used to train a graph neural network architecture that combines implicit methods and Jacobi iteration physical laws to obtain an earthquake simulation graph neural network model. This model fully utilizes the physical relation sparse matrix B and the physical relation sparse matrix B. And the data value of large time step node acceleration data, through message transmission. Message aggregation adopts The model uses Jacobi calculation logic for message passing and aggregation; message passing, aggregation, and updating employ an MLP (Multilayer Perceptron) to handle high-dimensional data flow. The model architecture originates from the implicit Jacobi iteration process, embedding strong physical information to enhance data stability and interpretability. The preprocessing features of the model are more physically embedded, and Jacobi iteration is simulated through multiple message passing and residual connections, resulting in high model stability. Finally, leveraging the powerful generalization ability of the seismic simulation graph neural network model, based on the current force matrix information, the seismic simulation graph neural network model and inverse projection mapping are used to perform seismic simulation on the target area. Inverse projection mapping using the projection matrix obtains the large-time-step predicted acceleration of sparse unit nodes in the target area, enabling rapid generalization calculations for new working conditions. This invention integrates implicit iterative graph networks and spectrograms... The meta-method for earthquake simulation, with its neural network model architecture derived from the Jacobian iteration process of the implicit method, embeds strong physical information within the model, resulting in high stability and enhanced long-term computational stability. It establishes a mapping between large time steps and low-order units to high-order units and small time steps, significantly reducing computational scale. Through the fitting capabilities of neural networks, it establishes a mapping between high-order units at small time steps and low-order units at large time steps projected onto a low-dimensional manifold, further reducing computational scale by combining this with the low-dimensional manifold. The neural network's generalization performance enables rapid calculation of new operating conditions, greatly shortening computation time and providing a computational foundation for earthquake simulation in ultra-large-scale regions. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, for those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 This is a flowchart of the earthquake simulation method that integrates implicit iterative graph networks and spectral element method provided in an embodiment of the present invention. Figure 2 A schematic diagram of the sparse matrix topological relationship information of the earthquake simulation method that integrates implicit iterative graph networks and spectral element method provided in an embodiment of the present invention; Figure 3 A schematic diagram of the network computation framework for the earthquake simulation method that integrates implicit iterative graph networks and spectral element method provided in an embodiment of the present invention; Figure 4 This is a schematic diagram illustrating the computational loss of the earthquake simulation graph neural network model in the earthquake simulation method that integrates implicit iterative graph networks and the spectral element method provided in this embodiment of the invention. Figure 5 This is a schematic diagram of the acceleration calculation accuracy results of the earthquake simulation method that integrates implicit iterative graph network and spectral element method provided in the embodiment of the present invention, where a is the true value, b is the predicted value, and c is the error value; Figure 6 This diagram illustrates the displacement calculation accuracy of the earthquake simulation method integrating implicit iterative graph networks and spectral element method provided in this embodiment of the invention, where a is the true value, b is the predicted value, and c is the error value.

[0018] The implementation, functional features, and advantages of this invention will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0019] It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the scope of the invention.

[0020] Reference Figure 1 This embodiment proposes a seismic simulation method that integrates implicit iterative graph networks and the spectral element method, including the following steps: S10 uses the spectral element method to perform seismic simulation calculations in the target area and obtains the nodal acceleration data of high-order elements and small time steps at small time steps. S20 performs sparse mesh generation and interpolation mapping, and projects the mesh onto a low-dimensional manifold, generating sparse physical constraint information for the region during sparse mesh generation. The small-time-step node acceleration data is mapped to low-order units by point and subjected to frame extraction processing according to a preset time step. The data is then projected onto a low-dimensional manifold to obtain large-time-step node acceleration data and the low-order unit computational force matrix of the current frame. ; S30, based on the regional sparse physical constraint information The low-order unit computational force matrix The solution is obtained by combining an undamped method with an implicit method, utilizing the sparse physical constraint information of the region. and the low-order unit computational force matrix The physical relation sparse matrix I and physical relation sparse matrix II are obtained by Jacobi iteration and projection onto a low-dimensional manifold processing method. And the physical relation sparse matrix B and the physical relation sparse matrix B Sparse matrix topological relationship information; S40, using a graph neural network architecture that combines implicit methods and Jacobi iterations to apply the normalized physical relation sparse matrix B and the physical relation sparse matrix C, the physical relation sparse matrix D is used. The large-time-step node acceleration data is used for convergence training to obtain a neural network model for the earthquake simulation map. During model training, the normalized sparse time-step node acceleration data in the large-time-step node acceleration data is used as the node feature, and the normalized physical relation sparse matrix B and the physical relation sparse matrix B are used as the features. The elements of the implicit method iteration matrix are formed as edge features, and the topological relationship information of the sparse matrix is ​​used as topological information. The iterative process of the implicit method is simulated through residual connection. S50, based on the current force matrix information and using the earthquake simulation graph neural network model, perform working condition generalization prediction on the target area, and use the projection matrix to perform inverse projection mapping to obtain the large time step predicted acceleration of the sparse unit nodes of the target area.

[0021] The earthquake simulation method of this application, which integrates implicit iterative graph networks and the spectral element method, first uses the spectral element method to perform earthquake simulation calculations on the target area, obtaining small-time-step node acceleration data at high-order elements and small time steps. The small-time-step node acceleration data includes the acceleration information of dense physical element nodes at small time steps. Then, it performs processing from high-order elements to low-order elements, from small time steps to large time steps, and projects onto a low-dimensional manifold to obtain large-time-step node acceleration data. Simultaneously, it generates regional sparse physical constraint information during sparse mesh generation. The large-time-step node acceleration data includes acceleration information of sparse physical unit nodes at large time-step points; then, a database is built based on the regional sparse physical matrix information. and the low-order unit computational force matrix The physical relation sparse matrix B and the physical relation sparse matrix B are obtained by using an undamped method combined with an implicit method. And the physical relation sparse matrix B and the physical relation sparse matrix B The database also includes sparse matrix topological relationship information, and large-time-step node acceleration data obtained by projecting onto a low-dimensional manifold; then, the physical relationship sparse matrix B and physical relationship sparse matrix B are analyzed. The large-time-step node acceleration data is normalized, and the normalized data is used to train a graph neural network architecture that combines implicit methods and Jacobi iteration physical laws to obtain an earthquake simulation graph neural network model. This model fully utilizes the physical relation sparse matrix B and the physical relation sparse matrix B. The data value message transmission, aggregation, and updating of large time-step node acceleration data are handled using an MLP (Multilayer Perceptron) to map the high-dimensional data computation process. The model architecture originates from the implicit Jacobian iteration process, embedding strong physical information to enhance data stability and interpretability. The preprocessing features of the model are more physically embedded. Jacobian iteration is simulated through multiple message passing and residual connections, resulting in high model stability. Finally, leveraging the powerful generalization ability of the seismic simulation graph neural network model, seismic simulation of the target area is performed based on the current force matrix information using the seismic simulation graph neural network model and inverse projection mapping, employing a projection matrix for inverse projection mapping. The method acquires the large-time-step predicted acceleration of sparse unit nodes in the target region and rapidly generalizes calculations to new working conditions. The seismic simulation method of this invention, which integrates implicit iterative graph networks and the spectral element method, uses a graph neural network model whose architecture originates from the Jacobian iteration process of the implicit method. The model itself embeds strong physical information, exhibiting high stability and enhancing the long-term computational stability of the data. It establishes a relationship between large time steps and low-order units mapping to high-order units and small time steps, significantly reducing the computational scale. Through the generalization performance of the neural network, it rapidly calculates new working conditions, greatly shortening computation time and enabling rapid seismic simulation, thus providing a foundation for ultra-large-scale seismic calculations.

[0022] Understandably, existing spectral element methods are for seismic simulation calculations using high-order units and small time steps. Low-order units and large time steps are named in relation to the calculation methods of the spectral element method; units with exponents lower than those in the spectral element method are considered low-order units, and frame extraction at small time steps corresponds to large time steps. Specifically, the target region is sparsely divided into high-order units, and acceleration data at small time steps is processed by frame extraction to obtain acceleration data at large time steps. In a preferred embodiment of the present invention, the exponent (order) of the polynomial representing the characteristics of the grid unit is higher than the exponent (order) of the corresponding polynomial representing the characteristics of the low-order units, and the ratio of the time step size of the large time step to the time step size of the small time step is not less than 10:1. Preferably, the function representing the characteristics of the grid unit is a polynomial of not less than order 5 as the basis function, and the function representing the characteristics of the grid unit is a polynomial of not more than order 3 as the basis function.

[0023] Understandably, existing calculation methods can be used to obtain the small-time-step node acceleration data of the target region under high-order units and small time steps. Specifically, the small-time-step node acceleration data of the dense unit grid under small time steps is obtained based on the regional dense physical matrix information and the dense unit node force matrix of the target region under high-order units. Specifically, the regional dense physical matrix information is determined based on the physical properties of the grid of the target region. Understandably, in another embodiment of the present invention, high-order is a relative representation of low-order, that is, the solution of the present invention mainly uses a neural network to establish a mapping relationship between low-order units and high-order units. The ratio of the time step size of the large time step to the time step size of the small time step can also be 15:1 or 20:1 or other ratios, which are set according to the actual situation.

[0024] Research has shown that the spectral element method (SEM) can be considered a method that uses higher-order interpolation functions (similar to the pseudospectral method) on top of the finite element method (FEM) to achieve higher computational efficiency. In the traditional FEM, the functional expressions characterizing the mesh element properties generally use low-order Lagrange interpolation polynomials as basis functions, while the SEM often uses high-order Lagrange interpolation polynomials as basis functions. This is the main difference between the SEM and the FEM. It is generally believed that using 6th-8th order Lagrange polynomials (higher-order elements) as basis functions can well guarantee the accuracy and stability of the calculation. Although the higher the order, the more accurate the calculation results, the larger the memory and computational load required, and the longer the calculation time.

[0025] Currently, existing methods for increasing the time step mainly involve spatial filtering to suppress high wavenumber wavefields, allowing for larger time steps to stabilize the calculation; and using inverse time discretization transform to correct the numerical dispersion noise inherent in large time step iterations, thereby achieving accurate simulations with large time steps. However, these traditional numerical calculation methods are computationally intensive and lack universality. Furthermore, existing neural network simulations of earthquake propagation mostly employ data-driven methods, lacking sufficient physical dynamism, making them unsuitable for long-term simulations, and exhibiting relatively low interpretability.

[0026] Understandably, in traditional explicit earthquake simulations, iterative calculations using high-order elements and small time steps require multiple iterations to obtain the acceleration of the physical grid element nodes at the current moment (current frame) within a small time step. Specifically, the steps of the undamped implicit method can be mainly expressed as follows: , , , Indicates the previous moment in a smaller time step. This indicates the current moment in a small time step. This indicates the time step size corresponding to the smaller time step. This represents the dense physical constraint information of the target region under the mesh division corresponding to the higher-order cells. and These represent the acceleration information of the current frame at higher-order units and smaller time steps, respectively, and the computational force matrix (the computational force of the current frame obtained through implicit transformation). One-quarter can be taken. 1 / 2 can be taken. The mass matrix is ​​in the higher-order unit cell. This represents the current computational power matrix at higher-order units and small time steps. The stiffness matrix of the higher-order element is obtained by iteratively solving the linear equations to obtain the current acceleration of the element mesh at each time step. Iterative solution methods include Jacobi iteration, Gauss-Seidel iteration, and relaxation method iteration, etc., but the number of iterations is large and the computation is large.

[0027] In specific implementation, step S10 involves obtaining the regional dense physical matrix information of the target region under the higher-order unit. and dense element node force matrix Based on the regional dense physical matrix information and the force matrix of the dense unit nodes Calculate and obtain the acceleration data at small time steps. This can be understood by using the traditional Jacobi iteration as an example, which calculates... , After that, , Using the logic of Jacobi iteration, such as Perform calculations, where B and This is the matrix after Jacobian calculation. The iteration stops when the error between the two solutions is calculated and the calculated error is less than a specified value. For the first The solution value of the second time. For the first The solution value.

[0028] Furthermore, using the formula Processing is performed by Jacobi iteration and projection onto a low-dimensional manifold based on the projection matrix. We obtain the first sparse matrix B of physical relations and the second sparse matrix B of physical relations. And the physical relation sparse matrix B and the physical relation sparse matrix B The sparse matrix topological relationship information, where, This represents the sparse physical constraint information of the region. This represents the low-order unit computational force matrix of the current frame. Indicates the previous moment in a large time step. Indicates the current moment within a large time step. This indicates the time step size corresponding to the larger time step. For acceleration data of large time step nodes, the acceleration metric of the previous frame is used. It is the acceleration metric for the current frame in the large time step node acceleration data.

[0029] Furthermore, the sparse physical constraint information of the region and the low-order unit computational force matrix Feature processing is performed using the logic of Jacobi iteration and projection onto a low-dimensional manifold to obtain... Construct a sparse matrix based on physical relations, B1 and B2. The graph network structure topology.

[0030] Understandably, in the scheme of the present invention, the data used in training and acquiring the neural network model of the earthquake simulation image includes the sparse matrix I and the sparse matrix II obtained by the projection onto the low-dimensional manifold processing method, as well as the sparse matrix topological relationship information of the sparse matrix I and the sparse matrix II, and the large time step node acceleration data obtained by the projection onto the low-dimensional manifold, and the low-order unit computation force matrix of the current frame.

[0031] Furthermore, snapshots are constructed based on data at large time steps, and singular value decomposition is performed to construct a projection matrix; Sparse physical constraint information for the region and the low-order unit computational force matrix The feature is obtained by using Jacobi iteration and projecting the projection matrix onto the low-dimensional manifold. Construct a sparse matrix based on physical relations, B1 and B2. The graph network structure topology.

[0032] Furthermore, the computational principle of Jacobi iteration in the implicit method is as follows: D represents the main diagonal elements of the assembly implicit method, L and U are the upper and lower diagonal matrix elements of the assembly implicit method, respectively, and the projection matrix is ​​obtained using singular value decomposition. `data` represents the large-time-step node acceleration data, and `W`, `S`, and `V` represent the left singular vector, eigenvalue, and right singular vector, respectively. The projection matrix uses... The projection process is as follows In the scheme of this invention, the proportion of cumulative energy accounted for by the retained singular values ​​is calculated, the number of retained singular values ​​is selected, and a method is adopted. The first m vectors form the projection matrix, which is represented by the number of singular values ​​required to achieve 90% energy percentage.

[0033] Furthermore, the time step size of the large time step is 10-20 times the time step size of the small time step. In a specific embodiment of the present invention, the time step size of the small time step is 0.001 seconds, and the time step size of the large time step is 0.1 seconds.

[0034] Furthermore, the regional sparse physical matrix information includes the regional sparse stiffness matrix. , region sparse quality matrix and regional sparse damping matrix ; Use formula , Calculate and obtain the sparse physical constraint information of the region. and the low-order unit computational force matrix , Represented as the sparse element node force matrix of the current frame. and These represent the displacement and velocity of the previous frame at a large time step, respectively. ∈[0.2,0.35].

[0035] Furthermore, step S50 also includes using the formula and formula Calculations are performed to obtain the predicted displacement of the sparse nodes of the target region in the current frame. and prediction speed , For the large time step, predict the acceleration. , , These represent the predicted velocity, predicted acceleration, and predicted displacement of the sparse nodes in the target region in the previous frame. , .

[0036] Further, in step S40, the sparse matrix topological relationship information is divided into source nodes and target nodes, and the graph neural network architecture is a multi-messaging and residual connection network simulating the Jacobian iteration architecture relationship. In the scheme of the present invention, constraint calculation is performed from the source node toward the target node.

[0037] Please refer to Figure 2 The technical concept of this invention is to obtain the calculated physical relation sparse matrix B and the physical relation sparse matrix B. For topological information, the topological relationships are divided into source nodes and target nodes, and edge features B. The function values ​​of the matrix are given, and the point features are the acceleration variables to be determined. Then, the edge features and point features are processed (normalized), and then trained and calculated using a graph neural network to simulate the iterative solution process of traditional algorithms.

[0038] Traditional earthquake simulation methods rely heavily on explicit or implicit methods to construct equation systems, resulting in computationally intensive calculations that cannot utilize historical data. Please refer to [reference needed]. Figure 3 The method of this invention incorporates preprocessing results obtained from traditional earthquake simulation methods as training data when training the earthquake simulation graph neural network model, thereby determining the sparse physical constraint information in the region. After obtaining information such as mass matrix, stiffness matrix, and damping matrix, an implicit method is used to establish the iteration matrix. Then, the preprocessing features of the data are established using a principle similar to the Jacobian iteration in the implicit method. Figure 3 In this diagram, D represents the main diagonal element of the implicit assembly method, and L and U represent the upper and lower diagonal matrix elements of the implicit assembly method, respectively. It is the low-order unit computation force matrix of the current frame in the implicit method. It is the acceleration state at time t. yes The acceleration state at any given moment.

[0039] The present invention will be described in detail below using a one-dimensional acoustic wave equation simulation as an example: The differential form of a one-dimensional sound wave is: ,in, The characters are represented as follows: u represents displacement, f represents applied force, and v represents wave speed. The second derivative with respect to time, It is the second derivative of space.

[0040] Converting it to the acoustic wave equation of the spectral element method, it can be written as: Using the implicit method described above, it is transformed into a system of linear equations with acceleration as the variable to be solved. ; by using Jacobi iteration and projecting onto a low-dimensional manifold , Given a node topology matrix, construct the node indices of the graph, using the values ​​of the B and f' matrices projected onto the low-dimensional manifold as edge features (in this example, f'). (and the normalized value of f'), with the state variable as the point feature (in this example, the normalized acceleration vector). A neural network model for earthquake simulation graphs was established. The first 200 frames of 30 working conditions were used as training data, and the following 800 frames were used as inference data. The model was trained, tested, and validated to obtain the neural network model for earthquake simulation graphs.

[0041] The loss curve for obtaining the training neural network model of the earthquake simulation image is as follows: Figure 4 As shown, the network converges to a high degree after more than 200 training iterations. Because the network maintains a high level of physical knowledge, the required data volume and computation time are significantly reduced. The first 200 frames are used as training data, and the subsequent frames are used as inference data. Figure 5 As can be seen, the calculation results are excellent. Near frame 200, the accuracy decreases slightly due to the rapid changes in the boundaries, but the overall calculation precision remains high. Figure 6 As can be seen, the displacement calculation for the 399th frame is based on the large time step predicted acceleration, and the calculation accuracy is high.

[0042] The earthquake simulation method integrating implicit iterative graph networks and spectral element method provided by this invention employs the following innovative approaches: the model architecture originates from the Jacobian iteration process of the implicit method, the model itself embeds strong physical information, and the model has high stability; the remaining two physical quantities (displacement and acceleration) are calculated by embedding the newmark-beta method, enhancing the long-term computational stability of the data; a relationship is established between large time steps and low-order units mapping to high-order units and fine time steps, greatly reducing the computational scale and lowering the computational requirements; and the generalization ability of neural networks is used to quickly calculate new working conditions, greatly shortening the computation time. The beneficial effects include: the model architecture conforms to the implicit method's Jacobian iteration process, and the embedded newmark-beta method enhances the long-term stability of the data and improves the clarity of the physical information of the neural network; the model establishes a mapping relationship between large time steps and low-order units and small time steps and high-order units, greatly reducing the computational requirements on the equipment; the model architecture is reasonably designed, requiring only a small amount of data to achieve good results, and the number of training iterations is also low, resulting in good performance in long-term prediction and generalization to new conditions; due to the use of larger time steps and low-order units to map high-order units and fine time steps, the computational requirements are reduced, while the computational accuracy can reach the same level.

[0043] The present invention also provides an earthquake simulation system that integrates implicit iterative graph networks and spectral element method, including a processing unit, which is used to implement the earthquake simulation method integrating implicit iterative graph networks and spectral element method as described above.

[0044] It should be understood that the above are merely illustrative examples and do not constitute any limitation on the technical solutions of the present invention. In specific applications, those skilled in the art can make settings as needed, and the present invention does not impose any restrictions on this.

[0045] It should be noted that the workflow described above is merely illustrative and does not limit the scope of protection of this invention. In practical applications, those skilled in the art can select some or all of the workflow to achieve the purpose of this embodiment according to actual needs, and no restrictions are imposed here.

[0046] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or system that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or system. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or system that includes that element.

[0047] Through the above description of the embodiments, those skilled in the art can clearly understand that the methods of the above embodiments can be implemented by means of software plus necessary general-purpose hardware platforms. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium (such as read-only memory / random access memory, magnetic disk, optical disk) and includes several instructions to cause a terminal device (which may be a mobile phone, computer, server, air conditioner, or network device, etc.) to execute the methods described in the various embodiments of the present invention.

[0048] The above are merely preferred embodiments of the present invention and do not limit the patent scope of the present invention. Any equivalent regional or procedural transformations made based on the content of the present invention's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of the present invention.

Claims

1. A seismic simulation method integrating implicit iterative graph networks and the spectral element method, characterized in that, Includes the following steps: S10 uses the spectral element method to perform seismic simulation calculations in the target area and obtains the nodal acceleration data of high-order elements and small time steps at small time steps. S20, perform sparse mesh partitioning and interpolation mapping and project onto a low-dimensional manifold. During sparse mesh partitioning, generate sparse physical constraint information of the region. Map the small time step node acceleration data to low-order units according to the point position and perform frame extraction processing according to the preset time step. Project onto the low-dimensional manifold to obtain large time step node acceleration data under large time step and the low-order unit computation force matrix of the current frame. S30, based on the sparse physical constraint information of the region and the computational power matrix of the low-order unit, the undamped implicit method is used to solve the problem. The sparse physical constraint information of the region and the computational power matrix of the low-order unit are used to obtain the physical relation sparse matrix one, physical relation sparse matrix two, and the sparse matrix topological relation information of the physical relation sparse matrix one and the physical relation sparse matrix two through Jacobian iteration and projection onto the low-dimensional manifold processing method. S40, a graph neural network architecture combining implicit method and Jacobi iteration is adopted. The normalized physical relation sparse matrix one, the physical relation sparse matrix two, and the large time step node acceleration data are used for convergence training to obtain the earthquake simulation graph neural network model. During model training, the normalized sparse time node acceleration in the large time step node acceleration data is used as node features, the elements of the implicit method iteration matrix formed by the normalized physical relation sparse matrix one and the physical relation sparse matrix two are used as edge features, and the topological relation information of the sparse matrix is ​​used as topological information. The iterative process of the implicit method is simulated through residual connection. S50, based on the current force matrix information and using the earthquake simulation graph neural network model, perform working condition generalization prediction on the target area, and use the projection matrix to perform inverse projection mapping to obtain the large time step predicted acceleration of the sparse unit nodes of the target area.

2. The earthquake simulation method integrating implicit iterative graph networks and the spectral element method according to claim 1, characterized in that, Using formula Processing is performed by Jacobi iteration and projection onto a low-dimensional manifold based on the projection matrix. We obtain the first sparse matrix B of physical relations and the second sparse matrix B of physical relations. And the physical relation sparse matrix B and the physical relation sparse matrix B The sparse matrix topological relationship information, where, This represents the sparse physical constraint information of the region. This represents the low-order unit computational force matrix of the current frame. Indicates the previous moment in a large time step. Indicates the current moment within a large time step. This indicates the time step size corresponding to the larger time step. For acceleration data of large time step nodes, the acceleration metric of the previous frame is used. It is the acceleration metric for the current frame in the large time step node acceleration data.

3. The earthquake simulation method integrating implicit iterative graph networks and the spectral element method according to claim 2, characterized in that, Snapshots are constructed based on data at large time steps, and singular value decomposition is performed to construct the projection matrix; Sparse physical constraint information for the region and the low-order unit computational force matrix The feature is obtained by using Jacobi iteration and projecting the projection matrix onto the low-dimensional manifold. Construct a sparse matrix based on physical relations, B1 and B2. The graph network structure topology.

4. The earthquake simulation method integrating implicit iterative graph networks and the spectral element method according to claim 3, characterized in that, The computational principle of Jacobi iteration in implicit methods is as follows: D represents the main diagonal elements of the assembly implicit method, L and U are the upper and lower diagonal matrix elements of the assembly implicit method, respectively, and the projection matrix is ​​obtained using singular value decomposition. `data` represents the large-time-step node acceleration data, and `W`, `S`, and `V` represent the left singular vector, eigenvalue, and right singular vector, respectively. The first m vectors form the projection matrix, and the projection process is as follows: .

5. The earthquake simulation method integrating implicit iterative graph networks and the spectral element method according to claim 2, characterized in that, The regional sparse physical matrix information includes the regional sparse stiffness matrix. , region sparse quality matrix and regional sparse damping matrix ; Using formula , Calculate and obtain the sparse physical constraint information of the region. and the low-order unit computational force matrix , Represented as the sparse element node force matrix of the current frame. and These represent the displacement and velocity of the previous frame at a large time step, respectively. ∈[0.2,0.35].

6. The seismic simulation method integrating implicit iterative graph networks and the spectral element method according to any one of claims 2 to 5, characterized in that, In step S10, the regional dense physical matrix information of the target region under the higher-order unit is obtained. And the force matrix of dense unit nodes, based on the regional dense physical matrix information The small-time-step node acceleration data is obtained by calculating the force matrix of the dense unit nodes.

7. The seismic simulation method integrating implicit iterative graph networks and the spectral element method according to any one of claims 2 to 5, characterized in that, The time step of the small time step is 0.001 seconds, and the time step of the large time step is 0.1 seconds.

8. The seismic simulation method integrating implicit iterative graph networks and the spectral element method according to any one of claims 1 to 5, characterized in that, Step S50 also includes, Using formula and formula Calculations are performed to obtain the predicted displacement of the sparse nodes of the target region in the current frame. and prediction speed , For the large time step, predict the acceleration. , , These represent the predicted velocity, predicted acceleration, and predicted displacement of the sparse nodes in the target region in the previous frame. , .

9. The seismic simulation method integrating implicit iterative graph networks and the spectral element method according to any one of claims 1 to 5, characterized in that, In step S40, The sparse matrix topology relationship information is divided into source nodes and target nodes, and the graph neural network architecture is an architecture relationship that simulates Jacobi iteration by multiple message passing and residual connection networks.

10. A seismic simulation system integrating implicit iterative graph networks and the spectral element method, characterized in that, The system includes a processing unit for implementing the seismic simulation method that integrates implicit iterative graph networks and the spectral element method as described in any one of claims 1 to 9.

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