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

Abstract

The application discloses a seismic simulation method and system fusing an implicit iterative graph network and a spectral element method, obtains small time step node acceleration data; performs grid sparse division and interpolation mapping processing and projects to a low-dimensional manifold to obtain large time step node acceleration data and a low-order unit calculation moment matrix of a current frame; obtains physical relation sparse matrix one, physical relation sparse matrix two and sparse matrix topological relation information of the physical relation sparse matrix one and the physical relation sparse matrix two through Jacobian iteration and projection to a low-dimensional manifold processing method; obtains a seismic simulation graph neural network model; adopts the seismic simulation graph neural network model to perform prediction, and uses a projection matrix to project back to large time step predicted acceleration of a sparse unit node of a target region. The method greatly shortens the calculation time by mapping the high-order unit small time step and the low-order unit large time step through the neural network fitting capability, and realizes fast seismic simulation.

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 used in seismic simulation 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 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 number of high-order unit grids 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:

[0006] 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.

[0007] 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. ;

[0008] 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;

[0009] 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.

[0010] 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.

[0011] 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. topological information of sparse matrix of physical relationship of the region, indicates sparse physical constraint information of the region, indicates a low-order unit calculation force matrix of the current frame, indicates the last time under a large time step, indicates the current time under a large time step, indicates a time step corresponding to a large time step, is an acceleration amount of the last frame in the acceleration data of the node under the large time step, is an acceleration amount of the current frame in the acceleration data of the node under the large time step.

[0012] Further, a snapshot is constructed according to the data under the large time step, and singular value decomposition is performed to construct a projection matrix;

[0013] to the sparse physical constraint information of the region and the low-order unit calculation force matrix Jacobi iteration is used, and a projection matrix is used to project to a low-dimensional manifold to obtain , and a graph network structure topological relationship based on a physical relationship sparse matrix one B and a physical relationship sparse matrix two is constructed.

[0014] Further, the calculation principle of Jacobi iteration in the implicit method is , D is the main diagonal element of the assembled implicit method, L and U are respectively the upper diagonal matrix element and the lower diagonal matrix element of the assembled implicit method, the projection matrix is obtained by singular value decomposition, , data is the acceleration data of the node under the large time step, W, S and V are respectively left singular vectors, eigenvalues and right singular vectors, the first m vectors of are used to constitute the projection matrix, and the projection process is .

[0015] Further, the sparse physical matrix information of the region includes a sparse stiffness matrix of the region , a sparse mass matrix of the region and a sparse damping matrix of the region ;

[0016] is calculated by using the formula , to obtain the sparse physical constraint information of the region and the low-order unit calculation force matrix , indicates a sparse unit node force matrix of the current frame, and respectively indicate displacement and velocity of the last frame under the large time step, ∈[0.2, 0.35].

[0017] Further, in step S10, the region dense physical matrix information of the target region under the high-order unit is obtained and the dense unit node force matrix, the region dense physical matrix information and the dense unit node force matrix are used to obtain the small time step node acceleration data.

[0018] Further, the time step length of the small time step is 0.001 seconds, and the time step length of the large time step is 0.1 seconds.

[0019] Further, step S50 further comprises

[0020] The formula and the formula are used for calculation to obtain the predicted displacement and the predicted velocity of the region sparse node of the target region in the current frame , , , are the predicted velocity, the predicted acceleration, and the predicted displacement of the region sparse node of the target region in the last frame respectively , .

[0021] Further, in step S40,

[0022] The sparse matrix topological relationship information is divided into source nodes and target nodes, and the graph neural network architecture is a multi-message passing and residual connection network architecture simulating the architecture relationship of the Jacobi iteration.

[0023] The application also provides a seismic simulation system fusing an implicit iterative graph network and a spectral element method, comprising a processing unit, which is used to implement the seismic simulation method fusing the implicit iterative graph network and the spectral element method.

[0024] Advantages:

[0025] The seismic simulation method fusing the implicit iterative graph network and the spectral element method of the application first uses the spectral element method to perform seismic simulation calculation on a target region to obtain small time step node acceleration data under a high-order unit and a small time step, and the small time step node acceleration data comprises acceleration information of dense physical unit nodes at a small time step time point; then, processing from a high-order unit to a low-order unit, from a small time step to a large time step, and projection to a low-dimensional manifold is performed to obtain large time step node acceleration data under a large time step, and region sparse physical constraint information is generated when the grid is sparsely divided The large time step node acceleration data at the large time step includes acceleration information of the sparse physical unit node at a large time step time point; then, a database is built based on the region sparse physical matrix information and the low-order unit calculation force matrix ; according to the data projected to the low-dimensional manifold, a sparse matrix topology relationship information of the physical relationship sparse matrix one B, the physical relationship sparse matrix two and the physical relationship sparse matrix one B and the physical relationship sparse matrix two is solved by using a non-damped combined implicit method, and the physical relationship sparse matrix one B, the physical relationship sparse matrix two and the large time step node acceleration data are obtained by Jacobian iteration and projection to the low-dimensional manifold; then, the physical relationship sparse matrix one B, the physical relationship sparse matrix two and the large time step node acceleration data are normalized, a graph neural network architecture of physical law using the combined implicit method and Jacobian iteration is used for model training, a seismic simulation graph neural network model is obtained, and the data value of the physical relationship sparse matrix one B, the physical relationship sparse matrix two and the large time step node acceleration data is fully utilized; the message passing is , which transmits and aggregates messages according to the Jacobian calculation logic; the transmission, aggregation and updating of messages adopt MLP (Multi-Layer Perceptron) to process high-dimensional data flow; the architecture of the model is derived from the process of Jacobian iteration of the implicit method, the model itself is embedded with strong physical information, the data stability and interpretability are enhanced, the physicality of the pre-processed features of the model is stronger, the Jacobian iteration is simulated through multiple message passing and residual connection, and the stability of the model is high; finally, based on the current moment information, the target area is simulated by using the powerful generalization ability of the seismic simulation graph neural network model and inverse projection mapping, and the sparse element node large time step prediction acceleration of the target area is obtained by using the projection matrix for inverse projection mapping, so that the new working condition is calculated quickly; the seismic simulation method of the fusion of the implicit iteration graph network and the spectral element method, the architecture of the seismic simulation graph neural network model is derived from the process of Jacobian iteration of the implicit method, the model itself is embedded with strong physical information, the stability of the model is high, and the long-time calculation stability of the data is enhanced; the relationship between the large time step and the low-order element mapping high-order element and small time step is established, so that the calculation scale is greatly shortened; the mapping of the high-order element small time step and the low-order element large time step to the low-dimensional manifold is established by the fitting ability of the neural network, and the calculation scale is greatly reduced by combining the low-dimensional manifold; the new working condition is calculated quickly by the generalization performance of the neural network, the calculation time is greatly shortened, the seismic simulation is quickly realized, and a calculation basis is provided for the seismic simulation of a super large scale area. BRIEF DESCRIPTION OF DRAWINGS

[0026] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments or prior art description will be briefly introduced as follows, and obviously, other drawings can be obtained by those skilled in the art without any creative labor.

[0027] Figure 1 The flow chart of the seismic simulation method of the fusion of the implicit iteration graph network and the spectral element method provided by the embodiments of the present application is shown in the figure.

[0028] Figure 2 The sparse matrix topological relationship information schematic diagram of the seismic simulation method of the fusion of the implicit iteration graph network and the spectral element method provided by the embodiments of the present application is shown in the figure.

[0029] Figure 3 The network calculation framework schematic diagram of the seismic simulation method of the fusion of the implicit iteration graph network and the spectral element method provided by the embodiments of the present application is shown in the figure.

[0030] Figure 4 The calculation loss schematic diagram of the seismic simulation graph neural network model in the seismic simulation method of the fusion of the implicit iteration graph network and the spectral element method provided by the embodiments of the present application is shown in the figure.

[0031] Figure 5 The acceleration calculation precision result schematic diagram of the seismic simulation method fusing the implicit iterative graph network and the spectral element method provided by the embodiment of the present application, wherein a is a true value, b is a predicted value, and c is an error value;

[0032] Figure 6 The displacement calculation precision result schematic diagram of the seismic simulation method fusing the implicit iterative graph network and the spectral element method provided by the embodiment of the present application, wherein a is a true value, b is a predicted value, and c is an error value.

[0033] The implementation, functional features and advantages of the present application will be further described with reference to the embodiments and the accompanying drawings. DETAILED DESCRIPTION

[0034] It should be understood that the specific embodiments described herein are merely intended to explain the present application and not to limit the present application.

[0035] With reference to Figure 1 , the embodiment provides a seismic simulation method fusing an implicit iterative graph network and a spectral element method, including the following steps.

[0036] S10, performing seismic simulation calculation on a target region by using a spectral element method to obtain small-time-step node acceleration data under small-time-step and high-order elements;

[0037] S20, performing grid sparse division and interpolation mapping processing and projecting to a low-dimensional manifold, and generating regional sparse physical constraint information when performing grid sparse division , mapping the small-time-step node acceleration data to low-order elements according to point positions and performing frame extraction processing according to a preset time step, and projecting to a low-dimensional manifold to obtain large-time-step node acceleration data under a large time step and a low-order element calculation moment matrix of a current frame ;

[0038] S30, based on the regional sparse physical constraint information , the low-order element calculation moment matrix , solving by using an undamped combined implicit method, using the regional sparse physical constraint information and the low-order element calculation moment matrix , obtaining physical relationship sparse matrix one B, physical relationship sparse matrix two and sparse matrix topological relationship information of the physical relationship sparse matrix one B and the physical relationship sparse matrix two by Jacobian iteration and projection to a low-dimensional manifold processing method;

[0039] S40, the physical law graph neural network architecture combining the implicit method and the Jacobian iteration utilizes the normalized physical relationship sparse matrix one B and the physical relationship sparse matrix two and the large time step node acceleration data to perform convergence training, and obtain a seismic simulation graph neural network model; during model training, normalized sparse time node acceleration after normalization processing of the large time step node acceleration data is taken as node features, and the normalized physical relationship sparse matrix one B and the physical relationship sparse matrix two to form implicit method iteration matrix elements as edge features, and the sparse matrix topological relationship information is taken as topological information, and a residual connection is used to simulate an iteration process of the implicit method;

[0040] S50, based on current force matrix information and by using the seismic simulation graph neural network model, a working condition generalization prediction is performed on the target region, and a projection matrix is used for inverse projection mapping to obtain large time step prediction acceleration of sparse element nodes of the target region.

[0041] The seismic simulation method of the fusion implicit iteration graph network and the spectral element method in the application first performs seismic simulation calculation on a target region by using the spectral element method to obtain high-order element, small time step, and small time step node acceleration data, and the small time step node acceleration data includes acceleration information of dense physical element nodes at a small time step time point; then, processing from high-order element to low-order element, from small time step to large time step, and projection to low-dimensional manifold is performed to obtain large time step node acceleration data at a large time step, and regional sparse physical constraint information is generated at the time of grid sparse division wherein the large time step node acceleration data at the large time step includes acceleration information of sparse physical element nodes at a large time step time point; then, a database is built based on the regional sparse physical matrix information and the low-order element calculation force matrix obtained by using the undamped implicit method, the physical relationship sparse matrix one B, the physical relationship sparse matrix two and the physical relationship sparse matrix one B and the physical relationship sparse matrix two the sparse matrix topological relationship information, the database further includes the large time step node acceleration data obtained by projection to a low-dimensional manifold; then, the physical relationship sparse matrix one B, the physical relationship sparse matrix two and the large time step node acceleration data are normalized, and the data after normalization processing is used to perform model training by using the physical law graph neural network architecture combining the implicit method and the Jacobian iteration to obtain a seismic simulation graph neural network model, and the physical relationship sparse matrix one B and the physical relationship sparse matrix two And the data value message transmission, aggregation and update of large time step node acceleration data adopt MLP (multi-layer perceptron) to map high-dimensional data calculation process, the architecture of the model is derived from the process of Jacobian iteration of implicit method, the model itself is embedded with strong physical information, enhancing data stability and interpretability, the pre-processing feature embedding of the model is more physical, simulating Jacobian iteration through multiple message passing and residual connection, the stability of the model is high, finally, based on the current moment information, the seismic simulation of the target area is carried out by using the seismic simulation graph neural network model and inverse projection mapping, and the sparse unit node of the target area is obtained by using the projection matrix for inverse projection mapping to obtain the large time step prediction acceleration, and the new working condition is calculated quickly; The seismic simulation method of the present application fuses implicit iteration graph network and spectral element method, the architecture of the seismic simulation graph neural network model is derived from the process of Jacobian iteration of implicit method, the model itself is embedded with strong physical information, the stability of the model is high, and the long-time calculation stability of data is enhanced; The relationship between large time step and low-order unit mapping high-order unit and small time step is established, which greatly shortens the scale of calculation; The new working condition is calculated quickly through the generalization performance of neural network, the calculation time is greatly shortened, and the seismic simulation is realized quickly, which provides a basis for super large scale seismic calculation.

[0042] It can be understood that the existing spectral element method is for high-order unit, small time step seismic simulation calculation, and low-order unit, large time step is the corresponding naming of the calculation method of the spectral element method, which is lower than the index of the spectral element method, that is, low-order unit, and small time step frame extraction corresponds to large time step; Specifically, the target area is sparsely divided into high-order units, and the acceleration data under small time step is extracted to obtain the acceleration data under large time step. In a preferred embodiment of the present application, high-order represents that the index (order) of the polynomial function expression representing the characteristics of the grid unit is higher than that of the low-order corresponding function expression representing the characteristics of the grid unit, and the ratio of the time step length of the large time step to the time step length of the small time step is not less than 10:1; Preferably, wherein the function expression representing the characteristics of the grid unit is not less than 5-order polynomial as the base function, and the function expression representing the characteristics of the grid unit is not more than 3-order polynomial as the base function.

[0043] It can be understood that the small time step node acceleration data of the target region under the high order unit and the small time step can be obtained by the existing calculation method. Specifically, the small time step node acceleration data under the dense unit grid and the small time step is obtained based on the region dense physical matrix information of the target region under the high order unit and the dense unit node force matrix calculation. It can be understood that the region dense physical matrix information is determined based on the physical properties of the divided unit grid of the target region. It can be understood that in another embodiment of the present application, the high order is a relative representation of the low order, that is, the scheme of the present application mainly establishes the mapping relationship between the low order unit and the high order unit by using the neural network. The ratio of the time step length of the large time step to the time step length of the small time step can also be 15:1 or 20:1 or other ratios, which is set according to the actual situation.

[0044] It is found through research that the spectral element method can be considered as a method using higher order interpolation functions (similar to the pseudo-spectral method) on the basis of the finite element method to obtain higher calculation progress. In the traditional finite element method, the function expression representing the characteristics of the grid element is generally selected as a low-order Lagrange interpolation polynomial as a basis function, while in the spectral element method, a high-order Lagrange interpolation polynomial is often selected as a basis function. This is the main difference between the spectral element method and the finite element method. It is generally believed that using 6-8 order Lagrange polynomials (high order units) as basis functions can well guarantee the accuracy and stability of the calculation. Although the higher the order, the more accurate the calculation result, the more memory and computation required, and the longer the calculation time.

[0045] At present, the existing method for improving the time step mainly suppresses the high wave number wave field through spatial filtering, so that a larger time step can be used to stabilize the calculation; the numerical dispersion noise inherent in the large time step iteration is corrected by the inverse time discrete transform method, so that accurate large time step simulation is realized; these traditional numerical calculation methods have large calculation amount and lack universality. Moreover, in the process of simulating the propagation of earthquakes by using the existing neural network, a data-driven method is mostly used, which has insufficient physical driving and is difficult to meet the long-time simulation, and has low interpretability.

[0046] It can be understood that in the simulation of earthquakes by using the traditional explicit method, the acceleration of the physical grid element node at the current time (current frame) under the small time step is obtained by solving through multiple iterations when the high order unit and the small time step are used for iterative calculation. Specifically, the steps of solving by using the undamped implicit method can be represented as: , ,

[0047] , represents the last time under the small time step, represents the current time under the 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.

[0048] 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.

[0049] 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. represents the last time of the large time step, represents the current time of the large time step, represents the time step corresponding to the large time step, is the acceleration amount of the last frame in the large time step node acceleration data, is the acceleration amount of the current frame in the large time step node acceleration data.

[0050] Further, the region sparse physical constraint information and the low-order unit calculation force matrix are processed by using the Jacobi iteration and the logic of projection to the low-dimensional manifold to obtain , and a graph network structure topological relationship based on the physical relationship sparse matrix one B and the physical relationship sparse matrix two is constructed.

[0051] Understandably, in the scheme of the application, the data in training the seismic simulation graph neural network model includes the physical relationship sparse matrix one and the physical relationship sparse matrix two obtained by the projection to the low-dimensional manifold processing method, the sparse matrix topological relationship information of the physical relationship sparse matrix one and the physical relationship sparse matrix two, and the large time step node acceleration data under the large time step and the low-order unit calculation force matrix of the current frame obtained by the projection to the low-dimensional manifold.

[0052] Further, a snapshot is constructed according to the data under the large time step, and singular value decomposition is performed to construct a projection matrix;

[0053] Further, the region sparse physical constraint information and the low-order unit calculation force matrix are processed by using the Jacobi iteration and the logic of projection to the low-dimensional manifold to obtain , and a graph network structure topological relationship based on the physical relationship sparse matrix one B and the physical relationship sparse matrix two is constructed.

[0054] Further, the calculation principle of the Jacobi iteration in the implicit method is , D is the main diagonal element of the assembled implicit method, L and U are respectively the upper diagonal matrix element and the lower diagonal matrix element of the assembled implicit method, the projection matrix is obtained by singular value decomposition, , data is the large time step node acceleration data under the large time step, W, S and V are respectively the left singular vector, the eigenvalue and the right singular vector, the projection matrix is obtained by , and the projection process is In the scheme of the application, the cumulative energy proportion occupied by the reserved singular values is calculated, the number of the reserved singular values is selected, and the projection matrix is obtained by ​​The first m vectors of the matrix constitute a projection matrix, and the projection matrix is represented as the number of singular values required to take 90% of the energy proportion.

[0055] Further, the time step length of the large time step is 10-20 times the time step length of the small time step. In a specific embodiment of the present application, the time step length of the small time step is 0.001 seconds, and the time step length of the large time step is 0.1 seconds.

[0056] Further, the region sparse physical matrix information includes region sparse stiffness matrix , region sparse mass matrix , and region sparse damping matrix ; the region sparse physical constraint information and the low-order element calculation force matrix are calculated and obtained by using the formula , , , which is represented as the sparse element node force matrix of the current frame, and , which are respectively represented as the displacement amount and the velocity amount of the previous frame under the large time step, ∈[0.2, 0.35].

[0057] Further, step S50 further includes calculating and obtaining the predicted displacement and the predicted velocity of the region sparse node of the target region in the current frame by using the formula , , is the predicted acceleration of the large time step, , , are respectively the predicted velocity, the predicted acceleration, and the predicted displacement of the region sparse node of the target region in the previous frame, , .

[0058] 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-message passing and residual connection network architecture relationship simulating Jacobi iteration. In the scheme of the present application, the source node performs constraint calculation towards the target node.

[0059] Please refer to Figure 2 , the technical concept of the present application, by calculating the physical relationship sparse matrix one B and the physical relationship sparse matrix two as topological information, the topological relationship is divided into source nodes and target nodes, and the edge feature 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.

[0060] 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.

[0061] The present invention will be described in detail below using a one-dimensional acoustic wave equation simulation as an example:

[0062] 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.

[0063] 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.

[0064] The loss curve when acquiring the trained seismic simulation graph neural network model is as shown in Figure 4 More than 200 training can converge to a good level, and since the network maintains a high level of physical knowledge, the amount of data and computing time required is greatly reduced. The first 200 frames are taken as training data, and the latter is taken as inference data, and from Figure 5 It can be seen that the calculation result is excellent, and near 200 frames, the calculation accuracy decreases due to the rapid change of the boundary, but the overall calculation accuracy is high. From Figure 6 It can be seen that the calculation accuracy is high based on the large time step to predict the acceleration to calculate the displacement of the 399th frame.

[0065] The seismic simulation method provided by the fusion of the implicit iterative graph network and the spectral element method, the innovative means adopted includes: the model architecture is derived from the process of Jacobian iteration of the implicit method, the model itself is embedded with strong physical information, the stability of the model is high, and the remaining two physical quantities (displacement and acceleration) are calculated by embedding the newmark-beta method, which enhances the long-time calculation stability of the data; The relationship between large time steps and low-order elements and high-order elements and fine time steps is established, which greatly shortens the scale of calculation and reduces the requirements of the computer; the generalization of the neural network is used to quickly calculate new working conditions, which greatly shortens the calculation time. The beneficial effects include: the model architecture conforms to the process of Jacobian iteration of the implicit method, and the newmark-beta method is embedded to enhance the long-time stability of the data and improve the physical information clarity of the neural network; the model establishes the mapping relationship between large time steps and low-order elements and small time steps and high-order elements, which greatly reduces the requirements of the equipment for calculation; the model architecture design is reasonable, and a small amount of data is required to obtain good results, and the number of training required is also low, and the effect is good in long-time prediction and generalization of new working conditions; since a larger time step and low-order element mapping high-order element and fine time step are used, the requirements of the equipment for calculation are reduced, but the calculation accuracy can reach the same calculation accuracy.

[0066] The present application also provides a seismic simulation system that fuses an implicit iterative graph network and a spectral element method, comprising a processing unit, the processing unit is used to realize the seismic simulation method that fuses the implicit iterative graph network and the spectral element method as described above.

[0067] It should be understood that the above is only for illustration, and does not constitute any limitation on the technical solutions of the present application. In specific applications, those skilled in the art can set up as needed, and the present application does not limit this.

[0068] It should be noted that the above-described workflow is merely illustrative and does not limit the scope of protection of the present application, and in actual applications, a person skilled in the art can select part or all of them to achieve the purpose of the embodiment scheme according to actual needs, which is not limited here.

[0069] It should be noted that in this paper, the term "includes", "contains" or any other variant thereof is intended to cover non-exclusive inclusion, so that the process, method, article or system including a series of elements not only includes those elements, but also includes other elements not explicitly listed, or includes elements inherent to such process, method, article or system. Without more limitations, the element defined by the sentence "includes a" does not exclude the presence of other identical elements in the process, method, article or system including the element.

[0070] From the above description of the embodiments, those skilled in the art can clearly understand that the above-mentioned embodiment method can be realized by software and the necessary general hardware platform, of course, it can also be realized by hardware, but in many cases the former is a better embodiment. Based on such understanding, the technical solutions of the present application can be embodied in the form of a software product, which is stored in a storage medium (such as a read-only memory / random access memory, a magnetic disk, an optical disk) and includes a number of instructions for making a terminal device (which can be a mobile phone, a computer, a server, an air conditioner, or a network device, etc.) execute the method described in each embodiment of the present application.

[0071] The above is only the preferred embodiment of the present application, and does not limit the patent scope of the present application, and any equivalent region or equivalent process transformation using the content of the present application specification and drawings, or direct or indirect application in other related technical fields, are also included in the patent protection scope of the present application.

Claims

1. A method of seismic simulation fusing an implicit iterative graph network with a spectral element method, characterized in that, The method comprises the following steps: S10, performing seismic simulation calculation on the target region by using the spectral element method to obtain small time step node acceleration data under small time step and high order element; S20, performing grid sparse division and interpolation mapping processing and projecting to a low-dimensional manifold, generating regional sparse physical constraint information during grid sparse division, mapping the small time step node acceleration data to low order element according to point position and performing frame extraction processing according to a preset time step, projecting to a low-dimensional manifold to obtain large time step node acceleration data under large time step and low order element calculation force matrix of a current frame; S30, solving based on the regional sparse physical constraint information and the low order element calculation force matrix by using undamped combined implicit method, obtaining physical relationship sparse matrix one, physical relationship sparse matrix two and sparse matrix topological relationship information of the physical relationship sparse matrix one and the physical relationship sparse matrix two by Jacobian iteration and projecting to a low-dimensional manifold processing method using the regional sparse physical constraint information and the low order element calculation force matrix; S40, performing convergence training by using a physical law graph neural network architecture combining implicit method and Jacobian iteration using the normalized physical relationship sparse matrix one, the physical relationship sparse matrix two and the large time step node acceleration data to obtain a seismic simulation graph neural network model, during model training, taking normalized sparse time node acceleration in the large time step node acceleration data as node features, taking implicit method iteration matrix elements formed by the normalized physical relationship sparse matrix one and the physical relationship sparse matrix two as edge features, and taking the sparse matrix topological relationship information as topological information, and simulating the iteration process of implicit method through residual connection; S50, performing working condition generalization prediction on the target region based on current force matrix information and using the seismic simulation graph neural network model, and obtaining large time step prediction acceleration of sparse element nodes of the target region by using a projection matrix for inverse projection mapping.

2. The seismic simulation method of claim 1, wherein Adopting formula Through Jacobian iteration and based on projection matrix projection to low-dimensional manifold processing is , get physical relationship sparse matrix one B, physical relationship sparse matrix two And the sparse matrix topology relationship information of the physical relationship sparse matrix one B and the physical relationship sparse matrix two , wherein, Indicate the area sparse physical constraint information, Indicate the low-order unit calculation moment matrix of the current frame, Indicate the last time under large time step, Indicate the current time under large time step, Indicate the time step corresponding to large time step, It is the acceleration amount of the last frame in the large time step node acceleration data, It is the acceleration amount of the current frame in the large time step node acceleration data.

3. The seismic simulation method of claim 2, wherein constructing a snapshot according to data under large time step, and performing singular value decomposition to construct a projection matrix; sparse physical constraint information for the region and the low-order unit calculation force matrix Using the Jacobi iteration, and using the logic of projecting to the low-dimensional manifold using the projection matrix, feature processing is obtained , the graph network structure topology relationship based on the physical relationship sparse matrix one B and the physical relationship sparse matrix two ​ 4. The seismic simulation method of claim 3, wherein The calculation principle of the Jacobian iteration in the implicit method is , D is the main diagonal element of the assembled implicit method, L and U are the upper and lower diagonal matrix elements of the assembled implicit method, the projection matrix is obtained by singular value decomposition, , data is the large time step node acceleration data of the large time step, W, S and V are the left singular vector, the eigenvalue and the right singular vector, respectively, the first m vectors of are used to form the projection matrix, and the projection process is .

5. The seismic simulation method of claim 2, wherein zone-sparse physical matrix information including a zone-sparse stiffness matrix , a zone-sparse mass matrix , and a zone-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 of any one of claims 2 to 5, wherein In step S10, the region dense physical matrix information of the target region under the high-order unit is acquired and the dense unit node force matrix, the small time step node acceleration data is acquired according to the region dense physical matrix information and the dense unit node force matrix.

7. The seismic simulation method of any one of claims 2 to 5, wherein 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 of any one of claims 1 to 5, wherein The step S50 further comprises, are calculated by using the formula and the formula , to obtain the predicted displacement and the predicted velocity of the region sparse nodes of the target region in the current frame, the predicted acceleration of the large time step, , , the predicted velocity, the predicted acceleration and the predicted displacement of the region sparse nodes of the target region in the previous frame, respectively, , .

9. The method according to any one of claims 1 to 5, wherein the method is a seismic simulation method of fusing an implicit iterative graph network and a spectral element method. In the step S40, The sparse matrix topological relationship information is divided into a source node and a target node, and the graph neural network architecture is an architecture relationship of simulating a Jacobi iteration by a multi-message passing and residual connection network.

10. A seismic simulation system of fusing an implicit iterative graph network and a spectral element method, comprising a processing unit for implementing the seismic simulation method of fusing an implicit iterative graph network and a spectral element method according to any one of claims 1 to 9. ​

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