Training method and calculation method of multi-physics coupling calculation model

Abstract

The application relates to the field of computer calculation, in particular to a training method and a calculation method of a multi-physical field coupling calculation model, and solves the technical problems that in the prior art, a simulation model is difficult to realize real-time coupling and high-precision simulation of multiple physical fields, and the technical problems of large consumption of calculation resources and low efficiency. A training method of a multi-physical field coupling calculation model provided in the application firstly represents a mapping relationship between multiple physical fields as multiple PINO models, each PINO model corresponding to a mapping relationship between a group of physical fields; then a corresponding pre-trained PINO model is called to construct and train a multi-physical-multi-scale neural network, so that the physical fields correct each other in dynamic interaction, gradually approach a self-consistent coupling solution, and the modeling difficulty of complex system simulation is reduced. Since the physical law is used as a priori, excellent generalization ability is still shown when data is scarce or working conditions change, and the dependence on a large amount of high-fidelity training data is reduced.

Description

Technical Field

[0001] This application relates to the field of computer computing, and more specifically, to training and computation methods for multiphysics coupled computation models. Background Technology

[0002] Multiphysics coupling refers to the complex phenomenon in which different physical fields (such as structure, temperature, fluid, and electromagnetism) interact and influence each other within a specific spatiotemporal range in the same system. The essence of multiphysics coupling lies in the dynamic correlation between multiple physical fields; for example, mechanical vibration (structural field) can cause temperature changes (temperature field). It is widely present in numerous scientific and engineering fields, ranging from microelectronic devices to climate systems.

[0003] With increasing demands for accuracy in engineering system simulations, complex simulations employing multiphysics coupling can reveal the relationships between real physical systems. Traditional numerical simulation methods, such as the finite element method (FEM), consume significant computational resources and have long simulation times when handling multiphysics coupling. Furthermore, the need for complex boundary conditions and mesh generation for multiphysics coupling leads to low efficiency. Especially when dealing with cross-scale, multi-media coupling, and dynamic evolution scenarios, the scalability and framework integration capabilities of traditional numerical simulation methods are significantly insufficient.

[0004] Among existing solutions, grid-based numerical simulations can achieve multiphysics coupling simulations using tools such as COMSOL and ANSYS, but solving large global matrix equations leads to slow computation speed and high memory consumption. Separate coupling methods, which transfer data between different physics fields through interpolation and mapping, partially alleviate the computational burden, but in fluid-structure interaction scenarios (i.e., physical scenarios where there is a two-way interaction between fluids and solid structures), it is still difficult to achieve real-time coupling and high-precision simulation of multiphysics. Summary of the Invention

[0005] The purpose of this application is to provide a training method and a calculation method for a multiphysics coupling calculation model, which solves the technical problems in the existing technology that simulation models are difficult to achieve real-time coupling and high-precision simulation of multiphysics, and that consume a lot of computing resources and are inefficient.

[0006] As a first aspect of this application, this application provides a method for training a multiphysics coupled computational model, comprising: The initial information of the physical field to be solved is constructed. The initial information includes the physical field information of the physical field to be solved and the information of the external input parameters corresponding to the physical field to be solved. The physical field information includes the physical field to be solved and the governing equations, geometric model, boundary conditions and initial conditions corresponding to the physical field to be solved. The information of the external input parameters includes the external input parameters and the functional relationship corresponding to the external input parameters. Based on the initial information of the physical field to be solved, a physical information neural operator model is constructed and trained, wherein the physical information neural operator model represents the mapping relationship between the physical fields to be solved; A multi-physics-multi-scale neural network is constructed based on the physical information neural operator model, and trained based on the physical field trial functions of multiple physical fields to be solved. The multi-physics-multi-scale neural network represents the coupling mapping relationship between the physical fields to be solved. The input of the multi-physics-multi-scale neural network is the physical field trial function of the physical field to be solved, and the output is the coupling trial function of the physical field to be solved. The multiphysics coupling computation model includes at least one trained physical information neural operator model and a multiphysics-multiscale neural network.

[0007] In one embodiment of this application, a physical information neural operator model is constructed and trained based on the initial information of the physical field to be solved, including: Based on the physical field to be solved, the governing equations corresponding to the physical field to be solved, the external input parameters corresponding to the physical field to be solved, and the corresponding functional relationships, an initial operator model is constructed. The initial operator model includes a branch network and a backbone network. The branch matrix output by the branch network and the backbone matrix output by the backbone network can reflect the physical field trial function of the physical field to be solved. Based on the governing equations corresponding to the physical field to be solved and the functional relationship between the external input parameters corresponding to the physical field to be solved, the partial differential equations are derived. Construct a loss function based on the partial differential equations corresponding to the physical fields to be solved; Constraints are constructed based on the geometric model, boundary conditions, and initial conditions of the physical field to be solved; Based on the initial operator model, the loss function, and the constraints, the initial operator model is trained using training data to obtain a physical information neural operator model. The training data includes the numerical values ​​of the physical field to be solved and the numerical values ​​of the external input parameters corresponding to the physical field to be solved.

[0008] In one embodiment of this application, a loss function is constructed based on the partial differential equation corresponding to the physical field to be solved, including: Obtain the physical field trial function of the physical field to be solved; Based on the physical field trial function of the physical field to be solved, create the virtual scalar variables and virtual vector variables required by the zero coordinate transformation module; Calculate the auxiliary derivative tensor based on the virtual scalar variable and the virtual vector variable; Based on the virtual scalar variable, the virtual vector variable, and the auxiliary derivative tensor, calculate the second derivative of the physical field trial function with respect to spatial coordinates; A loss function is constructed based on the partial differential equations corresponding to the physical field to be solved and the second derivatives of the physical field trial functions with respect to spatial coordinates.

[0009] In one embodiment of this application, a multi-physics-multi-scale neural network is constructed based on a physical information neural operator model, and the multi-physics-multi-scale neural network is trained based on physical field trial functions of multiple physical fields to be solved, including: Constructing a multi-physics-multi-scale initial neural network based on fully connected layers; The physical information neural operator model corresponding to the physical field to be solved is called into the multi-physics-multi-scale initial neural network to form a multi-physics-multi-scale neural network. The initial physical field trial functions of multiple physical fields to be solved are input into the multi-physics-multi-scale neural network for coupled calculation to obtain the coupled trial function of each physical field to be solved. Calculate the loss value corresponding to each loss function included in the composite loss function, wherein the composite loss function includes a coupling loss function, which is constructed from multiple initial physical field trial functions and coupling trial functions of the physical fields to be solved; When the loss value corresponding to each loss function is less than or equal to the corresponding preset threshold, the coupling trial function of each physical field to be solved is output, and the training ends; When the loss value corresponding to any loss function is greater than the corresponding preset threshold, the coupling trial function of the physical field to be solved is used as the initial physical field trial function of the physical field to be solved, and the process returns to the step: inputting the initial physical field trial functions of multiple physical fields to be solved into the multi-physics-multi-scale neural network for coupling calculation to obtain the coupling trial function of each physical field to be solved.

[0010] In one embodiment of this application, initial physical field trial functions of multiple physical fields to be solved are input into the multi-physics-multi-scale neural network for coupled calculation to obtain a coupled trial function for each physical field to be solved, including: The corresponding physical information neural operator model is invoked based on the physical field to be solved; The initial physical field trial function of the physical field to be solved is input into the corresponding physical information neural operator model for calculation, and the coupling function of the physical field to be solved associated with the physical field to be solved is obtained.

[0011] In one embodiment of this application, training a multi-physics-multi-scale neural network based on physical field trial functions of multiple physical fields to be solved further includes: When the loss value corresponding to any loss function is greater than the corresponding preset threshold, the number of iterations is incremented by one. When the number of iterations is greater than or equal to the maximum number of iterations, the predicted value of the physical field to be solved is output, and the training ends. When the number of iterations is less than the maximum number of iterations, the coupled trial function of the physical field to be solved is used as the initial physical field trial function of the physical field to be solved, and the process returns to the step: inputting the initial physical field trial functions of multiple physical fields to be solved into the multi-physics-multi-scale neural network for coupled calculation to obtain the coupled trial function of each physical field to be solved.

[0012] In one embodiment of this application, the composite loss function further includes a physical loss function and a data loss function; Among these, training a multi-physics-multi-scale neural network based on the physical field trial functions of multiple physical fields to be solved also includes: When the coupling loss value corresponding to the coupling loss function is greater than the corresponding preset threshold, an adaptive algorithm is used to update the weight of the coupling loss function in the composite loss function calculated in the current iteration. The coupling loss function is updated based on the updated weights of the coupling loss function in the composite loss function, the coupling trial function corresponding to the current iteration, and the initial physics trial function.

[0013] In one embodiment of this application, the training method further includes: The number of physical information neural operator models is determined based on the number of physical fields to be solved and the external input parameters corresponding to the physical fields to be solved.

[0014] In one embodiment of this application, training a multi-physics-multi-scale neural network based on physical field trial functions of multiple physical fields to be solved further includes: The mean square error is calculated based on the coupling trial function of each physical field to be solved and the actual physical field trial function of the physical field to be solved; When the mean square error is greater than or equal to the preset error, the coupling trial function of the physical field to be solved is used as the initial physical field trial function of the physical field to be solved, and the process returns to the step: inputting the initial physical field trial functions of multiple physical fields to be solved into the multi-physics-multi-scale neural network for coupling calculation to obtain the coupling trial function of each physical field to be solved.

[0015] As a second aspect of this application, this application also provides a multiphysics coupling calculation method, including: Obtain the real-time values ​​of the external input parameters corresponding to the physical field to be solved; The real-time values ​​of the external input parameters are input into the multiphysics coupling calculation model for calculation to obtain the predicted value of the physical field to be solved. The multiphysics coupling calculation model is trained using the training method described above.

[0016] This application provides a training method for a multiphysics coupled computational model. First, the mapping relationships between multiphysics fields are represented as multiple PINO models, each corresponding to a set of mapping relationships between physics fields. Then, the corresponding pre-trained PINO models are used to construct a multiphysics-multiscale neural network, and coupled iterative training is performed on the multiphysics-multiscale neural network. This allows the physics fields to mutually correct each other in dynamic interaction, gradually approximating a self-consistent coupled solution, thus reducing the modeling difficulty of complex system simulations. Furthermore, because it uses physical laws as prior knowledge, it still exhibits excellent generalization ability even when data is scarce or operating conditions change, reducing the dependence on large amounts of high-fidelity training data. Attached Figure Description

[0017] 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, the drawings described below are only embodiments of this application. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0018] Figure 1 The diagram shown is a flowchart illustrating a training method for a multiphysics coupling computation model provided in an embodiment of this application.

[0019] Figure 2 The diagram shown is a flowchart illustrating a training method for a multiphysics coupling computation model provided in another embodiment of this application.

[0020] Figure 3 The diagram shown is a flowchart illustrating a training method for a multiphysics coupling computation model provided in another embodiment of this application.

[0021] Figure 4 The diagram shown is a flowchart illustrating a training method for a multiphysics coupling computation model according to another embodiment of this application.

[0022] Figure 5a The diagram shown is a schematic diagram of the calculated potential under a first conductivity provided in an embodiment of this application.

[0023] Figure 5b The diagram shown is a schematic diagram of the calculated potential under a second conductivity provided in another embodiment of this application.

[0024] Figure 5c The diagram shown is a schematic diagram of the calculated potential under a third conductivity provided in another embodiment of this application.

[0025] Figure 6a The diagram shown is a schematic representation of the pressure calculation results under a first conductivity level provided in an embodiment of this application.

[0026] Figure 6b The diagram shown is a schematic diagram of the pressure calculation results under a second conductivity provided in another embodiment of this application.

[0027] Figure 6c The diagram shown is a schematic diagram of the pressure calculation results under a third conductivity provided in another embodiment of this application.

[0028] Figure 7a The diagram shown is a schematic representation of the pressure calculation results provided in an embodiment of this application.

[0029] Figure 7b The diagram shown is a schematic representation of the calculated potential provided in another embodiment of this application.

[0030] Figure 8 The diagram shown is a flowchart of a multiphysics coupling calculation method provided in another embodiment of this application.

[0031] Figure 9 The diagram shown is a block diagram of an electronic device provided in an embodiment of this application. Detailed Implementation

[0032] The technical solutions of this application will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this application. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0033] In the description of this application, it should be noted that the terms "upper", "lower", "front", "horizontal", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this application.

[0034] In the description of this application, it should be noted that, unless otherwise explicitly specified and limited, the term "installation" should be interpreted broadly. For example, it can refer to a fixed connection, a detachable connection, or an integral connection; it can refer to a mechanical connection or an electrical connection; it can refer to a direct connection or an indirect connection through an intermediate medium; and it can refer to the internal connection between two components. Those skilled in the art can understand the specific meaning of the above terms in this application based on the specific circumstances.

[0035] The present application will now be described in further detail with reference to specific embodiments and accompanying drawings.

[0036] Exemplary control method As a first aspect of this application, this application provides a training method for a multiphysics coupled computational model. This multiphysics coupled computational model, within the same computational framework, can solve for one or more other physical fields based on multiple physical fields, thus reflecting the mutual influence between the multiple physical fields. For example, the multiphysics coupled computational model can solve for a third physical field based on two of the three physical fields, or it can solve for two other physical fields based on one of the three physical fields.

[0037] Taking electrohydrodynamics as an example, it can be understood as follows: in a one-dimensional flat plate channel or homogeneous porous medium filled with an electrolyte solution, fluid motion is driven by both a pressure gradient and an applied electric field gradient. The electroosmotic effect is characterized by the Zeta potential at the solid-liquid interface. Simultaneously, the fluid flow carries a net charge, generating convective currents, which in turn affect the electric field distribution. Therefore, electrohydrodynamics is essentially a two-way strong coupling. That is, the electro-hydrodynamic coupling calculation model corresponding to electrohydrodynamics is a coupling model of electroosmotic flow (flow under potential gradient) and pressure flow (flow under pressure gradient), which can reflect the pressure field and electric potential field when electroosmotic flow and pressure flow are coupled under one-dimensional conditions. Based on the Darcy flow assumption and the incompressibility condition, the total fluid velocity It is a linear superposition of pressure-driven flow and electroosmotic flow, and the superposition formula is:

[0038] In the formula, For fluid velocity, For pressure, For electric potential, , These are the dielectric constants of porous media and fluids, respectively. It is the Zeta potential. It is the dynamic viscosity of the fluid. It is a characteristic scale of the channel.

[0039] set up , These are the flow coefficients driven by pressure and the electrokinetic coefficients driven by electroosmosis, respectively.

[0040] For steady-state incompressible flow, the flux divergence is zero, i.e. This leads to information about stress. and electric potential The second-order differential equation:

[0041] Furthermore, a modified current continuity equation needs to be considered to describe charge conservation, introducing a strong coupling mechanism. Total current density. It includes not only the conduction current determined by Ohm's law, but also the net charge density carried by fluid motion. The resulting convective current, therefore, the total current density The expression is:

[0042] In the formula, It is the electrical conductivity of the medium. In this application, the electrical conductivity is defined with respect to spatial coordinates. It is a one-dimensional function. Under steady-state conditions and without external charge injection, the divergence of the current is zero, i.e. .

[0043] fluid velocity Substituting the expression into the total current density The expression for the second governing equation can be obtained by differential expansion:

[0044] Therefore, the mathematical model of the current-electric coupling calculation model can be reduced to conductivity. Regarding the two dependent variables and A system of linear second-order ordinary differential equations: .

[0045] Therefore, the linear second-order ordinary differential equations are used as the core constraint when constructing and training the current-electric coupling calculation model.

[0046] Figure 1 The diagram shown is a flowchart illustrating a training method for a multiphysics coupled computation model according to an embodiment of this application. Figure 1 As shown, the training method for a multiphysics coupled computation model provided in this application includes the following steps: S100: Construct initial information for multiple physical fields to be solved. The initial information includes the physical field information of the physical field to be solved and the information of the external input parameters corresponding to the physical field to be solved. Among them, the physical field information includes the physical field to be solved and the governing equations, geometric model, boundary conditions and initial conditions corresponding to the physical field to be solved, and the information of the external input parameters includes the external input parameters and the functional relationship corresponding to the external input parameters. Specifically, the number of physical fields to be solved depends on the application scenario of the corresponding model. There can be one or more physical fields to be solved. For example, M physical fields to be solved: Taking the hydroelectric coupling calculation model as an example, the physical fields to be solved can be three: fluid velocity, pressure, and electric potential. Alternatively, the physical fields to be solved can be only pressure or only electric potential.

[0047] The physical field information of the physical field to be solved includes the physical field to be solved ( ), governing equations of the physical field to be solved (e.g., Navier-Stokes equations, Poisson equations), and geometric models (e.g., computational thresholds). ), boundary conditions (e.g., boundary) (boundary conditions) and initial conditions.

[0048] Specifically, external input parameters refer to the unknowns involved in solving the governing equations of a physical field to be solved, such as external physical fields, material properties, and source terms. External input parameters can be expressed in functional form (e.g., ), that is, the functional relationship corresponding to the external input parameters, where This represents the functional relationship of the first external input parameter, ... This represents the functional relationship of the Nth external input parameter. There can be one or more external input parameters. The number of external input parameters depends on the number of unknowns involved in the governing equations of the physical field to be solved.

[0049] S200: Construct and train a physical information neural operator model based on the initial information of the physical field to be solved; The physical information neural operator model is used to represent the mapping relationship between the physical fields to be solved. Once the physical information neural operator model is constructed, it represents the mapping relationship between two physical fields in a set of physical fields to be solved. Inputting the physical field trial function of one of the physical fields into the physical information neural operator model will output the physical field trial function of the other physical field in the set. For example, if the first physical information neural operator model represents the mapping relationship between the first and second physical fields to be solved, and its input is the physical field trial function of the first physical field, then its output is the physical field trial function of the second physical field; similarly, if its input is the physical field trial function of the second physical field, then its output is the physical field trial function of the first physical field. The Physics-Informed Neural Operator (PINO) model, hereinafter referred to as the PINO model, is designed to achieve efficient and physically consistent solutions to multi-physics partial differential equations by deeply integrating prior physical knowledge into the learning process of a neural network. Therefore, for a control equation used in multi-physics calculations, it is necessary to build a PINO model corresponding to the physical field to be solved for fitting.

[0050] The physical field trial function of the physical field to be solved refers to an auxiliary function introduced when solving partial differential equations. It is a bridge connecting continuous physical laws (partial differential equations) and discrete numerical calculations.

[0051] Constructing a physical information neural operator model involves two processes: building the model framework of the physical information neural operator model and training the built model framework. (1) The model framework of the physical information neural operator model is built based on the governing equations of the physical fields to be solved. For example, if the number of physical fields to be solved is M, The governing equations of the physical field to be solved are: ; In the formula, For partial differential operators, For the physical field to be solved, The function relationship of external input parameters can represent material properties, external force terms, initial conditions, and boundary conditions.

[0052] (2) Training the physical information neural operator model is the solution operator for multiphysics mapping. Train the corresponding mapping relationship and solve the operator. The mapping relationship is as follows:

[0053] In the formula, This represents the trainable parameters in the PINO model. The functional relationship for external input parameters. Let M be the physical field to be solved, N be the number of external input parameters, and M be the number of physical fields to be solved.

[0054] Once the PINO model is constructed, the mapping relationship corresponding to the physical field to be solved can be obtained, that is:

[0055] In the formula, For the first i A physical field trial function to be solved. For the first i The functional relationship between the external input parameters of a physical field to be solved. This represents the trainable parameters in the PINO model. x The spatial coordinates of the physical field to be solved under one-dimensional conditions; Once the PINO model corresponding to the physical field to be solved is trained, the PINO model corresponding to the physical field to be solved can be called, and the physical field trial function of the physical field to be solved can be calculated.

[0056] S300: Construct a multi-physics-multi-scale neural network based on the physical information neural operator model, and train the multi-physics-multi-scale neural network based on the physical field trial functions of multiple physical fields to be solved; In this context, the multi-physics-multi-scale neural network represents the coupling mapping relationship between the physical fields to be solved. The input of the multi-physics-multi-scale neural network is the physical field trial function of the physical field to be solved, and the output is the coupling trial function of the physical field to be solved. For example, if there are three physical fields to be solved, the physical field trial functions of the three physical fields are input into the constructed and trained multi-physics-multi-scale neural network for coupling calculation to obtain the coupling trial function of the three physical fields to be solved.

[0057] Specifically, firstly, based on the fully connected layers of DeepM&Mnet, a parameterized multi-physics, multi-scale neural network is built. This multi-physics-multi-scale neural network Taking the spatial coordinates of the physical field to be solved under one-dimensional conditions as input, the coupled trial function of the physical field to be solved is output in parallel, specifically:

[0058] in, Let be the initial physical field trial function for the first physical field to be solved, ..., Let be the initial physical field trial function for the Mth physical field to be solved.

[0059] The physical field trial function and spatial coordinates of the physical field to be solved are input into a multi-physics-multi-scale neural network for computation, thereby obtaining the coupled trial function of the physical field to be solved. In other words, during the training of the multi-physics-multi-scale neural network, the physical field trial function of each physical field to be solved is used for training.

[0060] It should be noted that the coupling trial function of the physical field to be solved can be the coupling trial function obtained during any iteration of the training process.

[0061] Once the multiphysics-multiscale neural network is trained, a multiphysics coupling computation model is obtained. This model includes multiple PINO models trained by S200 and a multiphysics-multiscale neural network trained by S300.

[0062] This application provides a training method for a multiphysics coupled computational model. First, the mapping relationships between multiphysics fields are represented as multiple PINO models, each corresponding to a set of mapping relationships between physics fields. Then, the corresponding pre-trained PINO models are used to construct a multiphysics-multiscale neural network, and coupled iterative training is performed on the multiphysics-multiscale neural network. This allows the physics fields to mutually correct each other in dynamic interaction, gradually approximating a self-consistent coupled solution, thus reducing the modeling difficulty of complex system simulations. Furthermore, because it uses physical laws as prior knowledge, it still exhibits excellent generalization ability even when data is scarce or operating conditions change, reducing the dependence on large amounts of high-fidelity training data.

[0063] In one embodiment of this application, as Figure 2 As shown, the specific construction method of the Physical Information Neural Operator Model (PINO model), namely S200 (constructing and training the Physical Information Neural Operator Model based on the initial information of the physical field to be solved), includes the following steps: S210: Based on the physical field to be solved, the governing equations corresponding to the physical field to be solved, the external input parameters corresponding to the physical field to be solved, and the corresponding functional relationships, an initial operator model is constructed. The initial operator model includes a branch network and a backbone network. The branch matrix output by the branch network and the backbone matrix output by the backbone network can reflect the physical field trial function of the physical field to be solved. Specifically, assume that the number of physical fields to be solved is M, which are respectively The corresponding governing equation is:

[0064] In the formula, For partial differential operators, Let M be the numerical values ​​of the physical fields to be solved. The function relationship is the external input parameters corresponding to the physical field to be solved, that is, the external input parameters are in the form of a function relationship, and N is the number of external input parameters.

[0065] At this point, the corresponding solution operator for the physical field to be solved... The mapping relationship is as follows:

[0066] in, This represents the trainable parameters.

[0067] Therefore, using the computational approach of MIONet, N branch networks and M backbone networks are created. Through these networks, M physical field trial functions of the physics field to be solved can be calculated. That is, the branch matrix output by the branch networks and the backbone matrix output by the backbone networks reflect the physical field trial functions of the physics field to be solved. For example, for the i-th physical field trial function... ,but for:

[0068] in, This represents the branch matrix of the outputs of N branch networks, where the i-th branch network uses the functional relationship of the external input function corresponding to the i-th physical field to be solved. For input; This is the backbone matrix output by the i-th backbone network, where the i-th backbone network uses training points (i.e., spatial coordinates). For input; as well as These are the weights and the biases, respectively.

[0069] Therefore, it can be based on Based on the above relationships, an initial operator model is constructed, which may include a branch network and a backbone network.

[0070] S220: Derivation of partial differential equations based on the governing equations of the physical field to be solved and the functional relationship between the external input parameters of the physical field to be solved; Partial differential equations (PEDs) are equations that contain unknown functions and their partial derivatives, and can describe the continuous changes of the physical field to be solved in space and time.

[0071] The corresponding partial differential equations can be derived from the conservation laws, the governing equations of the physical field to be solved, and the functional relationships of the external input parameters.

[0072] S230: Construct a loss function based on the partial differential equations corresponding to the physical field to be solved; A soft constraint can be applied to penalize the initial operator model during training using a loss function.

[0073] S240: Construct constraints based on the geometric model, boundary conditions, and initial conditions of the physical field to be solved; Specifically, the geometric model refers to the computational threshold. Boundary conditions refer to the boundary conditions. Boundary conditions.

[0074] The constraints, constructed based on the geometric model, boundary conditions, and initial conditions of the physical field to be solved, are hard constraints that penalize the initial operator model during training. Hard constraints can be designed by transforming the network output to ensure that the constraints are satisfied. For example, for Dirichlet boundary conditions, the network output can be constructed as follows:

[0075] in, Satisfy the hard constraints. Let be the initial physical field trial function of the physical field.

[0076] For example, for periodic boundary conditions, use the upgraded topological mapping: .

[0077] S250: Based on the initial operator model, loss function, and constraints, the initial operator model is trained according to the training data to obtain the physical information neural operator model. The training data includes the numerical values ​​of the physical field to be solved and the numerical values ​​of the external input parameters corresponding to the physical field to be solved.

[0078] The initial operator model structure and constraints are established through steps S210-S240. Then, the initial operator model is pre-trained using training data to obtain the pre-trained physical information neural operator model, i.e., the pre-trained PINO model. This PINO model is used in subsequent multi-physics, multi-scale neural network training processes.

[0079] Optionally, the specific method for constructing the loss function, namely S230 (constructing the loss function based on the partial differential equation corresponding to the physical field to be solved), further includes the following steps: S2301: Obtain the physical field trial function of the physical field to be solved; Specifically, the physical field trial function of the physical field to be solved can be pre-constructed, that is, the physical field trial function of the physical field to be solved is:

[0080] Where M is the number of physical fields to be solved, and N is the number of external input parameters.

[0081] S2302: Based on the physical field trial function of the physical field to be solved, create the virtual scalar vector and virtual vector variables required by the zero coordinate transformation module; That is, the loss function of the PINO model is constructed by combining the Zero Coordinate Shift (ZCS) algorithm.

[0082] For example: Suppose the physical field trial function of the i-th physical field to be solved is: ; Introducing virtual scalar variable z=0 and virtual vector variable , will affect spatial coordinates Differentiate, and apply the coordinates in space The derivative is transformed into the derivative with respect to the dummy scalar variable, thus unifying the derivative calculation for all sampling points, as follows:

[0083] S2303: Calculate the auxiliary derivative tensor based on the virtual scalar variables and virtual vector variables; Specifically, the formula for calculating the auxiliary derivative tensor is as follows:

[0084] in, To assist in the differentiation of the tensor.

[0085] S2304: Construct a loss function based on the partial differential equations corresponding to the physical field to be solved and the second derivatives of the physical field trial functions with respect to spatial coordinates; Specifically, the loss functions include the driving loss function, the physical equation loss function, and the boundary condition loss function. That is: = + + ; in, For loss function, , as well as These are the loss weights for the driving loss function, the physical equation loss function, and the boundary condition loss function, respectively. To drive the loss function, The loss function of the physical equation, This is the boundary condition loss function.

[0086] in,

[0087] in, The driving loss function measures the difference between the observed values ​​and the actual values ​​in the PINO model. This is the physical equation loss function, used to measure how well the output of the PINO model satisfies the governing equations. The boundary condition loss function ensures that the solution of the observed values ​​satisfies the constraints under the boundary or initial conditions. ; in, , , Calculation thresholds training points, boundaries Or the initial training points and the sampling points of the real dataset.

[0088] Optionally, for special partial differential equations (i.e., special PDEs), when constructing the loss function, it is also necessary to add the residual terms corresponding to the characteristic equations and design corresponding normalization constraints. For example, for multi-scale problems or complex boundary problems, strategies such as computational threshold splicing, adaptive sampling, or Fourier feature networks can be introduced.

[0089] In this application, during the training of the PINO model, a loss function is constructed by combining the zero-coordinate transformation algorithm. This transforms the high-dimensional and complex automatic differentiation of spatial coordinates in the training of the Physical Information Neural Operator Model (PINO model) into efficient automatic differentiation of virtual scalars (a "single-root, multi-leaf" problem). By optimizing the calculation process of coordinate derivatives, training efficiency is significantly improved without changing the network architecture or data. Converting the automatic differentiation of training point coordinates in PINO model training into automatic differentiation of virtual scalars using the ZCS algorithm drastically reduces the training time of a single PINO, shortening the original training time of several days to several hours, greatly reducing computational resource requirements and time consumption.

[0090] In another embodiment of this application, the training process of the multi-physics-multi-scale neural network (hereinafter referred to as the DeepM&Mnet model) is as follows: Figure 3 As shown, S300 (constructing a multi-physics-multi-scale neural network based on the physical information neural operator model, and training the multi-physics-multi-scale neural network based on the physical field trial functions of multiple physical fields to be solved) specifically includes the following steps: S310: Constructing a multi-physics-multi-scale initial neural network based on fully connected layers; S320: Call the physical information neural operator model corresponding to the physical field to be solved into the multi-physics-multi-scale initial neural network to form a multi-physics-multi-scale neural network; That is, firstly, an initial neural network is built based on a fully connected layer, and then the physical information neural operator model corresponding to the physical field to be solved is called into the initial neural network to replace the internal modules in the initial neural network.

[0091] Specifically, the physical information neural operator model corresponding to the physical field to be solved is obtained through S200 pre-training.

[0092] S330: The initial physical field trial function of the physical field to be solved is input into a multi-physics-multi-scale neural network for coupled calculation to obtain the coupled trial function of each physical field to be solved.

[0093] Specifically, the initial physical field trial function of the physical field to be solved can be pre-constructed or calculated from the corresponding PINO model.

[0094] Optionally, S330 (inputting the initial physical field trial function of the physical field to be solved into a multi-physics-multi-scale neural network for coupled calculation to obtain the coupled trial function of each physical field to be solved) specifically includes the following steps: S3301: Call the corresponding physical information neural operator model according to the physical field to be solved; For example, if there are multiple physical fields to be solved, namely the first physical field, the second physical field, and the third physical field, then there are three corresponding physical information neural operator models invoked: the first physical information neural operator model (first PINO model), the second physical information neural operator model (second PINO model), and the third physical information neural operator model (third PINO model). The first PINO model represents the mapping relationship between the first and second physical fields to be solved. The second PINO model represents the mapping relationship between the second and third physical fields to be solved. The third PINO model represents the mapping relationship between the second and third physical fields to be solved.

[0095] S3302: Input the initial physical field trial function of the physical field to be solved into the corresponding physical information neural operator model for calculation, and obtain the coupling function of the physical field to be solved associated with the physical field to be solved; For example, by inputting the initial physical field trial function of the first physical field to be solved into the first PINO model for calculation, the coupled trial function of the second physical field to be solved can be obtained. By inputting the initial physical field trial function of the second physical field to be solved into the second PINO model for calculation, the coupling trial function of the third physical field to be solved can be obtained. By inputting the initial physical field trial function of the third physical field to be solved into the third PINO model for calculation, the coupling trial function of the first physical field to be solved can be obtained.

[0096] Correspondingly, a coupling loss function can be constructed based on the mean square error (MSE) between the initial physical field trial function and the coupling trial function (calculated by the third PINO model) of the first physical field to be solved, the mean square error (MSE) between the initial physical field trial function and the coupling trial function (calculated by the first PINO model) of the second physical field to be solved, and the mean square error (MSE) between the initial physical field trial function and the coupling function (calculated by the second PINO model) of the third physical field to be solved.

[0097] S340: Calculate the loss value corresponding to each loss function included in the composite loss function; Specifically, the composite loss function It may include only the coupling loss function .

[0098] Specifically, the composite loss function Including coupling loss function Physical loss function and data loss function .

[0099] Wherein, the coupling loss function The calculation formula is:

[0100] in, Let the coupling loss function be... Let be the initial physical field trial function to be solved. Let be the physical field trial function of the physical field to be solved, calculated by the PINO model in the j-th iteration. Let ZCS be the auxiliary derivative tensor for the j-th iteration.

[0101] Optional, physical loss function and data loss function These are used to monitor whether a multi-physics, multi-scale neural network satisfies the constraints of the physical equations and the degree of deviation from the true value during iterative training. When the deviation from the true value is large, the physical loss function... and data loss function It participates in the construction of the loss function. That is, the composite loss function includes the coupling loss function. Or, the composite loss function includes the coupling loss function and the physical loss function. and data loss function .

[0102] S350: Determine whether the loss value corresponding to each loss function is less than or equal to the corresponding preset threshold; Specifically, each loss function included in the composite loss function corresponds to a preset threshold. For example, the composite loss function corresponds to preset threshold one, the physical loss function corresponds to preset threshold two, and the data loss function corresponds to preset threshold three. These three preset thresholds can be the same or different.

[0103] When S350 determines "yes," meaning the loss value of each loss function in the composite loss function is less than or equal to its corresponding preset threshold, the DeepM&Mnet model training is complete, training ends, and the coupling trial function for each physics field to be solved is output. Then, S360 is executed.

[0104] If the judgment result of S350 is negative, meaning that the loss value corresponding to at least one of the composite loss functions is greater than the corresponding preset threshold, the training is not yet over and the next iteration of training needs to be performed. This involves incrementing the iteration count by one, i.e., n = n + 1, where n is the number of iterations. This is equivalent to executing S370.

[0105] S360: Output the coupled trial function of the physical field to be solved, and end the training.

[0106] When the coupling loss and other monitoring losses (such as the data loss value calculated by the data loss function and the physical field loss value calculated by the physical field loss function) converge to a preset threshold or reach the maximum number of iterations, the final stable coupling trial function of the physical field to be solved is output. For example, in the case of current-electric coupling, the coupling trial function corresponding to the physical field to be solved is output, such as the velocity field, pressure field, and electric potential field. The coupling trial function corresponding to the physical field to be solved is a self-consistent solution that achieves dynamic equilibrium between the various physical fields under the drive of physical information.

[0107] S370: Increment the number of iterations, i.e., n = n + 1.

[0108] S380: Determine if the number of iterations is greater than the maximum number of iterations; That is, it determines whether n after the increment operation is greater than the maximum number of iterations. When the result of S380 is yes, it means that the number of iterations has reached the maximum number of iterations. At this time, the training ends, and then the coupled trial function of the physical field to be solved obtained by the nth iteration is output, that is, S360 is executed.

[0109] If the result of S380 is negative, it means that the number of iterations has not yet reached the maximum number of iterations. At this time, the coupled trial function of the physical field to be solved obtained by the current iteration is used as the initial physical field trial function, that is, S390 is executed.

[0110] S390: Use the coupled trial function of the physical field to be solved as the initial physical field trial function of the physical field to be solved, and return to step S330 to perform the next iteration calculation. Continue the iteration calculation in this way until the training is completed.

[0111] This application iteratively calls a pre-trained PINO model, enabling the various physical fields to mutually correct each other through dynamic interaction, gradually approximating a self-consistent coupled solution. Compared with traditional purely data-driven machine learning models, this method effectively avoids "non-physical solutions" that violate physical laws, ensuring the rationality of the solution. Furthermore, because it uses physical laws as a priori information, the model exhibits excellent generalization ability when data is scarce or operating conditions change, reducing its dependence on large amounts of high-fidelity training data.

[0112] Optionally, the composite loss function includes the coupling loss function, the physical loss function, and the data loss function. In this case, S300 (training a multi-physics-multi-scale neural network based on the physical trial functions of multiple physical fields to be solved) also includes the following steps: S391: When the coupling loss value corresponding to the coupling loss function is greater than the corresponding preset threshold, an adaptive algorithm is used to update the weight of the coupling loss function in the composite loss function calculated in the current iteration. S392: Update the coupling loss function based on the updated weights of the coupling loss function in the composite loss function, the predicted physics trial function calculated in the current iteration, and the initial physics trial function.

[0113] In the next iteration, the coupling loss function used to calculate the loss in the coupling loss function is the updated coupling loss function.

[0114] In one embodiment of this application, as Figure 4 As shown, S300 (training a multi-physics-multi-scale neural network based on the physical field trial functions of multiple physical fields to be solved) also includes the following steps: S393: Calculate the mean square error based on the coupled trial function of each physical field to be solved and the actual physical field trial function of the physical field to be solved; For example, the formula for calculating the mean square error of the i-th physical field to be solved can be:

[0115] In the formula, Let be the mean square error of the i-th physical field to be solved. It is the coupled trial function corresponding to the current iteration calculation of the i-th physical field to be solved. Let be the actual physical field trial function for the i-th physical field to be solved. N is the number of sampling points within the calculation threshold.

[0116] S394: Determine whether the mean square error is less than the preset error; When the judgment result of S394 is yes, that is, the mean square error is less than the preset error, the training ends.

[0117] When the judgment result of S394 is negative, that is, the mean square error is greater than or equal to the preset error, the coupling trial function of the physical field to be solved obtained by the current iteration calculation is used as the initial physical field trial function of the physical field to be solved, and 330 is executed, that is, the next iteration calculation is performed.

[0118] In other words, this application monitors the coupled model by monitoring the computational accuracy obtained from the coupled model. If the accuracy is low, training continues to improve the prediction accuracy of the coupled model.

[0119] The following section uses a hydroelectric coupling computational model as an example. Under one-dimensional reaction conditions, and with the physical fields to be solved being pressure field, electric potential field, pressure field, and electric potential field respectively, the training process of the hydroelectric coupling computational model is described. Specifically: As mentioned above, the mathematical model of the current-electric coupling calculation model can be reduced to conductivity. Regarding the two dependent variables and A system of linear second-order ordinary differential equations: .

[0120] Therefore, a current-electric coupling calculation model can be constructed based on this set of equations.

[0121] (a) Conductivity under one-dimensional conditions The change is represented by the physical field to be solved, which is pressure P(X), and the electric potential V is the external input parameter. That is, the pre-trained PINO model is the PINO model corresponding to pressure. After the current-electric coupling calculation model is trained using the method described above, the following diagram illustrates the calculated pressure predictions obtained by the trained current-electric coupling calculation model under three different conductivities: Figures 5a-5c As shown.

[0122] (II) Under one-dimensional conditions, the conductivity changes, the physical field to be solved is the electric potential V(X), the pressure P is the external input parameter, and the pre-trained PINO model is the PINO model corresponding to the electric potential. After the current-electric coupling calculation model is trained using the above-described training method, the following diagram illustrates the calculation results of the predicted electric potential values ​​obtained by the trained current-electric coupling calculation model under three different conductivity conditions: Figures 6a-6cAs shown.

[0123] (iii) Under one-dimensional conditions, at the same conductivity Under the given conditions, the physical fields to be solved are electric potential V(X) and pressure P(X). The pre-trained PINO models are the PINO models corresponding to electric potential and voltage. After the current-electric coupling calculation model is trained using the training method described above, the following diagram illustrates the calculation results of the predicted electric potential and voltage values ​​obtained by the trained current-electric coupling calculation model under three different conductivities: Figures 7a-7b As shown.

[0124] As a second aspect of this application, this application also provides a multiphysics coupling calculation method. Figure 8 The diagram shown is a flowchart illustrating a multiphysics coupling calculation method according to an embodiment of this application. Figure 8 As shown, the multiphysics coupling calculation method provided in this application includes the following steps: S1: Obtain the real-time values ​​of the external input parameters corresponding to the physical field to be solved; S2: Input the real-time values ​​of external input parameters into the multiphysics coupling calculation model for calculation to obtain the predicted values ​​of the physical field to be solved; The multiphysics coupling calculation model was trained using the training method described above.

[0125] Once the multiphysics coupling calculation model has been trained using the training method described above, in practical applications, the real-time values ​​of the external input parameters corresponding to the physical field to be solved are input into the multiphysics coupling calculation model for calculation, thereby obtaining the predicted value corresponding to the physical field to be solved, thus realizing multi-coupling simulation calculation.

[0126] Exemplary electronic devices As a third aspect of this application, this application also provides an electronic device, including a processor and a memory, wherein a computer program is stored in the memory, and when the processor executes the computer program, it executes the training method for a multiphysics coupling calculation model described above.

[0127] Specifically, the internal structure of electronic devices can be as follows: Figure 9As shown, the electronic device includes a processor, a memory, a network interface, and an input device connected via a device bus. The processor provides computational and control capabilities. The memory includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores operating devices and computer programs. The internal memory provides an environment for the operation of the operating devices and computer programs stored in the non-volatile storage medium. The network interface is used to communicate with external terminals via a network connection. When the computer program is executed by the processor, it follows the steps of a training method for a multiphysics coupling computation model according to various embodiments of this specification, as described in the above embodiments.

[0128] The processor may include the main processor, as well as baseband chips, modems, etc.

[0129] The memory stores a program for executing the technical solution of this application, and may also store operating devices and other key business functions. Specifically, the program may include program code, which includes computer operation instructions. More specifically, the memory may include read-only memory (ROM), other types of static storage devices capable of storing static information and instructions, random access memory (RAM), other types of dynamic storage devices capable of storing information and instructions, disk storage, flash memory, etc.

[0130] The processor can be a general-purpose processor, such as a general-purpose central processing unit (CPU), a microprocessor, etc., or an application-specific integrated circuit (ASIC), or one or more integrated circuits used to control the execution of the program of the present application. It can also be a digital signal processor (DSP), an application-specific integrated circuit (ASIC), an off-the-shelf programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components.

[0131] Input devices may include devices that receive data and information input by the user, such as keyboards, mice, cameras, scanners, light pens, voice input devices, touch screens, pedometers, or gravity sensors.

[0132] Output devices may include devices that allow information to be output to the user, such as displays, printers, speakers, etc.

[0133] The communication interface may include any transceiver-like device for communicating with other devices or communication networks, such as Ethernet, Radio Access Network (RAN), Wireless Local Area Network (WLAN), etc.

[0134] The processor executes the program stored in the memory and calls other devices, which can be used to implement the various steps of the training method for a multiphysics coupled computation model provided in the above embodiments of this specification.

[0135] The electronic device may also include a display component and a voice component. The display component may be a liquid crystal display screen or an e-ink display screen. The input device of the electronic device may be a touch layer covering the display component, or a button, trackball or touchpad set on the casing of the electronic device, or an external keyboard, touchpad or mouse, etc.

[0136] Those skilled in the art will understand that Figure 9 The structures shown are merely block diagrams of a portion of the structure related to the scheme described in this specification, and do not constitute a limitation on the electronic devices to which the scheme described in this specification is applied. Specific electronic devices may include more or fewer components than those shown in the figures, or may combine certain components, or may have different component arrangements.

[0137] Exemplary computer program products and storage media In addition to the methods and devices described above, the training method for a multiphysics coupled computation model provided in the embodiments of this specification can also be a computer program product, which includes computer program instructions. When the computer program instructions are run by a processor, the processor performs the steps in the training method for a multiphysics coupled computation model according to various embodiments of this specification as described in the "Exemplary Methods" section above.

[0138] The aforementioned computer program product can be implemented through hardware, software, or a combination thereof. In one optional embodiment, the computer program product is specifically embodied in a computer storage medium; in another optional embodiment, the computer program product is specifically embodied in a software product, such as a software development kit (SDK), etc.

[0139] The computer program product can be written in any combination of one or more programming languages ​​to perform the operations of the embodiments of this specification. The programming languages ​​include object-oriented programming languages ​​such as Java and C++, as well as conventional procedural programming languages ​​such as the "C" language or similar programming languages.

[0140] Furthermore, embodiments of this specification also provide a computer-readable storage medium having a computer program stored thereon, the computer program being executed by a processor to train a multiphysics coupling computation model according to various embodiments of this specification as described in the "Exemplary Methods" section above.

[0141] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this specification can include non-volatile and / or volatile memory. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory may include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in a variety of forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), RAMbus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0142] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0143] The embodiments described above are merely illustrative of several implementation methods outlined in this specification. While the descriptions are specific and detailed, they should not be construed as limiting the scope of the solutions provided in this specification. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this specification, and these all fall within the scope of protection of this specification. Therefore, the scope of protection for this patent should be determined by the appended claims.

Claims

1. A training method for a multiphysics coupled computational model, characterized in that, include: The initial information of the physical field to be solved is constructed. The initial information includes the physical field information of the physical field to be solved and the information of the external input parameters corresponding to the physical field to be solved. The physical field information includes the physical field to be solved and the governing equations, geometric model, boundary conditions and initial conditions corresponding to the physical field to be solved. The information of the external input parameters includes the external input parameters and the functional relationship corresponding to the external input parameters. Based on the initial information of the physical field to be solved, a physical information neural operator model is constructed and trained, wherein the physical information neural operator model represents the mapping relationship between the physical fields to be solved; A multi-physics-multi-scale neural network is constructed based on the physical information neural operator model, and trained based on the physical field trial functions of multiple physical fields to be solved. The multi-physics-multi-scale neural network represents the coupling mapping relationship between the physical fields to be solved. The input of the multi-physics-multi-scale neural network is the physical field trial function of the physical field to be solved, and the output is the coupling trial function of the physical field to be solved. The multiphysics coupling computation model includes at least one trained physical information neural operator model and a multiphysics-multiscale neural network.

2. The training method according to claim 1, characterized in that, Based on the initial information of the physical field to be solved, a physical information neural operator model is constructed and trained, including: Based on the physical field to be solved, the governing equations corresponding to the physical field to be solved, the external input parameters corresponding to the physical field to be solved, and the corresponding functional relationships, an initial operator model is constructed. The initial operator model includes a branch network and a backbone network. The branch matrix output by the branch network and the backbone matrix output by the backbone network can reflect the physical field trial function of the physical field to be solved. Based on the governing equations corresponding to the physical field to be solved and the functional relationship between the external input parameters corresponding to the physical field to be solved, the partial differential equations are derived. Construct a loss function based on the partial differential equations corresponding to the physical fields to be solved; Constraints are constructed based on the geometric model, boundary conditions, and initial conditions of the physical field to be solved; Based on the initial operator model, the loss function, and the constraints, the initial operator model is trained using training data to obtain a physical information neural operator model. The training data includes the numerical values ​​of the physical field to be solved and the numerical values ​​of the external input parameters corresponding to the physical field to be solved.

3. The training method according to claim 2, characterized in that, The loss function is constructed based on the partial differential equations corresponding to the physical field to be solved, including: Obtain the physical field trial function of the physical field to be solved; Based on the physical field trial function of the physical field to be solved, create the virtual scalar variables and virtual vector variables required by the zero coordinate transformation module; Calculate the auxiliary derivative tensor based on the virtual scalar variable and the virtual vector variable; Based on the virtual scalar variable, the virtual vector variable, and the auxiliary derivative tensor, calculate the second derivative of the physical field trial function with respect to spatial coordinates; A loss function is constructed based on the partial differential equations corresponding to the physical field to be solved and the second derivatives of the physical field trial functions with respect to spatial coordinates.

4. The training method according to claim 1, characterized in that, A multi-physics, multi-scale neural network is constructed based on a physical information neural operator model, and trained using physical field trial functions of multiple physical fields to be solved, including: Constructing a multi-physics-multi-scale initial neural network based on fully connected layers; The physical information neural operator model corresponding to the physical field to be solved is called into the multi-physics-multi-scale initial neural network to form a multi-physics-multi-scale neural network. The initial physical field trial functions of multiple physical fields to be solved are input into the multi-physics-multi-scale neural network for coupled calculation to obtain the coupled trial function of each physical field to be solved. Calculate the loss value corresponding to each loss function included in the composite loss function, wherein the composite loss function includes a coupling loss function, which is constructed from multiple initial physical field trial functions and coupling trial functions of the physical fields to be solved; When the loss value corresponding to each loss function is less than or equal to the corresponding preset threshold, the coupling trial function of each physical field to be solved is output, and the training ends; When the loss value corresponding to any loss function is greater than the corresponding preset threshold, the coupling trial function of the physical field to be solved is used as the initial physical field trial function of the physical field to be solved, and the process returns to the step: inputting the initial physical field trial functions of multiple physical fields to be solved into the multi-physics-multi-scale neural network for coupling calculation to obtain the coupling trial function of each physical field to be solved.

5. The training method according to claim 4, characterized in that, The initial physical field trial functions of multiple physical fields to be solved are input into the multi-physics-multi-scale neural network for coupled computation, resulting in the coupled trial function of each physical field to be solved, including: The corresponding physical information neural operator model is invoked based on the physical field to be solved; The initial physical field trial function of the physical field to be solved is input into the corresponding physical information neural operator model for calculation, and the coupling function of the physical field to be solved associated with the physical field to be solved is obtained.

6. The training method according to claim 5, characterized in that, Training a multi-physics, multi-scale neural network based on the physical field trial functions of multiple unsolved physical fields also includes: When the loss value corresponding to any loss function is greater than the corresponding preset threshold, the number of iterations is incremented by one. When the number of iterations is greater than or equal to the maximum number of iterations, the predicted value of the physical field to be solved is output, and the training ends. When the number of iterations is less than the maximum number of iterations, the coupled trial function of the physical field to be solved is used as the initial physical field trial function of the physical field to be solved, and the process returns to the step: inputting the initial physical field trial functions of multiple physical fields to be solved into the multi-physics-multi-scale neural network for coupled calculation to obtain the coupled trial function of each physical field to be solved.

7. The training method according to claim 4, characterized in that, The composite loss function also includes a physical loss function and a data loss function; Among these, training a multi-physics-multi-scale neural network based on the physical field trial functions of multiple physical fields to be solved also includes: When the coupling loss value corresponding to the coupling loss function is greater than the corresponding preset threshold, an adaptive algorithm is used to update the weight of the coupling loss function in the composite loss function calculated in the current iteration. The coupling loss function is updated based on the updated weights of the coupling loss function in the composite loss function, the coupling trial function corresponding to the current iteration, and the initial physics trial function.

8. The training method according to claim 4, characterized in that, The training method also includes: The number of physical information neural operator models is determined based on the number of physical fields to be solved and the external input parameters corresponding to the physical fields to be solved.

9. The training method according to claim 4, characterized in that, Training a multi-physics, multi-scale neural network based on the physical field trial functions of multiple unsolved physical fields also includes: The mean square error is calculated based on the coupling trial function of each physical field to be solved and the actual physical field trial function of the physical field to be solved; When the mean square error is greater than or equal to the preset error, the coupling trial function of the physical field to be solved is used as the initial physical field trial function of the physical field to be solved, and the process returns to the step: inputting the initial physical field trial functions of multiple physical fields to be solved into the multi-physics-multi-scale neural network for coupling calculation to obtain the coupling trial function of each physical field to be solved.

10. A multiphysics coupling calculation method, characterized in that, include: Obtain the real-time values ​​of the external input parameters corresponding to the physical field to be solved; The real-time values ​​of the external input parameters are input into the multiphysics coupling calculation model for calculation to obtain the predicted value of the physical field to be solved. The multiphysics coupling calculation model is trained using the training method described in any one of claims 1-9.

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