Multi-subnetwork collaborative modeling method for unsupervised solution of multi-domain electromagnetic field

Abstract

The invention discloses a multi-sub-network collaborative modeling method for unsupervised solution of a multi-domain electromagnetic field, and the method comprises the steps: carrying out the partitioning of a computational domain in a solving region according to medium parameters and field source information, and dividing the whole region into a plurality of physical sub-regions; a neural network model is independently deployed in each sub-region and is used for fitting electromagnetic field distribution in the region, so that the learning ability and modeling precision of the network for local physical characteristic changes are improved; a cross-network continuity coupling mechanism is constructed between sub-regions, and a continuity loss function of a magnetic field tangential component corresponding to a vector magnetic potential value continuity constraint and a space derivative thereof is introduced at an interface of adjacent regions, so that physical coupling between sub-networks is realized; and the boundary continuity of the electromagnetic field solution among different regions and the consistency of the overall solution are ensured. The method has the advantages of being high in universality, high in capacity of adapting to complex boundary conditions and the like, and is suitable for modeling and simulation calculation of multi-region, multi-material and multi-source coupling field problems.

Description

Technical Field

[0001] The present invention relates to the intersection of electromagnetic field computing and artificial intelligence, and specifically to an unsupervised solution method for multi-domain electromagnetic field problems, which adopts a multi-subnetwork collaborative modeling strategy and belongs to the technical field of electromagnetic field intelligent computing and physical information neural network modeling. Background Art

[0002] In the numerical calculation of electromagnetic fields, traditional numerical methods such as the finite element method (FEM) face challenges such as difficult meshing, high consumption of computing resources, and poor adaptability when dealing with complex electromagnetic problems involving multiple regions, multiple materials, and multiple source couplings. This is especially true when faced with complex geometric structures or areas where the local medium undergoes drastic changes, making it difficult to strike a balance between accuracy and efficiency.

[0003] In recent years, electromagnetic field modeling methods based on physics-informed neural networks (PINNs) have garnered widespread attention. PINNs utilize partial differential equation residuals as network losses for training, enabling end-to-end solutions without relying on large amounts of labeled data. This approach is highly scalable and versatile. However, single neural networks often struggle to balance local expressiveness with global coordination when processing electromagnetic properties across scales and regions, resulting in low accuracy and unstable training.

[0004] Therefore, there is an urgent need for an efficient modeling method for complex multi-domain electromagnetic field problems to improve the local fitting ability of the network, the consistency of physical coupling between regions, and the accuracy of key boundary areas, so as to achieve efficient and accurate modeling and solution of complex electromagnetic problems. Summary of the Invention

[0005] Technical problem: The purpose of the present invention is to provide a multi-subnetwork collaborative modeling method for unsupervised solution of multi-domain electromagnetic fields. The technical problems to be solved mainly include: 1. High-precision modeling of electromagnetic field characteristics under multi-region media; 2. Consistent coupling of physical information between networks; 3. Dependence of traditional neural network electromagnetic prediction process on labeled data.

[0006] Technical solution: To achieve the above objectives, the present invention provides the following technical solutions for a multi-subnetwork collaborative modeling method for unsupervised solution of multi-domain electromagnetic fields:

[0007] The method adopts a regional network deployment strategy, an interface continuity coupling strategy, an unsupervised training mechanism, and a multi-subnetwork collaborative modeling strategy. The computational domain is partitioned within the solution area based on medium parameters and field source information, and the overall area is split into multiple physical sub-areas. A neural network model is independently deployed within each sub-area to fit the electromagnetic field distribution within the area, thereby improving the network's learning ability and modeling accuracy for changes in local physical properties. By constructing a cross-network continuity coupling mechanism between sub-areas, a vector magnetic potential A is introduced at the interface between adjacent areas. z The value continuity constraint of and the continuity loss function of the tangential component of its spatial derivative H are used to realize the physical coupling between the sub-networks and ensure the boundary continuity of the electromagnetic field solution in different regions and the consistency of the overall solution.

[0008] The multi-subnetwork collaborative modeling strategy specifically includes the following steps:

[0009] Step 1: Based on the physical characteristics of each region in the electromagnetic field problem, divide the solution area into several physical sub-regions;

[0010] Step 2: Deploy an independent neural network model in each sub-region to learn and fit the distribution of the electromagnetic field in the region;

[0011] Step 3: At the interface between any two adjacent sub-regions, the vector magnetic potential continuity constraint and the continuity loss of the tangential component of the magnetic field represented by its derivative are imposed to achieve physical information coupling between multiple networks;

[0012] Step 4: Use the basic partial differential equations of the electromagnetic field to construct a physical residual loss function, and perform end-to-end training on multiple sub-networks simultaneously under unsupervised conditions to obtain the overall electromagnetic field solution that meets the constraints of physical laws.

[0013] The sub-areas are divided based on dielectric parameters including dielectric constant, magnetic permeability, electrical conductivity and current density and field source distribution characteristics.

[0014] The vector magnetic potential is the vector magnetic potential A in the two-dimensional problem z , the derivative H is A z The partial derivatives with respect to the spatial variables are used to construct the tangential continuity loss of the magnetic field intensity H.

[0015] The end-to-end training uses a loss function that is a weighted combination of multiple sub-region physical residual losses, interface continuity losses, and boundary condition losses.

[0016] The regional network deployment strategy divides the overall calculation area into multiple sub-areas based on the physical medium parameters and field source distribution of different areas in the solution domain; and independently deploys a neural network model in each sub-area to learn and predict the electromagnetic field distribution in the area.

[0017] The interface continuity coupling strategy constructs the continuity loss term of the vector magnetic potential and the continuity loss term of its derivative at the interface of each sub-region; by explicitly adding these physical boundary constraints to the loss function, parameter coupling and physical consistency between different sub-networks are achieved.

[0018] In the unsupervised training mechanism, all sub-networks are jointly trained under unsupervised conditions; the training objective consists of the physical partial differential equation residual loss, interface continuity loss and boundary condition loss, and does not rely on explicit simulation data or observation samples, achieving end-to-end solution.

[0019] This method does not rely on electromagnetic field observation data or finite element simulation results. It is completely based on the physical constraints of the residual and boundary continuity of the partial differential equations constructed by Maxwell's equations. It achieves end-to-end electromagnetic field solution through unsupervised optimization of neural networks, that is, unsupervised modeling and solution are performed completely through physical constraints.

[0020] Beneficial effects: Improve regional adaptability and modeling accuracy: Adopt a regional neural network deployment strategy, build a local exclusive network model for different physical medium parameters and field source characteristics, significantly enhance the neural network's ability to express heterogeneous media and local characteristics, and improve the overall solution accuracy. Ensure physical consistency and global continuity: By introducing continuity loss constraints on the vector magnetic potential and the tangential component of the magnetic field at the interface, the numerical incoherence problem of traditional PINNs in the interface area is avoided. Achieve an unsupervised and efficient solution mechanism: The proposed method relies entirely on the basic control equations of the electromagnetic field and the continuity physical conditions. It does not require explicit simulation data or measurement samples, has a high degree of unsupervised modeling capabilities, reduces dependence on data, and improves versatility and migration capabilities. It has the advantages of strong versatility and strong adaptability to complex boundary conditions. It is suitable for modeling and simulation calculations of multi-region, multi-material, and multi-source coupled field problems. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 This is the overall architecture diagram of the present invention.

[0022] Figure 2 Schematic diagram of the PDEs loss construction process. DETAILED DESCRIPTION

[0023] The multi-subnetwork collaborative modeling method for unsupervised solution of multi-domain electromagnetic fields of the present invention adopts a regional network deployment strategy, an interface continuity coupling strategy, an unsupervised training mechanism, and a multi-subnetwork collaborative modeling strategy. The calculation domain is partitioned according to the medium parameters and field source information in the solution area, and the overall area is split into multiple physical sub-areas. A neural network model is independently deployed in each sub-area to fit the electromagnetic field distribution in the area, thereby improving the network's learning ability and modeling accuracy for changes in local physical properties. By constructing a cross-network continuity coupling mechanism between sub-areas, a vector magnetic potential A is introduced at the interface between adjacent areas. z The value continuity constraint of and the continuity loss function of the tangential component of its spatial derivative H are used to realize the physical coupling between the sub-networks and ensure the boundary continuity of the electromagnetic field solution in different regions and the consistency of the overall solution.

[0024] in:

[0025] Regional network deployment strategy: The overall calculation area is divided into multiple sub-areas based on the physical medium parameters and field source distribution in different areas of the solution domain; a neural network model is independently deployed in each sub-area to learn and predict the electromagnetic field distribution in the area.

[0026] Interface continuity coupling strategy: At the interface of each sub-region, the continuity loss term of the vector magnetic potential and the continuity loss term of its derivative are constructed respectively; by explicitly adding these physical boundary constraints in the loss function, parameter coupling and physical consistency between different sub-networks are achieved.

[0027] Unsupervised training mechanism: All sub-networks are jointly trained under unsupervised conditions; the training objective consists of the physical partial differential equation residual loss, interface continuity loss and boundary condition loss, and does not rely on explicit simulation data or observation samples to achieve end-to-end solution.

[0028] The multi-subnetwork collaborative modeling strategy specifically includes the following steps:

[0029] Step 1: Problem setting: Divide the electromagnetic field action area into physical sub-areas, each with different magnetic permeability and current density distribution;

[0030] Step 2: Network construction: Deploy an independent neural network model in each sub-region. The network input is the physical space feature information, and the network residual is calculated according to Maxwell's equations. This is used to learn and fit the distribution of the electromagnetic field in this region.

[0031] Step 3: Coupling constraints: At the interface between any two adjacent sub-regions, apply the vector magnetic potential continuity constraint and the continuity loss of the tangential component of the magnetic field represented by its derivative to achieve physical information coupling between multiple networks; clarify the physical continuity conditions:

[0032]

[0033] Among them, A z1 、A z2 are the vector magnetic potentials on both sides of the interface, H 1t With H 2t are the tangential components of the magnetic field on both sides of the interface.

[0034] Introducing the above continuity conditions into the total loss of the network training process;

[0035]

[0036] in, is the residual of the equation of each independent sub-network in step 2; L coupling The network coupling loss, L boundary Boundary loss constructed for the outer boundary of the region.

[0037] Step 4: Optimize the training. Use AdamW to minimize the total loss constructed in step 3 as the optimization goal. Use a dynamic learning rate adjustment strategy to optimize the network training. Adjust and optimize the parameters of all networks constructed in step 2. Finally, accurately predict the vector magnetic potential and further calculate other physical quantities.

[0038] This method does not rely on electromagnetic field observation data or finite element simulation results. It is completely based on the physical constraints of the residual and boundary continuity of the partial differential equations constructed by Maxwell's equations. It achieves end-to-end electromagnetic field solution through unsupervised optimization of neural networks, that is, unsupervised modeling and solution are performed completely through physical constraints.

Claims

1. A multi-subnetwork collaborative modeling method for unsupervised solution of multi-domain electromagnetic fields, characterized by: The method adopts a regional network deployment strategy, an interface continuity coupling strategy, an unsupervised training mechanism, and a multi-subnetwork collaborative modeling strategy. The computational domain is partitioned within the solution area based on medium parameters and field source information, and the overall area is split into multiple physical sub-areas. A neural network model is independently deployed within each sub-area to fit the electromagnetic field distribution within the area, thereby improving the network's learning ability and modeling accuracy for changes in local physical properties. By constructing a cross-network continuity coupling mechanism between sub-areas, a vector magnetic potential A is introduced at the interface between adjacent areas. z The value continuity constraint of and the continuity loss function of the tangential component of its spatial derivative H are used to realize the physical coupling between the sub-networks and ensure the boundary continuity of the electromagnetic field solution in different regions and the consistency of the overall solution.

2. The multi-subnetwork collaborative modeling method for unsupervised solution of multi-domain electromagnetic fields according to claim 1, characterized in that: The multi-subnetwork collaborative modeling strategy specifically includes the following steps: Step 1: Based on the physical characteristics of each region in the electromagnetic field problem, divide the solution area into several physical sub-regions; Step 2: Deploy an independent neural network model in each sub-region to learn and fit the distribution of the electromagnetic field in the region; Step 3: At the interface between any two adjacent sub-regions, the vector magnetic potential continuity constraint and the continuity loss of the tangential component of the magnetic field represented by its derivative are imposed to achieve physical information coupling between multiple networks; Step 4: Use the basic partial differential equations of the electromagnetic field to construct a physical residual loss function, and perform end-to-end training on multiple sub-networks simultaneously under unsupervised conditions to obtain the overall electromagnetic field solution that meets the constraints of physical laws.

3. The multi-subnetwork collaborative modeling method for unsupervised solution of multi-domain electromagnetic fields according to claim 1, characterized in that: The sub-areas are divided based on dielectric parameters including dielectric constant, magnetic permeability, electrical conductivity and current density and field source distribution characteristics.

4. The multi-subnetwork collaborative modeling method for unsupervised solution of multi-domain electromagnetic fields according to claim 1, characterized in that: The vector magnetic potential is the vector magnetic potential A in the two-dimensional problem z , the derivative H is A z The partial derivatives with respect to the spatial variables are used to construct the tangential continuity loss of the magnetic field intensity H.

5. The multi-subnetwork collaborative modeling method for unsupervised solution of multi-domain electromagnetic fields according to claim 1, characterized in that: The end-to-end training uses a loss function that is a weighted combination of multiple sub-region physical residual losses, interface continuity losses, and boundary condition losses.

6. The multi-subnetwork collaborative modeling method for unsupervised solution of multi-domain electromagnetic fields according to claim 1, characterized in that: The regional network deployment strategy divides the overall calculation area into multiple sub-areas based on the physical medium parameters and field source distribution of different areas in the solution domain; and independently deploys a neural network model in each sub-area to learn and predict the electromagnetic field distribution in the area.

7. The multi-subnetwork collaborative modeling method for unsupervised solution of multi-domain electromagnetic fields according to claim 1, characterized in that: The interface continuity coupling strategy constructs the continuity loss term of the vector magnetic potential and the continuity loss term of its derivative at the interface of each sub-region; by explicitly adding these physical boundary constraints to the loss function, parameter coupling and physical consistency between different sub-networks are achieved.

8. The multi-subnetwork collaborative modeling method for unsupervised solution of multi-domain electromagnetic fields according to claim 1, characterized in that: In the unsupervised training mechanism, all sub-networks are jointly trained under unsupervised conditions; The training objective consists of the residual loss of the physical partial differential equation, the interface continuity loss, and the boundary condition loss. It does not rely on explicit simulation data or observation samples and achieves end-to-end solution.

9. The multi-subnetwork collaborative modeling method for unsupervised solution of multi-domain electromagnetic fields according to claim 1, characterized in that: This method does not rely on electromagnetic field observation data or finite element simulation results. It is completely based on the physical constraints of the residual and boundary continuity of the partial differential equations constructed by Maxwell's equations. It achieves end-to-end electromagnetic field solution through unsupervised optimization of neural networks, that is, unsupervised modeling and solution are performed completely through physical constraints.

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