Optimization method and device of equivalent circuit operator

Abstract

The application is suitable for the technical field of electromagnetic simulation, and provides an optimization method and device for equivalent circuit operators, comprising: obtaining a first discrete mesh graph of a conductor structure; constructing a second discrete mesh graph of the conductor structure according to a plurality of key nodes and a plurality of key edges extracted from the first discrete mesh graph; the mesh granularity of the first discrete mesh graph is greater than the mesh granularity of the second discrete mesh graph. According to a partial element equivalent circuit algorithm, an equivalent circuit operator corresponding to the second discrete mesh graph is determined; the equivalent circuit operator comprises an inductance matrix and a capacitance matrix. The equivalent circuit operator is optimized through a structured matrix network to obtain a target equivalent circuit operator; the structured matrix network is constructed based on preset circuit physical constraints and a circuit topological relationship of the conductor structure. The method realizes order reduction, light weighting and physical compliance of the equivalent circuit model without losing main electromagnetic characteristics, and significantly improves electromagnetic modeling and simulation efficiency.

Description

Technical Field

[0001] This application belongs to the field of electromagnetic simulation technology, and in particular relates to an optimization method and apparatus for equivalent circuit operators. Background Technology

[0002] With the continuous development of high-speed, high-density electronic systems and heterogeneous integrated packaging technologies, the dual requirements of computational accuracy and efficiency in electromagnetic simulation are becoming increasingly prominent. In complex structures composed of multiple chips, interposers, redistribution layers, and packaged embedded devices, there are common characteristics such as spatial non-uniformity of dielectric constant, coexistence of multi-scale geometric structures, and three-dimensional strongly coupled field distribution. Traditional full-wave numerical methods have significant bottlenecks in terms of computation time, memory consumption, and scalability.

[0003] The Partial Element Equivalent Circuit (PEEC) method is widely used in the current engineering field for interconnect and packaging modeling. This method has clear physical meaning and is compatible with conventional circuit simulation processes. However, when constructing equivalent circuits for complex conductor structures using related improvement techniques, there is still a problem of low electromagnetic simulation efficiency in large-scale integrated circuit problems due to the complexity of the equivalent circuit operators. Summary of the Invention

[0004] This application provides an optimization method and apparatus for equivalent circuit operators, which can solve the problem of low electromagnetic simulation efficiency in large-scale integrated circuit problems caused by the complexity of constructing equivalent circuits for complex conductor structures in existing methods.

[0005] In a first aspect, embodiments of this application provide an optimization method for an equivalent circuit operator, the method comprising: Obtain the first discrete mesh plot of the conductor structure; Based on multiple key nodes and multiple key edges extracted from the first discrete mesh graph, a second discrete mesh graph of the conductor structure is constructed; wherein the mesh granularity of the first discrete mesh graph is larger than that of the second discrete mesh graph. Based on the partial equivalent circuit algorithm, the equivalent circuit operator corresponding to the second discrete mesh diagram is determined; wherein, the equivalent circuit operator includes an inductance matrix and a capacitance matrix; The equivalent circuit operator is optimized by a structured matrix network to obtain the target equivalent circuit operator; wherein the structured matrix network is constructed based on the preset circuit physical constraints and the circuit topology relationship of the conductor structure.

[0006] In one possible implementation of the first aspect, constructing a second discrete mesh graph of the conductor structure based on a plurality of key nodes and a plurality of key edges extracted from the first discrete mesh graph includes: Based on prior physical knowledge, the multiple key nodes and multiple key edges are extracted from the first discrete mesh graph; wherein, the key nodes are used to characterize the charge degree of freedom of the conductor structure, and the key edges are used to characterize the current degree of freedom of the conductor structure. Based on the multiple key nodes and multiple key edges, the first discrete mesh graph is simplified into multiple rectangular elements using a rectangular mesh; wherein, each rectangular element includes a geometric center point and a branch; the branch connects adjacent geometric center points; each rectangular element includes charge elements and current elements, the geometric center point is equivalent to the charge element, and the branch is equivalent to the current element; The multiple key nodes are mapped to the geometric center points of the multiple rectangular elements, and the multiple key edges are mapped to the branches of the multiple rectangular elements, so as to construct the second discrete mesh graph.

[0007] In one possible implementation of the first aspect, determining the equivalent circuit operator corresponding to the second discrete mesh diagram according to the partial element equivalent circuit algorithm includes: Based on the geometric dimensions, relative positions, and dielectric parameters of the multiple rectangular surface elements in the second discrete mesh diagram, an integral equation for the electric field is established. Based on the electric field integral equation, the coupling relationship between the surface charge distribution and potential distribution of the conductor structure is discretized to obtain the potential coefficient matrix; The capacitance matrix is ​​calculated based on the potential coefficient matrix; wherein the capacitance matrix is ​​used to characterize the electrostatic coupling characteristics between each of the rectangular surface elements. Based on the relationship between current continuity and magnetic field integral, the coupling relationship between branch current and magnetic flux of the conductor structure is discretized to obtain the inductance matrix; wherein, the inductance matrix is ​​used to characterize the electromagnetic coupling characteristics between each branch. The capacitor matrix and the inductance matrix are combined to obtain the equivalent circuit operator that characterizes the circuit properties of the second discrete grid diagram.

[0008] In one possible implementation of the first aspect, optimizing the equivalent circuit operator through a structured matrix network to obtain the target equivalent circuit operator includes: Obtain the first state vector obtained by performing a transient simulation of the conductor structure under the first discrete mesh diagram using a partial element equivalent circuit operator, and the second state vector obtained by performing a transient simulation of the conductor structure under the second discrete mesh diagram using a partial element equivalent circuit operator. The structured parameters of the capacitor matrix and the inductor matrix are initialized according to the preset circuit physical constraints to obtain the initial model parameters; wherein, the preset circuit physical constraints include the symmetry of the capacitor matrix, the first physical constraint that the off-diagonal elements of the capacitor matrix are negative and the sum of the rows and columns is positive, and the second physical constraint that the inductor matrix is ​​symmetric and positive definite. Based on the second state vector and the initial model parameters, the state at the next time step is predicted in the discrete time domain using the structured matrix network, resulting in a predicted state vector at the next time step. Based on the training loss value calculated by the next time step state prediction vector and the first state vector, the initial model parameters of the structured matrix network are iteratively updated until the training loss value meets the preset convergence condition, thereby obtaining the target equivalent circuit operator.

[0009] In one possible implementation of the first aspect, the initialization of structured parameters for the capacitor matrix and the inductor matrix according to the preset circuit physical constraints to obtain initial model parameters includes: Based on the first physical constraint, the capacitor matrix is ​​initialized with structured parameters to obtain the initial training parameters of the capacitor. Based on the second physical constraint, the inductance matrix is ​​initialized with structured parameters to obtain the initial training parameters of the inductance. The initial training parameters of the capacitor and the initial training parameters of the inductor are combined to form the initial model parameters.

[0010] In one possible implementation of the first aspect, the step of initializing the structured parameters of the capacitance matrix according to the first physical constraint to obtain initial training parameters for the capacitance includes: Extract the negatives of the off-diagonal terms from the normalized capacitance matrix to obtain the processed capacitance matrix, and perform a soft inverse transformation on the lower triangular part of the extracted processed capacitance matrix to obtain the first initialization training parameters. The difference vector obtained by subtracting the diagonal term vector of the capacitance matrix from the row sum vector of the processed capacitance matrix is ​​subjected to a soft inverse transformation to obtain the second initialization training parameters. The first initial training parameters are subjected to a soft addition transformation to obtain a first transformation matrix, and an initial off-diagonal matrix is ​​constructed based on the first symmetric matrix of the first transformation matrix. The second initialization training parameters are subjected to a soft addition transformation to obtain a second transformation vector. The row sum vector of the first symmetric matrix is ​​added to the second transformation vector to obtain an initial diagonal term vector. Based on the constructed first symmetric matrix and the initial diagonal term vector, the initial training parameters of the capacitor satisfy the first physical constraint are formed.

[0011] In one possible implementation of the first aspect, the step of initializing the structured parameters of the inductor matrix according to the second physical constraint to obtain initial inductor training parameters includes: The inductance matrix is ​​subjected to symmetric positive definite processing and normalization processing to obtain the processed inductance matrix; The processed inductance matrix is ​​subjected to Choleski decomposition to obtain the decomposition result; The decomposition result is split into two matrices, which are used as the third initialization training parameter and the fourth initialization training parameter, respectively. The third initialization training parameter is the lower triangular matrix in the decomposition result, and the fourth initialization training parameter is the vector obtained by performing a soft inverse transformation on the diagonal of the decomposition result. After the fourth initialization training parameters are transformed by soft addition, they are combined with the third initialization training parameters to form a lower triangular matrix, thereby obtaining the inductor initial training parameters that satisfy the second physical constraint.

[0012] In one possible implementation of the first aspect, the step of predicting the state at the next time step in the discrete time domain using the structured matrix network based on the second state vector and the initial model parameters to obtain the next time step state prediction vector includes: The initial model parameters are embedded into the state space equation of the structured matrix network to obtain the core matrix of the state space equation; The core matrix is ​​discretized using the trapezoidal integral discretization method to obtain an iterative matrix in discrete recursive form; The second state vector is used as input, and implicit time iteration is performed through the iteration matrix; After the implicit time iteration operation is completed, the state prediction vector for the next time step is output.

[0013] In one possible implementation of the first aspect, the step of iteratively updating the initial model parameters of the structured matrix network based on the training loss value calculated using the next-time state prediction vector and the first state vector, until the training loss value satisfies a preset convergence condition, to obtain the target equivalent circuit operator, includes: The voltage and current vector and voltage and current change vector in the next moment state prediction vector are compared with the voltage and current vector and voltage and current change vector in the first state vector, respectively, and the voltage and current error and change error are calculated. The data loss value is obtained based on the voltage and current errors and the change error; Obtain the regularization loss value used to maintain the equivalent circuit operator in satisfying the preset circuit physical constraints; The regularization loss value and the data loss value are weighted and combined to obtain the training loss value; The training loss value is backpropagated to obtain the gradient of the initial model parameters, and the initial model parameters are iteratively updated using an adaptive moment estimation optimization algorithm. Repeat the above steps of calculating the training loss value and updating the initial model parameters until the training loss value meets the preset convergence condition and the iteration stops, thus obtaining the target equivalent circuit operator.

[0014] Secondly, embodiments of this application provide an optimization apparatus for an equivalent circuit operator, comprising: The acquisition module is used to acquire the first discrete grid diagram of the conductor structure; A construction module is used to construct a second discrete mesh graph of the conductor structure based on multiple key nodes and multiple key edges extracted from the first discrete mesh graph; wherein the mesh granularity of the first discrete mesh graph is larger than the mesh granularity of the second discrete mesh graph. The determination module is used to determine the equivalent circuit operator corresponding to the second discrete mesh diagram based on the partial element equivalent circuit algorithm; wherein, the equivalent circuit operator includes an inductance matrix and a capacitance matrix; An optimization module is used to optimize the equivalent circuit operator through a structured matrix network to obtain a target equivalent circuit operator; wherein the structured matrix network is constructed based on preset circuit physical constraints and the circuit topology relationship of the conductor structure.

[0015] Thirdly, embodiments of this application provide a terminal device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the optimization method of the equivalent circuit operator described in any of the preceding claims.

[0016] Fourthly, embodiments of this application provide a computer-readable storage medium storing a computer program that, when executed by a processor, implements the optimization method for the equivalent circuit operator described in any of the preceding claims.

[0017] Fifthly, embodiments of this application provide a computer program product that, when run on a terminal device, causes the terminal device to execute the optimization method for the equivalent circuit operator described in any of the first aspects.

[0018] The beneficial effects of the embodiments in this application compared with the prior art are: This application provides an optimization method for equivalent circuit operators. The method includes: first, obtaining a first discrete mesh diagram of the conductor structure; second, constructing a second discrete mesh diagram of the conductor structure based on multiple key nodes and edges extracted from the first discrete mesh diagram; wherein the mesh granularity of the first discrete mesh diagram is larger than that of the second discrete mesh diagram. Then, determining the equivalent circuit operator corresponding to the second discrete mesh diagram according to a partial equivalent circuit algorithm; wherein the equivalent circuit operator includes an inductance matrix and a capacitance matrix. Finally, optimizing the equivalent circuit operator using a structured matrix network to obtain a target equivalent circuit operator; wherein the structured matrix network is constructed based on preset circuit physical constraints and the circuit topology relationship of the conductor structure. This method extracts key structures through fine mesh coarsening, generates equivalent circuit operators using PEEC, and optimizes the inductance and capacitance matrices using a structured matrix network. Without losing the main electromagnetic characteristics, it achieves order reduction, lightweighting, and physical compliance of the equivalent circuit model, improving the accuracy of the equivalent circuit operator and significantly improving the efficiency of electromagnetic modeling and simulation. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in the embodiments of this application, 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 some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0020] Figure 1 This is a flowchart illustrating an optimization method for an equivalent circuit operator provided in an embodiment of this application; Figure 2 This is a schematic diagram illustrating state vector prediction using a structured matrix network according to an embodiment of this application; Figure 3 This is a flowchart illustrating an optimization method for equivalent circuit operators provided in an embodiment of this application; Figure 4 This is a schematic diagram of the structure of an optimization device for an equivalent circuit operator provided in an embodiment of this application; Figure 5 This is a schematic diagram of the structure of a terminal device provided in an embodiment of this application. Detailed Implementation

[0021] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application may also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods have been omitted so as not to obscure the description of this application with unnecessary detail.

[0022] It should be understood that, when used in this application specification and the appended claims, the term "comprising" indicates the presence of the described features, integrals, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or a collection thereof.

[0023] It should also be understood that the term “and / or” as used in this application specification and the appended claims means any combination of one or more of the associated listed items and all possible combinations, and includes such combinations.

[0024] As used in this application specification and the appended claims, the term "if" may be interpreted, depending on the context, as "when," "once," "in response to determination," or "in response to detection." Similarly, the phrase "if determined" or "if detected [the described condition or event]" may be interpreted, depending on the context, as meaning "once determined," "in response to determination," "once detected [the described condition or event]," or "in response to detection [the described condition or event]."

[0025] Furthermore, in the description of this application and the appended claims, the terms "first," "second," "third," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0026] References to "one embodiment" or "some embodiments" as described in this specification mean that one or more embodiments of this application include a specific feature, structure, or characteristic described in connection with that embodiment. Therefore, the phrases "in one embodiment," "in some embodiments," "in other embodiments," "in still other embodiments," etc., appearing in different parts of this specification do not necessarily refer to the same embodiment, but rather mean "one or more, but not all, embodiments," unless otherwise specifically emphasized. The terms "comprising," "including," "having," and variations thereof mean "including but not limited to," unless otherwise specifically emphasized.

[0027] With the development of high-speed, high-density electronic systems and heterogeneous integrated packaging, electromagnetic simulation has placed demands on both "high precision" and "high efficiency." In particular, in structures containing multiple chips, interposers, redistribution layers, and embedded devices, features such as spatial non-uniformity of dielectric constant, coexistence of multi-scale geometry, and three-dimensional strongly coupled field distribution often occur, putting traditional full-wave numerical solutions under significant pressure in terms of computation time, memory usage, and scalability.

[0028] In existing engineering techniques, Partial Element Equivalent Circuit (PEEC) algorithms are widely used for interconnect and package modeling due to their explicit circuit interpretation and compatibility with circuit simulation processes. For finite-size dielectrics and complex interconnect conductor structures, existing techniques include quasi-static partial element equivalent circuit methods (Compact PEEC, c-PEEC) and reduced-order compact partial element equivalent circuit operators (rc-PEEC). c-PEEC reduces the discretization scale by processing dielectric-related unknowns; rc-PEEC combines this with structure-preserving model order reduction (MOR) to obtain a more compact equivalent operator. These existing techniques offer advantages such as clear physical meaning, preservation of circuit interpretability, significant system size reduction compared to direct full-wave discretization, and good adaptability to complex package structures such as multilayer interconnects and via networks. However, the following obvious shortcomings still exist: First, the existing rc-PEEC operator construction process has a heavy computational burden. In heterogeneous integration and multi-layer interconnection scenarios, the traditional process needs to repeatedly perform geometric preprocessing, matrix assembly and model reduction, which is difficult to meet the needs of rapid iterative design. Second, in iterative design, layout optimization and frequent parameter updates scenarios, the overhead of repeated model generation is large, which is difficult to meet the needs of fast loop.

[0029] Beyond this fundamental theoretical research, some studies have introduced data-driven methods to train surrogate models of relevant topologies, replacing the tedious solution process. However, existing data-driven methods mostly focus on the direct mapping from geometry to response, lacking hard constraints on physical structure. When using unconstrained or weakly constrained neural network approximations, symmetry, passivity, reciprocity, and circuit topology consistency are easily disrupted, thus affecting broadband stability and co-simulation reliability.

[0030] In summary, while existing technologies have made progress in scaling, a contradiction remains between the ability to rapidly reconstruct operators and the ability to strictly maintain physical structure. The industry urgently needs a technical solution that can rapidly recover reduced-order compact partial-element equivalent circuit operators from sparse time-domain data while simultaneously strictly satisfying symmetry, positive definiteness, and topological constraints, in order to balance modeling efficiency, physical consistency, and simulation stability.

[0031] To address this, this application provides an optimization method for equivalent circuit operators. First, it introduces a high-performance, lightweight PEEC coarse operator fast extraction and solution engine, significantly compressing the model size while maintaining physical consistency. Simultaneously, it designs a parameter learning method based on a Structured Matrix Network (SMN). This network does not perform black-box mapping but learns key operator blocks under fixed topological constraints, incorporating symmetry, positive definiteness, and circuit connection relationships into the model structure. This allows coupling dynamics to be explicitly constrained during training, ensuring that the learned parameters always conform to the physical laws of the circuit.

[0032] Please see Figure 1 , Figure 1 This is a flowchart illustrating an optimization method for an equivalent circuit operator according to an embodiment of this application. As an example and not a limitation, this method can be applied to or run in a terminal device, and the method includes: S11. Obtain the first discrete mesh diagram of the conductor structure.

[0033] S12. Based on the multiple key nodes and multiple key edges extracted from the first discrete mesh graph, construct a second discrete mesh graph of the conductor structure; wherein the mesh granularity of the first discrete mesh graph is greater than that of the second discrete mesh graph.

[0034] S13. Based on the partial element equivalent circuit algorithm, determine the equivalent circuit operator corresponding to the second discrete mesh diagram; wherein, the equivalent circuit operator includes the inductance matrix and the capacitance matrix.

[0035] S14. The equivalent circuit operator is optimized by a structured matrix network to obtain the target equivalent circuit operator; wherein, the structured matrix network is constructed based on the circuit topology relationship of the preset circuit physical constraints and conductor structure.

[0036] Equivalent circuit operators are mathematical operators used to describe the electromagnetic properties of conductors or transmission structures. In this embodiment, the equivalent circuit operators specifically refer to the inductance matrix (L) and the capacitance matrix (C). The inductance matrix describes the magnetic coupling, self-inductance, and mutual inductance between different parts of the conductor structure. The capacitance matrix describes the electric field coupling, self-capacitance, and mutual capacitance between different parts of the conductor structure. The inductance matrix (L) and the capacitance matrix (C) together constitute the core mathematical expression of the Partial Element Equivalent Circuit Algorithm (PEEC), which can be used for simulation, solution, or circuit modeling. The Partial Element Equivalent Circuit Algorithm (PEEC) is an electromagnetic numerical method that transforms any three-dimensional conductor structure into a lumped RLC equivalent circuit. By performing network partitioning on the structure, the continuous electromagnetic field problem is transformed into circuit matrix equations, which can then be solved using circuit simulation.

[0037] In this embodiment, a discrete mesh diagram can be understood as a geometrically discrete model formed by subdividing a continuous conductor geometry into small mesh units, nodes, and edges. The finer the mesh, the higher the accuracy, but the greater the computational cost. The first discrete mesh diagram is the original, high-precision, high-granularity mesh. While it can ensure physical realism, it has a large data volume, dense matrix, and is computationally expensive. The second discrete mesh diagram is a coarsened mesh reconstructed based on key nodes and key edges. The second discrete mesh diagram has a lower mesh granularity than the first, with coarser granularity and fewer nodes, which can be used for order reduction and computational acceleration. Key nodes and key edges refer to nodes and edges that significantly contribute to circuit characteristics and electromagnetic coupling, such as current concentration areas, strong electric / magnetic field regions, ports, and connection points. Retaining key nodes and key edges ensures that the main electrical characteristics are not lost after mesh coarsening.

[0038] A Structured Matrix Network (SMN) can be understood as a neural network or structured mathematical model used for matrix reduction, compression, and optimization. In this embodiment, the Structured Matrix Network is not a black-box network; it incorporates physical prior constraints to maintain the matrix structure (such as symmetry, positive definiteness, sparsity, etc.).

[0039] Preset circuit physical constraints can be understood as the electromagnetic physical laws that need to be satisfied in the PEEC method. For example, the inductor matrix must satisfy positive definiteness, the capacitor matrix must satisfy symmetric positive semi-definiteness, and mutual inductance / mutual capacitance must satisfy reciprocity. Circuit topology relationships refer to the geometric and topological information such as the connection method of the conductor structure, port positions, and mesh adjacency relationships, which are used to ensure that the optimized matrix still conforms to the circuit connection of the original conductor structure.

[0040] The target equivalent circuit operator yields high-precision, small-scale, and physically compliant target capacitance and inductance matrices without structured matrix network optimization. These target capacitance and inductance matrices can be used for rapid simulation and model deployment.

[0041] Specifically, in this embodiment, the conductor structure (such as chip interconnects, wires, antennas, shielding structures, etc.) is first subjected to fine mesh subdivision to obtain a first discrete mesh map of the conductor structure. This first discrete mesh map has a dense mesh and many nodes, which can accurately reflect the geometric details and electromagnetic field distribution of the conductor structure and provide high-precision original electromagnetic information.

[0042] Next, key nodes and edges that significantly contribute to circuit characteristics and electromagnetic coupling are extracted from the fine-grained mesh (i.e., the first discrete mesh graph). Based on the extracted key nodes and edges, a second discrete mesh graph (coarsened mesh) is constructed. Redundant meshes with little impact on electromagnetic properties are removed from the first discrete mesh graph, resulting in a coarser-grained second discrete mesh graph with fewer nodes, while still retaining the main electrical characteristics of the conductor structure. It should be understood that constructing the second discrete mesh graph is for order reduction, matrix size reduction, and acceleration of subsequent calculations.

[0043] Then, the PEEC method is applied to the coarsened second discrete mesh graph to generate the corresponding equivalent circuit operators (i.e., inductance matrix L and capacitance matrix C). At this point, the size of inductance matrix L and capacitance matrix C has been significantly reduced, but redundancy, density, and computational complexity may still exist. Finally, a structured matrix network (SMN) is used to compress, denoise, and regularize the structure of inductance matrix L and capacitance matrix C, forcibly satisfying physical constraints (positive definiteness, symmetry, reciprocity, etc.) while preserving the original circuit topology and electromagnetic properties. The final output is a lightweight, physically compliant, and highly accurate target equivalent circuit operator.

[0044] It is understood that this application provides an optimization method for equivalent circuit operators. The method includes: first, obtaining a first discrete mesh diagram of the conductor structure; and constructing a second discrete mesh diagram of the conductor structure based on multiple key nodes and multiple key edges extracted from the first discrete mesh diagram, wherein the mesh granularity of the first discrete mesh diagram is larger than that of the second discrete mesh diagram. Then, determining the equivalent circuit operator corresponding to the second discrete mesh diagram according to a partial equivalent circuit algorithm, wherein the equivalent circuit operator includes an inductance matrix and a capacitance matrix. Finally, optimizing the equivalent circuit operator using a structured matrix network to obtain a target equivalent circuit operator, wherein the structured matrix network is constructed based on preset circuit physical constraints and the circuit topology relationship of the conductor structure. This application extracts key structures through fine mesh extraction and coarsening, generates equivalent circuit operators using the PEEC method, and optimizes the inductance and capacitance matrices using a structured matrix network with embedded physical priors. Without losing the main electromagnetic characteristics, it achieves order reduction, lightweighting, and physical compliance of the equivalent circuit model, significantly improving the efficiency of electromagnetic modeling and simulation, and is particularly suitable for efficient electromagnetic simulation and circuit analysis on terminal devices.

[0045] In one possible implementation, a second discrete mesh graph of the conductor structure is constructed based on multiple key nodes and multiple key edges extracted from the first discrete mesh graph, including: Based on prior physical knowledge, multiple key nodes and key edges are extracted from the first discrete mesh graph. Key nodes characterize the charge degree of freedom of the conductor structure, and key edges characterize the current degree of freedom of the conductor structure.

[0046] Based on multiple key nodes and multiple key edges, the first discrete mesh graph is simplified into multiple rectangular elements using a rectangular grid. Each rectangular element includes a geometric center point and branches; branches connect adjacent geometric center points; and rectangular elements include charge elements and current elements, with the geometric center point equivalent to a charge element and the branches equivalent to current elements.

[0047] A second discrete mesh graph is constructed by mapping multiple key nodes to the geometric center points of multiple rectangular elements and mapping multiple key edges to the branches of multiple rectangular elements.

[0048] Prior physical knowledge refers to the fundamental electromagnetic and circuit laws that guide the identification of key features in a mesh. This can include charge distribution patterns, current conduction characteristics, electromagnetic coupling strength, and the relationship between conductor geometry and electrical properties. Prior physical knowledge can be used to distinguish between critical and redundant structures in the mesh diagram. Critical nodes are core nodes selected from the fine mesh (i.e., the first discrete mesh diagram) based on prior knowledge of circuit and electromagnetic physics, used to characterize the charge degrees of freedom of the conductor structure. Charge degrees of freedom reflect the accumulation, distribution, and variation characteristics of charge on the conductor. Critical nodes typically correspond to areas of concentrated charge, geometric inflection points, port locations, and other positions that significantly affect electrical properties. Critical edges are core mesh edges identified from the fine mesh (i.e., the first discrete mesh diagram) based on prior physical knowledge, used to characterize the current degrees of freedom of the conductor structure. Current degrees of freedom reflect the conduction path, direction, and coupling relationships of current within the conductor. Critical edges generally correspond to key transmission branches such as main current paths and strong electromagnetic coupling paths.

[0049] A rectangular mesh can be understood as a mapping process from geometry to physics, specifically a physical mapping of the second discrete mesh. A rectangular cell is the basic rectangular mesh unit formed after simplification of the rectangular mesh. A rectangular cell is the fundamental building block of the second discrete mesh graph, containing two core parts: a geometric center point and branches. The geometric center point is the geometric center location of each rectangular cell, also known as a node. As the equivalent feature point of each rectangular cell, it can be used to map key nodes, effectively representing the charge distribution characteristics of the region. A branch is a line segment connecting the geometric center points (i.e., nodes) of adjacent rectangular cells. Branches can be used to map key edges, effectively representing the current conduction and coupling paths between adjacent cells. A rectangular cell can include charge cells and current cells; that is, the geometric center point of a rectangular cell can be equivalent to a charge cell, used to represent electrostatic and capacitive coupling; the branches connecting rectangular cells can be equivalent to current cells, used to represent electromagnetic and inductive coupling. The charge element and the current element are characterized by the geometric length, width, orientation, and geometric center position of their respective rectangular elements.

[0050] The specific process of constructing the second discrete mesh diagram of the conductor structure can be as follows: First, based on the laws of electromagnetic physics and the electrical properties of the conductor (i.e., prior physical knowledge), the fine mesh (i.e., the first discrete mesh diagram) is screened, eliminating redundant nodes and edges that have minimal impact on charge and current distribution, retaining only the key nodes that determine the conductor's charge degree of freedom and the key edges that determine the current degree of freedom, thus extracting the core electrical features. Then, using the identified key nodes and key edges as a constraint skeleton, the fine mesh (i.e., the first discrete mesh diagram) is normalized and simplified using a regular rectangular mesh, transforming complex and irregular fine mesh units into structurally regular rectangular facets, thus standardizing and simplifying the mesh form. Finally, the key nodes representing the charge degree of freedom are mapped one-to-one to the geometric center points of each rectangular facet; the key edges representing the current degree of freedom are mapped one-to-one to branches connecting adjacent geometric center points, ultimately forming a coarsened second discrete mesh diagram that retains the core electrical characteristics.

[0051] It should be understood that in this embodiment, by representing the charge degree of freedom with key nodes and the current degree of freedom with key edges, and only eliminating redundant mesh information, the core electromagnetic and circuit characteristics of the conductor are fully preserved. Although this affects the modeling accuracy of the equivalent circuit, the physical logic of the model remains rigorous and interpretable. Simplifying the irregular fine mesh into regular rectangular elements results in a more unified and standardized mesh structure, significantly reducing the computational complexity and data processing volume of subsequent equivalent circuit operator solutions. The number of elements in the coarsened second discrete mesh is greatly reduced, resulting in a highly lightweight mesh that is more suitable for running on terminal devices with limited computing power, meeting the requirements of real-time modeling. Furthermore, the center points and branch structures of the rectangular elements can be directly connected to the partial element equivalent circuit algorithm, simplifying the generation process of the inductance matrix and capacitance matrix and improving the coherence of modeling.

[0052] In one possible implementation, the equivalent circuit operator corresponding to the second discrete mesh diagram is determined according to a partial element equivalent circuit algorithm, including: Based on the geometric dimensions, relative positions, and dielectric parameters of multiple rectangular elements in the second discrete mesh diagram, an integral equation for the electric field is established.

[0053] Based on the electric field integral equation, the coupling relationship between the surface charge distribution and potential distribution of the conductor structure is discretized to obtain the potential coefficient matrix.

[0054] The capacitance matrix is ​​calculated based on the potential coefficient matrix. The capacitance matrix characterizes the electrostatic coupling properties between the rectangular surface elements.

[0055] Based on the continuity of current and the integral relationship of magnetic field, the coupling relationship between branch current and magnetic flux in a conductor structure is discretized to obtain the inductance matrix. The inductance matrix is ​​used to characterize the electromagnetic coupling characteristics between each branch.

[0056] By combining the capacitance matrix and the inductance matrix, an equivalent circuit operator characterizing the circuit properties of the second discrete grid diagram is obtained.

[0057] Specifically, the process of determining the equivalent circuit operators (i.e., capacitance matrix and inductance matrix) corresponding to the second discrete mesh diagram is as follows: First, taking each rectangular surface element as the basic unit, an electric field integral equation describing the potential generated by the charge on the surface element is established based on its geometric dimensions, relative position, and dielectric parameters. The electric field integral equation (EFIF) is the electromagnetic field equation describing the integral relationship between the surface charge of the conductor and the external / induced electric field, and it is the core equation for calculating the capacitance matrix. Geometric dimensions refer to the length, width, thickness, and area of ​​the rectangular surface element, which directly affect the magnitude of capacitance and inductance. Relative position refers to the spatial relationship (distance, angle, overlap, etc.) between the rectangular surface elements and between branches, determining the strength of electrostatic and magnetic coupling. Dielectric parameters include the dielectric constant ε and permeability μ of the surrounding medium, affecting the propagation and coupling strength of the electric and magnetic fields.

[0058] Next, the continuous charge-potential integral relationship is discretized into rectangular surface elements, resulting in a system of linear equations. This transforms the field relationship into a matrix relationship, yielding the potential coefficient matrix. The capacitance matrix is ​​then calculated based on this matrix, reflecting the electrostatic coupling characteristics between the rectangular surface elements. Here, surface charge distribution refers to the equivalent charge density on each rectangular surface element of the conductor surface, represented by the total charge on the surface elements after mesh discretization. Potential distribution refers to the electric potential at the geometric center point of each rectangular surface element, reflecting the electric potential energy of that region. Discretization of the coupling relationship can be understood as the process of breaking down the continuous electric field integral equations into a system of algebraic equations for rectangular surface elements, transforming the field relationship into a matrix relationship. The potential coefficient matrix quantifies the influence coefficients of the charge of each discrete surface element on the potential of all surface elements. It is the core discretization operator connecting surface charge and space potential, and also a prerequisite matrix for solving the capacitance matrix. The electrostatic coupling characteristic represents the charge-potential constraint relationship between rectangular surface elements generated by the electric field, manifested as capacitive coupling.

[0059] Then, by applying magnetic field integrals to the branch currents, a current-magnetic flux relationship is established. Combining this with current continuity (KCL), the relationship between magnetic flux and current is discretized into a matrix form, yielding the inductance matrix. The inductance matrix reflects the magnetic coupling between branches. Current continuity refers to the branch currents satisfying Kirchhoff's current law, i.e., the inflow equals the outflow, which is the fundamental physical constraint for constructing the inductance matrix. The magnetic field integral relationship refers to the equation describing the integral relationship between branch currents and the spatial magnetic field and magnetic flux, used to calculate self-inductance and mutual inductance. Branch currents are the equivalent currents on the branches between rectangular surface elements, and are the fundamental variables characterizing the current degrees of freedom in the PEEC method. Magnetic flux is the magnetic flux generated by the branch currents and passing through the loop, exhibiting a linear relationship with the current. The electromagnetic coupling characteristic represents the current-magnetic flux constraint relationship generated between branches through the magnetic field, manifested as inductive coupling.

[0060] Finally, the inductance matrix and capacitance matrix are unified as the core mathematical expression to describe the electromagnetic properties of the second discrete grid diagram, forming an equivalent circuit operator for subsequent simulation, optimization, and solution.

[0061] In some examples, the electric field integral equation (EFIE) holds true on the surface of the conductor structure and can be used to approximate the capacitance matrix C and inductance matrix L under a second discrete grid diagram.

[0062] Among them, self-potential coefficient (The inverse of the capacitance coefficient) can be approximated as: ; in, The vacuum permittivity, For the first The feature dimensions of a rectangular element For the first The area of ​​each rectangular element. For the first The region of a rectangular element Let be the position vector of an observation point on a rectangular surface element. Let be the source point position vector on the rectangular surface element. Indicates the area around the observation point a tiny area element, Indicates revolving around the source point A tiny area element.

[0063] mutual potential coefficient Under the condition of midpoint approximation, it can be expressed as: , ; in, For the first The center position of the first rectangular element is related to the first... The distance between the centers of the rectangular face elements For the first The center position vector of each rectangular element For the first The center position vector of each rectangular element For the first The region of a rectangular element For the first The area of ​​each rectangular element.

[0064] For a width of , length is The The region of a rectangular element , For discrete basis function vectors, The direction is parallel to the branch current. Among them, ; For the first A position vector of an observation point on a rectangular surface element.

[0065] Among them, the self-inductance terms of part of the inductance matrix It can be represented as: ; in, It is the analytic term of the weak singular integral of type 1 / R between rectangular surface elements; Indicates a branch The self-perceived item, The permeability of free space, Indicates a branch The characteristic dimensions of the corresponding rectangular element. m and n represent the summation indices of the boundary combinations in the width and length directions. This represents the position vector of an observation point on a rectangular surface element. This represents the position vector of a source point on a rectangular surface element. This represents the offset of the nth boundary along the length direction. This represents the offset of the m-th boundary in the width direction.

[0066] The original function for the analytic term is: ; in, This represents the vertical offset variable of the start / end point of the second rectangular element relative to the start / end point of the first rectangular element. The variable p represents the lateral offset of the left / right edge of the second rectangular element relative to the left / right edge of the first rectangular element, and p represents the normal offset variable.

[0067] For the self-inductance term, if the two rectangular elements coincide, then p=0, and the boundary substitution is: , ;in, Indicates a branch The length of the corresponding rectangular element, Indicates a branch The width of the corresponding rectangular element.

[0068] Therefore, the analytic term can also be written directly as: .

[0069] branch road and branch road Mutual inductance terms between Determined by the weighted inner product of the double area integrals, and derived under the midpoint approximation: , ; in, The permeability of free space, branch road The geometric midpoint coordinates, branch road The geometric midpoint coordinates, branch road directional vector, branch road directional vector, branch road Geometric midpoint and branch The distance between the geometric midpoints.

[0070] If the above calculations yield ,exist ( Indicates a branch The self-perceived item, Indicates a branch (the self-perceived term), then , This represents the corrected partial mutual inductance term.

[0071] Based on the above formula, the capacitance matrix C, inductance matrix L, and connection relationships under the second discrete grid diagram can be obtained.

[0072] It should be understood that in this embodiment, the matrix is ​​constructed from the integral equations of the electric and magnetic fields, rather than through empirical fitting, to ensure the physical correctness and reliable accuracy of the equivalent circuit.

[0073] In one possible implementation, the equivalent circuit operator is optimized using a structured matrix network to obtain the target equivalent circuit operator, including: The first state vector of the conductor structure is obtained by performing transient simulation of the partial element equivalent circuit operator under the first discrete mesh diagram, and the second state vector is obtained by performing transient simulation of the conductor structure under the second discrete mesh diagram.

[0074] The structured parameters of the capacitor matrix and inductor matrix are initialized according to the preset circuit physical constraints to obtain the initial model parameters. The preset circuit physical constraints include the first physical constraint of capacitor matrix symmetry and the requirement that the off-diagonal elements of the capacitor matrix are negative and the sum of its rows and columns is positive, and the second physical constraint of inductor matrix symmetry and positive definiteness.

[0075] Based on the second state vector and the initial model parameters, the state at the next time step is predicted in the discrete time domain using a structured matrix network, resulting in the next time step state prediction vector.

[0076] Based on the training loss value calculated by the next time step state prediction vector and the first state vector, the initial model parameters of the structured matrix network are iteratively updated until the training loss value meets the preset convergence condition, thus obtaining the target equivalent circuit operator.

[0077] Specifically, firstly, a high-precision PEEC transient simulation is performed on the fine-grained mesh (i.e., the first discrete mesh graph) to obtain a first state vector (as a truth label); and secondly, a fast PEEC transient simulation is performed on the coarse-grained mesh (i.e., the second discrete mesh graph) to obtain a second state vector (as the optimization starting point). The partial equivalent circuit operator transient simulation (i.e., PEEC transient simulation) can be understood as a dynamic simulation based on PEEC in the time domain, used to obtain the time-varying states of potential, current, and charge. The state vector refers to the node voltage, edge current, port current, and their derivatives corresponding to each node and edge at each time stamp obtained during the mesh transient simulation. The first state vector is a vector composed of the potential, current, and other states obtained from the PEEC transient simulation of the fine-grained mesh (i.e., the first discrete mesh graph), serving as the truth label for supervised learning. The second state vector is the state vector obtained from the unoptimized equivalent circuit operator simulation of the coarse-grained mesh (i.e., the second discrete mesh graph), serving as the initial input state of the network. It should be understood that by establishing a supervision signal, the coarse-grained mesh approximates the dynamic response of the fine-grained mesh.

[0078] Subsequently, based on preset circuit physical constraints, the capacitance matrix C is forcibly constrained to be symmetric, with negative off-diagonal elements and a positive sum of rows and columns; and the inductance matrix L is forcibly constrained to be symmetric and positive definite. According to these physical constraints, initial values ​​are assigned to the capacitance matrix C and the inductance matrix L to obtain initial model parameters, avoiding training from random or non-physical values ​​and allowing optimization to start from a physically valid space, avoiding invalid searches. The preset circuit physical constraints are embedded electromagnetic physical laws that must be satisfied to ensure that the matrices do not produce non-physical results. The first physical constraint refers to the constraint on the capacitance matrix, that is, the capacitance matrix C must satisfy symmetry (reflecting electrostatic reciprocity), negative off-diagonal elements (indicating negative coupling capacitance between different conductor regions, reflecting electric field cancellation characteristics), and a positive sum of rows and columns (i.e., row sum greater than 0, column sum greater than 0, ensuring a positive total capacitance, a passive system, and positive energy), which is a typical capacitance matrix physical constraint in the PEEC method. The second physical constraint refers to the constraint on the inductance matrix, that is, the inductance matrix must satisfy symmetry and positive definiteness, ensuring positive magnetic field energy and a stable system without divergence. The initial model parameters are the initial values ​​of the inductance and capacitance matrices to be optimized in the structured matrix network. Instead of starting with random values, we start with physically reasonable initial matrices, resulting in more stable training, fewer iterations, and less tendency to diverge, significantly improving training stability and convergence speed.

[0079] Then, using the second state vector as the initial input, and utilizing the parameters of the current capacitance matrix C and inductance matrix L, the potential and current at the next time step are recursively predicted in the discrete-time domain, outputting the next-time state prediction vector. Here, the discrete-time domain refers to dividing the time axis into multiple time steps and updating the state sequentially, corresponding to transient circuit simulation. The next-time state prediction vector is the potential / current state at the next time step predicted by the structured matrix network based on the current state.

[0080] Finally, the training loss is calculated using the predicted state (i.e., the predicted state vector for the next time step) and the ground truth value of the fine mesh (i.e., the first state vector). While maintaining physical constraints, the capacitance matrix C and inductance matrix L are used as learnable parameters. The parameters of capacitance matrix C and inductance matrix L are iteratively updated to gradually reduce the loss. When the training loss value meets the preset convergence condition, the optimized target equivalent circuit operator is output. The training loss value is an indicator used to measure the error between the predicted state after coarse mesh optimization and the real state of the fine mesh, such as mean square error (MSE). The preset convergence condition can be understood as a pre-set condition for ending training, such as the loss being less than a threshold, parameter changes being sufficiently small, or the number of iterations reaching a target; training stops when these conditions are met. It should be understood that by driving iteration through loss, the error introduced by the coarse mesh is automatically corrected, reducing reliance on human experience.

[0081] Understandably, in this embodiment, by learning the transient response of the fine mesh, the coarse mesh model can approximate high-precision simulation results while maintaining lightweight design, significantly improving the accuracy of the coarse mesh model. Furthermore, by directly predicting the circuit state in the discrete time domain, the optimization target aligns with the actual simulation scenario, resulting in more accurate dynamic response. The final target equivalent circuit operator is still based on the coarse mesh, requiring less computation and balancing lightweight design with high accuracy, making it ideal for real-time electromagnetic simulation of terminal devices. Moreover, the target equivalent circuit operator retains good mathematical properties, making inversion, simulation, and system analysis more stable and efficient, facilitating subsequent circuit solving and chip / package modeling.

[0082] In one possible implementation, the capacitor matrix and inductor matrix are initialized with structured parameters according to preset circuit physical constraints to obtain initial model parameters, including: Based on the first physical constraint, the capacitor matrix is ​​initialized with structured parameters to obtain the initial training parameters of the capacitor.

[0083] Based on the second physical constraint, the inductance matrix is ​​initialized with structured parameters to obtain the initial training parameters of the inductance.

[0084] The initial training parameters of the capacitor and the initial training parameters of the inductor are combined to form the initial model parameters.

[0085] The preset circuit physical constraints are embedded electromagnetic physical laws that must be satisfied to ensure that the matrix does not produce non-physical results. The first physical constraint refers to the constraint on the capacitance matrix, that is, the capacitance matrix C must satisfy symmetry, negative off-diagonal elements, and positive row and column sums, which is a typical physical constraint for the capacitance matrix in the PEEC method. The second physical constraint refers to the constraint on the inductance matrix, that is, the inductance matrix must satisfy symmetry and positive definiteness, ensuring that the magnetic field energy is positive and the system is stable and without divergence. In this embodiment, it is necessary to perform structured parameter initialization on the capacitance matrix according to the content of the first physical constraint to obtain the initial training parameters of the capacitance matrix; and, according to the content of the second physical constraint, to perform structured parameter initialization on the inductance matrix to obtain the initial training parameters of the inductance matrix, to ensure the physical consistency and feasibility of the parameters.

[0086] In some examples, the capacitance matrix is ​​initialized with structured parameters according to the first physical constraint to obtain the initial training parameters of the capacitance, including: Extract the negatives of the off-diagonal terms from the normalized capacitance matrix to obtain the processed capacitance matrix. Then, perform a soft inverse transformation on the lower triangular part of the extracted processed capacitance matrix to obtain the first initial training parameters.

[0087] The second initialization training parameters are obtained by performing a soft inverse transformation on the difference vector obtained by subtracting the diagonal term vector of the capacitance matrix from the row sum vector of the processed capacitance matrix.

[0088] The first initial training parameters are subjected to a soft transformation to obtain the first transformation matrix, and an initial off-diagonal matrix is ​​constructed based on the first symmetric matrix of the first transformation matrix.

[0089] The second initialization training parameters are subjected to a soft addition transformation to obtain the second transformation vector. The row sum vector of the first symmetric matrix is ​​then added to the second transformation vector to obtain the initial diagonal term vector.

[0090] Based on the constructed initial off-diagonal matrix and initial diagonal term vector, the initial training parameters of the capacitor satisfy the first physical constraint are formed.

[0091] Specifically, for the capacitance matrix, firstly, in the parameter initialization phase, from the normalized... Matrix (i.e., capacitance matrix) Extracting the negatives of off-diagonal terms from the normalized matrix yields the processed capacitance matrix. To satisfy the symmetry requirement in the first physical constraint, the processed capacitance matrix is ​​extracted. The lower triangular part is obtained, and the obtained lower triangular part is subjected to inverse softplus transform to obtain the first initial training parameters. .

[0092] Calculated capacitance matrix The current row sum is used to obtain a row sum vector. Then extract the diagonal terms of the capacitance matrix C to obtain the vector. The difference is obtained by subtracting the diagonal vector of the capacitance matrix from the row sum vector of the processed capacitance matrix. (Right now The second initialization training parameters are obtained by performing a softplus inverse transform. .

[0093] Then, in the matrix construction phase, the first initial training parameters are... The first transformation matrix is ​​obtained after softplus transformation. And based on the first symmetric matrix of the first transformation matrix Construct the initial off-diagonal matrix ,Right now The second initialization training parameters will be used. After the softplus transformation, the second transformation vector r is obtained, and the initial off-diagonal matrix is ​​calculated. The row and vector are combined and added to the second transformation vector r to obtain the initial diagonal vector D.

[0094] Finally, based on the constructed initial off-diagonal matrix Together with the initial diagonal vector D, they form the initial training parameters of the capacitor that satisfy the first physical constraint, i.e., C=D. W. Therefore, the capacitance matrix C satisfies the first physical constraint: "symmetric, off-diagonal elements are negative and the sum of each row and column is greater than zero".

[0095] In some examples, the inductance matrix is ​​initialized with structured parameters according to the second physical constraint to obtain the initial training parameters of the inductance, including: The inductance matrix is ​​subjected to symmetric positive definite processing and normalization to obtain the processed inductance matrix.

[0096] The processed inductance matrix was subjected to Choleski decomposition to obtain the decomposition results.

[0097] The decomposition result is split into two matrices, which are used as the third and fourth initialization training parameters, respectively. The third initialization training parameter is the lower triangular matrix in the decomposition result, and the fourth initialization training parameter is the vector obtained by performing a soft inverse transformation on the diagonal of the decomposition result.

[0098] After the fourth initialization training parameters are transformed by soft addition, they are combined with the third initialization training parameters to form a lower triangular matrix, thus obtaining the inductor initial training parameters that satisfy the second physical constraint.

[0099] Specifically, for the inductor matrix, firstly, for the inductor matrix... Symmetric positive definite (SPD) processing and normalization are performed to obtain the processed inductance matrix. Then process the inductor matrix Perform Cholesky decomposition to obtain the decomposition results. Split the decomposition results into two matrices to obtain the training parameters, namely the third initialization training parameters and the fourth initialization training parameters. Specifically, the lower triangular matrix in the decomposition results... As the third initialization training parameter; the vector obtained by performing a softplus inverse transform (i.e., soft plus inverse transform) on the diagonal of the decomposition result. These are used as the fourth initialization training parameters. Then, the fourth initialization training parameters are... After softplus transformation (i.e., soft addition transformation), and with the third initialization training parameters Together they form a complete lower triangular matrix Thus, the initial training parameters of the inductor that satisfy the second physical constraint are obtained. Due to the lower triangular matrix... It is a lower triangle with positive diagonals; therefore, the initial training parameters for the constructed inductor are... Strictly orthodox.

[0100] In one possible implementation, based on the second state vector and initial model parameters, the state at the next time step is predicted in the discrete-time domain using a structured matrix network, resulting in a predicted state vector for the next time step, including: The initial model parameters are embedded into the state-space equation of the structured matrix network to obtain the core matrix of the state-space equation.

[0101] The core matrix is ​​discretized using the trapezoidal integral discretization method to obtain an iterative matrix in discrete recursive form.

[0102] The second state vector is used as input, and implicit time iteration is performed through the iteration matrix.

[0103] After the implicit time iteration operation is completed, the state prediction vector for the next time step is output.

[0104] Specifically, firstly, the structured initialized capacitor and inductor matrices are substituted into the state-space equations of the structured matrix network to construct the core matrix that satisfies physical constraints, forming a complete and physically reasonable dynamic model. The state-space equations are the standard mathematical model describing the dynamic characteristics of a circuit, and their general form is: Where x is the state vector, , , , Let be the system matrix, and u be the excitation input vector. The system matrix is ​​directly determined by parameters such as capacitance and inductance. The core matrix is ​​the system matrix (mainly the state matrix) formed by embedding the initial capacitance and inductance parameters into the state-space equations. Input matrix (etc.) are the core of characterizing the dynamic characteristics of a system.

[0105] Then, the trapezoidal integral discretization method is used to transform the continuous-time state differential equation into a linear recursive formula for discrete time steps, resulting in a matrix form that can be directly used for computer iteration, i.e., the iteration matrix, thus realizing the transformation from continuous system to discrete iteration. The trapezoidal integral discretization method is a high-precision numerical method for discretizing continuous systems. It transforms the continuous-time differential equation into a discrete-time recursive formula through the trapezoidal integral rule, resulting in greater stability. The iteration matrix, obtained after gradient discretization, is a matrix form that can be directly iteratively calculated. It is used to deduce the next state from the current state and is the main computational component of the time iteration.

[0106] Finally, starting with the second state vector at the current moment, the discrete recursive formula is substituted to perform implicit time iterative calculation to solve for the state prediction vector at the next moment. After the iterative solution is completed, the final prediction result is output as the next moment state for subsequent simulation, control, or model training. Implicit time iterative calculation refers to the process where the next moment state appears on both sides of the equation in the iterative formula. It requires solving algebraic equations and features numerical stability and allows for large step sizes, making it suitable for rigid circuit systems.

[0107] In some examples, such as Figure 2 As shown, Figure 2 This is a schematic diagram of state vector prediction using a structured matrix network, provided in one embodiment of this application. Figure 2 In essence, this structured matrix network is a circuit / electromagnetic system solver based on Modified Nodal Analysis (MNA) and time-domain discretization (CN method). It constructs a state-space system from the physical topology using the learnable parameters obtained above, then discretizes and advances the time.

[0108] Figure 2 In the optimization loop, the learned parameters (initial training parameters of capacitor, initial training parameters of inductor, etc.) are embedded into the state-space equation based on a neural network, and the state transition operator is calculated using trapezoidal integral discretization. Based on Kirchhoff's Current Law (KCL), Kirchhoff's Voltage Law (KVL), and the constitutive relation of the conductor structure, the capacitance matrix C, inductance matrix L, and connection matrix are... And the resistor R, etc., are assembled into a continuous-time state-space equation form, that is The generalized state matrix E contains information about the energy storage elements (C, L) in the circuit. It is composed of the connection matrix The core matrix formed by the resistor R reflects the topological coupling and resistive loss of the circuit. represents the input matrix, which describes how external excitation is mapped to the state equations; v represents the state vector, which contains the state change vectors of node voltages and branch currents; u represents the excitation input vector, which is the externally applied voltage or current source signal. This represents the time derivative of the state vector.

[0109] For this differential equation An implicit second-order method is used for discretization, transforming the continuous system into a discrete iterative form, and the equivalent matrix is ​​pre-calculated: , This transforms the differential problem into an algebraic recursion, enabling implicit time progression. This represents the discrete state transition matrix, i.e., the system iteration matrix after discretization using the trapezoidal rule, which corresponds to the linear transformation matrix of the state at the next time step. This represents the discrete input matrix, i.e., the input iteration matrix discretized by the trapezoidal rule, corresponding to the linear transformation matrix of the external excitation. Indicates the time step.

[0110] The final result is: ; ; ; in, Represents the intermediate predicted state vector; Represents the current state vector; Represents the derivative vector of the current state; This represents the state derivative prediction vector for the next time step. This represents the activation input vector for the next time step; This represents the state prediction vector for the next time step.

[0111] It should be noted that, Figure 2 In this context, Learnable Parameters(C, L) represents the learnable parameter part (capacitance matrix C, inductance matrix L); Inputs at time t represents the input part (the input at time t); SystemAssembly represents the system assembly module; Trapezoidal Discretization represents the trapezoidal discretization module; Time-Stepping (Implicit Update) represents the time-step update module (implicit update); and Outputs represents the output part.

[0112] The learnable parameters section describes the generation paths for the initial training parameters of the capacitor and the initial training parameters of the inductor. Among them, Represents the capacitance matrix; (Node Node) represents a node × node matrix (where the nodes are the geometric center points of rectangular facets); Norc_scale indicates that the capacitance matrix is ​​normalized according to the capacitance scale; Represents the normalized capacitance matrix; ParaSoftplus 1 This represents parameterization and soft-applied inverse transform; This represents the first initial training parameters (i.e., the original off-diagonal capacitor parameters). The second initialization training parameters (i.e., the original row and capacitance parameters) are represented; Softplus represents the soft addition transformation; Assemble represents matrix assembly; the physical constraint form of the capacitance matrix is ​​C=D. W represents the initial off-diagonal matrix W and the initial diagonal term vector D, arranged according to the physical rule (C=D). W) is assembled into the final initial training parameters for the capacitor. Represents the capacitor matrix; (Edge) represents the branch × branch matrix; Norl_scale represents the inductance matrix. Normalize according to inductance; Represents the normalized inductance matrix; ParaCholesky Softplus 1 Representation of parameterization, Choreski decomposition, and soft-addition inverse transform; This represents the third initialization training parameters (i.e., the original off-diagonal inductance parameters). The fourth initialization training parameters (i.e., the original diagonal inductance parameters) are represented; Softplus represents the soft addition transformation; Assemble represents matrix assembly; SPD Matrix L represents the symmetric positive definite inductance matrix L. Here, PhysicalConstraint represents physical constraints; Symmetry represents symmetry; and Positive Definiteness represents positive definiteness.

[0113] In the input section, State represents the state vector at the current time; Derivative represents the time derivative of the state vector at the current time; and Excitation represents the external excitation signal of the circuit. This represents the node voltage vector at the current moment, where N represents the batch size and m represents the number of nodes and branches. This represents the rate of change of the node voltage at the current moment; This indicates the external stimulus (such as a current / voltage source) at the next moment.

[0114] In the system assembly module, E represents the generalized state matrix; B represents the core matrix; B represents the input matrix. Represents the connection matrix (topology matrix); Represents the transpose of the connection matrix; R represents resistance. Construct E,A,B means constructing the generalized state matrix E, the core matrix A, and the input matrix B; Using indicates the parameters used. In the trapezoidal discretization module, Represents the discrete state transition matrix. Represents a discrete input matrix. Indicates the time step; Precompute Once perIteration indicates , Pre-calculate only once before the time step update.

[0115] In the time step update module, Represents the intermediate predicted state vector; Represents the current state vector; Represents the derivative vector of the current state; This represents the state derivative prediction vector for the next time step. This represents the activation input vector for the next time step; This represents the predicted state vector for the next time step. In the output, NextState represents the state vector for the next time step; NextDerivative represents the time derivative of the state vector for the next time step. This represents the node voltage vector at the next moment; This represents the rate of change of the node voltage at the next moment; In one possible implementation, the initial model parameters of the structured matrix network are iteratively updated based on the training loss value calculated using the next-time state prediction vector and the first state vector, until the training loss value satisfies a preset convergence condition, resulting in the target equivalent circuit operator, including: The voltage and current vectors and voltage and current change vectors in the next state prediction vector are compared with the voltage and current vectors and voltage and current change vectors in the first state vector, respectively, and the voltage and current error and change error are calculated.

[0116] The data loss value is obtained based on the voltage and current errors and the change error.

[0117] Obtain the regularization loss value used to maintain the equivalent circuit operator in satisfying the preset circuit physical constraints.

[0118] The training loss value is obtained by weighting and combining the regularization loss value and the data loss value.

[0119] Backpropagation is performed on the training loss value to obtain the gradient of the initial model parameters, and the initial model parameters are iteratively updated using an adaptive moment estimation optimization algorithm.

[0120] Repeat the above steps of calculating the training loss value and updating the initial model parameters until the training loss value meets the preset convergence condition and the iteration stops, thus obtaining the target equivalent circuit operator.

[0121] The main steps for loss calculation and parameter update during the optimization training process are as follows: First, the predicted state vector at the next time step is compared with the true label of the first state vector to obtain the voltage and current error (i.e., comparing the voltage and current vector in the predicted state vector at the next time step with the voltage and current vector in the first state vector) and the change error (i.e., comparing the voltage and current change vector in the predicted state vector at the next time step with the voltage and current change vector in the first state vector). To avoid inconsistencies in dimensions, the voltage and current error and the change error are normalized according to their respective standard deviations and then the mean square error is calculated to obtain the data loss value. In this embodiment, in addition to the data error, a physical prior-related regularization term is added, namely, a regularized loss value that maintains the equivalent circuit operator satisfying the preset circuit physical constraints. The "data loss (i.e., data loss value) and constraint loss (i.e., regularized loss value)" are combined into a total loss (i.e., training loss value) as the optimization objective of this iteration. Then, backpropagation is performed on the training loss value to obtain the gradient of the initial model parameters, and the initial model parameters are updated using the Adam adaptive moment estimation optimization algorithm. In each round, the average loss is calculated, and the scheduler automatically reduces the learning rate based on convergence. Simultaneously, the mean absolute error (MAE) and the sub-loss curves are recorded to determine the stability and effectiveness of the training. Finally, iteration stops when the training loss value meets the preset convergence condition, yielding the final target equivalent circuit operator. Optimized initial model parameters are also obtained.

[0122] After iterative updates, the Structured Matrix Network (MNA) automatically exports and encapsulates the identified target equivalent circuit operators (i.e., target capacitance matrix C and target inductance matrix L) and topology connection matrix, and transmits them to the same solution process (MNA matrix) via a unified interface. Subsequently, within this process, frequency and time domain response calculations are directly performed, and a consistency comparison (e.g., amplitude, phase, time-domain waveform, and error indices) is conducted with the baseline response of the MNA. This verifies whether the trained model parameters can reproduce the dynamic behavior of the high-precision model within an independent physics solution framework.

[0123] In practical applications, such as Figure 3 As shown, Figure 3This is a flowchart illustrating an optimization method for equivalent circuit operators provided in an embodiment of this application. Figure 3 In the first stage (S21), the conductor structure is discretized into a rectangular mesh using the Partial Element Equivalent Circuit (PEEC) method. Based on prior physical knowledge, key nodes and edges in the conductor structure are represented as a coarse mesh composed of nodes and branches. Nodes correspond to the geometric center points of rectangular surface elements, and branches connect the geometric center points of adjacent rectangular surface elements. Assuming the surface of the conductor structure satisfies the Electric Field Integral Equation (EFIE), the initial values ​​of the equivalent circuit operators under the coarse mesh are calculated, namely the capacitance matrix C and the inductance matrix L. Subsequently, PEEC transient simulations are performed on both the coarse and fine meshes to obtain state vector sequences (i.e., the initial state vector sequence under the coarse mesh and the target state vector sequence under the fine mesh). This step outputs the inductance matrix L, capacitance matrix C, and training data (the initial state vector sequence under the coarse mesh and the target state vector sequence under the fine mesh) required for training initialization.

[0124] In stage S22, the training data (state vector matrix), relevant topology information (topology matrix), and initial matrices (inductance matrix L and capacitance matrix C) obtained from stage S21 are read. Preprocessing operations such as sample sorting, scaling normalization, and input / output alignment are performed to form a data batch that can be directly used for network training. In stage S23, using the initial values ​​of the equivalent circuit operators output from stage S21, along with the inductance matrix L and capacitance matrix C, structured parameters are initialized. Trainable parameters and corresponding constraint forms are established to ensure consistency between the initialized parameters and the circuit's physical structure. In stage S24, system matrix assembly and time-domain propagation prediction are performed. Specifically, in each training round, the system matrix is ​​assembled based on the current structured parameters, and state propagation and prediction are performed in the discrete time domain to obtain the estimated state value for the next time step. This step combines "matrix assembly" and "time-domain propagation prediction" into a single execution step to ensure a compact process and consistency.

[0125] In stage S25, the training loss value is calculated and parameters are updated via backpropagation. The prediction result output from stage S24 (i.e., the estimated state value at the next time step) is compared with the target state vector sequence to calculate the training loss value. An optimization algorithm is then used to update the network parameters, allowing the model to gradually approximate the target operator and state response. In stage S26, convergence judgment and iterative control are performed based on preset convergence conditions (such as loss threshold, loss reduction magnitude, and maximum number of training epochs): if the training loss value does not meet the preset convergence conditions, the process returns to stage S24 and continues the "assembly-prediction-update" iteration; if the training loss value meets the preset convergence conditions, the training process ends. The converged model parameters and the identified target equivalent circuit operator (including the trained key matrix) are exported for subsequent simulation, verification, or engineering deployment.

[0126] Compared with the prior art, the beneficial effects of the optimization method for equivalent circuit operators provided in this application mainly stem from the indispensable structured hard constraints, specifically including: (1) At the structural level, the capacitor matrix is ​​strictly symmetric, the off-diagonal elements are negative, and the sum of rows and columns is positive, avoiding physical distortion caused by improper soft penalty weights, and significantly improving the physical consistency and interpretability of the capacitor network.

[0127] (2) The inductance matrix is ​​guaranteed to be symmetric and positive definite throughout the training and inference process, avoiding numerical instability caused by entering the non-positive definite region during training, and maximizing the stability of solving linear equations and the robustness of broadband simulation.

[0128] (3) The optimization method provided in this application embodiment is compatible with the existing circuit simulation process and outputs a system matrix with clear physical meaning, which is conducive to realizing "fast, stable and interpretable" operator-level modeling in the scenario of heterogeneous integrated electromagnetic design automation.

[0129] It should be understood that the sequence number of each step in the above embodiments does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application.

[0130] An optimization method for an equivalent circuit operator corresponding to the above embodiment, Figure 4 A schematic diagram of the structure of an optimization device for an equivalent circuit operator provided in an embodiment of this application is shown. For ease of explanation, only the parts related to the embodiment of this application are shown.

[0131] Reference Figure 4 The optimization device 3 for the equivalent circuit operator in this embodiment includes: The acquisition module 31 is used to acquire the first discrete grid diagram of the conductor structure.

[0132] The construction module 32 is used to construct a second discrete mesh graph of the conductor structure based on multiple key nodes and multiple key edges extracted from the first discrete mesh graph; wherein the mesh granularity of the first discrete mesh graph is larger than the mesh granularity of the second discrete mesh graph.

[0133] The determination module 33 is used to determine the equivalent circuit operator corresponding to the second discrete mesh diagram based on the partial element equivalent circuit algorithm. The equivalent circuit operator includes the inductance matrix and the capacitance matrix.

[0134] The optimization module 34 is used to optimize the equivalent circuit operator through a structured matrix network to obtain the target equivalent circuit operator; wherein, the structured matrix network is constructed based on the circuit topology relationship of preset circuit physical constraints and conductor structure.

[0135] Furthermore, module 32 includes: The identification unit is used to extract multiple key nodes and multiple key edges from the first discrete mesh graph based on physical prior knowledge; wherein, key nodes are used to characterize the charge degree of freedom of the conductor structure, and key edges are used to characterize the current degree of freedom of the conductor structure.

[0136] Meshable cells are used to simplify the first discrete mesh graph into multiple rectangular elements by using a rectangular mesh based on multiple key nodes and multiple key edges. Each rectangular element includes a geometric center point and branches. Branches connect adjacent geometric center points. Each rectangular element includes charge elements and current elements. A geometric center point is equivalent to a charge element, and a branch is equivalent to a current element.

[0137] The mapping unit is used to map multiple key nodes to the geometric center points of multiple rectangular elements, and to map multiple key edges to the branches of multiple rectangular elements, so as to construct a second discrete mesh graph.

[0138] Furthermore, module 33 is defined as including: The first building unit is used to establish the electric field integral equation based on the geometric dimensions, relative positions, and dielectric parameters of multiple rectangular surface elements in the second discrete mesh diagram.

[0139] The first discrete element is used to discretize the coupling relationship between the surface charge distribution and potential distribution of the conductor structure based on the electric field integral equation, so as to obtain the capacitance matrix; wherein, the capacitance matrix is ​​used to characterize the electrostatic coupling characteristics between each rectangular surface element.

[0140] The second discrete unit is used to discretize the coupling relationship and obtain the inductance matrix; the inductance matrix is ​​used to characterize the electromagnetic coupling characteristics between each branch.

[0141] The first combination unit is used to combine the capacitor matrix and the inductor matrix to obtain an equivalent circuit operator that characterizes the circuit properties of the second discrete grid diagram.

[0142] Optimization module 34 includes: The state acquisition submodule is used to acquire the first state vector obtained by performing transient simulation of the conductor structure under the first discrete mesh diagram using the partial element equivalent circuit operator, and the second state vector obtained by performing transient simulation of the conductor structure under the second discrete mesh diagram using the partial element equivalent circuit operator.

[0143] The initialization submodule is used to initialize the structured parameters of the capacitor matrix and the inductor matrix according to the preset circuit physical constraints, so as to obtain the initial model parameters. The preset circuit physical constraints include the first physical constraint of capacitor matrix symmetry and the first physical constraint that the off-diagonal elements of the capacitor matrix are negative and the sum of the rows and columns is positive, and the second physical constraint that the inductor matrix is ​​symmetric and positive definite.

[0144] The prediction submodule is used to predict the state at the next time step in the discrete time domain based on the second state vector and the initial model parameters through a structured matrix network, and obtain the state prediction vector at the next time step.

[0145] The update submodule is used to iteratively update the initial model parameters of the structured matrix network based on the training loss value calculated by the next time step state prediction vector and the first state vector, until the training loss value meets the preset convergence condition, and the target equivalent circuit operator is obtained.

[0146] The initialization submodule includes: The first initialization unit is used to initialize the structured parameters of the capacitor matrix according to the first physical constraint, so as to obtain the initial training parameters of the capacitor.

[0147] The second initialization unit is used to perform structured parameter initialization of the inductance matrix according to the second physical constraint, so as to obtain the initial training parameters of the inductance.

[0148] The initialization combination unit is used to combine the initial training parameters of the capacitor and the initial training parameters of the inductor into the initial model parameters.

[0149] The first initialization unit is specifically used for: Extract the negatives of the off-diagonal terms from the normalized capacitance matrix to obtain the processed capacitance matrix. Then, perform a soft inverse transformation on the lower triangular part of the extracted processed capacitance matrix to obtain the first initial training parameters.

[0150] The second initialization training parameters are obtained by performing a soft inverse transformation on the difference vector obtained by subtracting the row sum vector of the processed capacitance matrix from the diagonal term vector.

[0151] The first initial training parameters are subjected to a soft transformation to obtain the first transformation matrix, and an initial off-diagonal matrix is ​​constructed based on the first symmetric matrix of the first transformation matrix.

[0152] The second initialization training parameters are subjected to a soft addition transformation to obtain the second transformation vector. The row sum vector of the first symmetric matrix is ​​then added to the second transformation vector to obtain the initial diagonal term vector.

[0153] Based on the constructed first symmetric matrix and the initial diagonal vector, the initial training parameters of the capacitor satisfy the first physical constraint are formed.

[0154] The second initialization unit is specifically used for: The inductance matrix is ​​subjected to symmetric positive definite processing and normalization to obtain the processed inductance matrix.

[0155] The processed inductance matrix was subjected to Choleski decomposition to obtain the decomposition results.

[0156] The decomposition result is split into two matrices, which are used as the third and fourth initialization training parameters, respectively. The third initialization training parameter is the lower triangular matrix in the decomposition result, and the fourth initialization training parameter is the vector obtained by performing a soft inverse transformation on the diagonal of the decomposition result.

[0157] After the fourth initialization training parameters are transformed by soft addition, they are combined with the third initialization training parameters to form a lower triangular matrix, thus obtaining the inductor initial training parameters that satisfy the second physical constraint.

[0158] The prediction submodule includes: The core matrix determination unit is used to embed the initial model parameters into the state space equation of the structured matrix network to obtain the core matrix of the state space equation.

[0159] The iterative matrix determination unit is used to discretize the core matrix using the trapezoidal integral discretization method to obtain the iterative matrix in discrete recursive form.

[0160] The implicit operation unit is used to take the second state vector as input and perform implicit time-time iterative operations through the iteration matrix.

[0161] The output unit is used to output the state prediction vector for the next time step after the implicit time iteration operation is completed.

[0162] The update submodule includes: The error calculation unit is used to compare the voltage and current vector and voltage and current change vector in the state prediction vector at the next moment with the voltage and current vector and voltage and current change vector in the first state vector, respectively, and calculate the voltage and current error and change error.

[0163] The data loss calculation unit is used to obtain the data loss value based on voltage and current errors and change errors.

[0164] The regularization calculation acquisition unit is used to acquire the regularization loss value used to maintain the equivalent circuit operator in satisfying the preset circuit physical constraints.

[0165] The training loss calculation unit is used to weight and combine the regularization loss value and the data loss value to obtain the training loss value.

[0166] The backpropagation computation unit is used to perform backpropagation calculation on the training loss value to obtain the gradient of the initial model parameters, and to iteratively update the initial model parameters using an adaptive moment estimation optimization algorithm. The training unit is used to repeat the above steps of calculating the training loss value and updating the initial model parameters until the training loss value meets the preset convergence condition and the iteration stops, thus obtaining the target equivalent circuit operator.

[0167] It should be noted that the information interaction and execution process between the modules in the above-mentioned equivalent circuit operator optimization device 3 are based on the same concept as the method embodiment of this application. For details on their specific functions and technical effects, please refer to the method embodiment section, which will not be repeated here.

[0168] This application also provides a terminal device, such as... Figure 5 As shown, Figure 5 This is a schematic diagram of the structure of a terminal device provided in an embodiment of this application. (Refer to...) Figure 5 The terminal device 4 in this embodiment includes a memory 41, a processor 42, and a computer program stored in the memory 41 and executable on the processor 42. When the processor 42 executes the computer program, it implements the steps in the optimization method embodiment of the equivalent circuit operator of any of the above-mentioned items.

[0169] This application also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, can implement the steps in the above-described method embodiments.

[0170] This application provides a computer program product that, when run on a mobile terminal, enables the mobile terminal to implement the steps described in the various method embodiments.

[0171] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments of this application can be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include at least: any entity or device capable of carrying the computer program code to a photographic device / terminal device, a recording medium, a computer memory, a read-only memory (ROM), a random access memory (RAM), an electrical carrier signal, a telecommunication signal, and a software distribution medium. Examples include USB flash drives, portable hard drives, magnetic disks, or optical disks.

[0172] In the above embodiments, the descriptions of each embodiment have different focuses. For parts that are not described in detail or recorded in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0173] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0174] In the embodiments provided in this application, it should be understood that the disclosed apparatus / network devices and methods can be implemented in other ways. For example, the apparatus / network device embodiments described above are merely illustrative. For instance, the division of modules or units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between apparatuses or units may be electrical, mechanical, or other forms.

[0175] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0176] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. An optimization method for an equivalent circuit operator, characterized in that, include: Obtain the first discrete grid diagram of the conductor structure; Based on multiple key nodes and multiple key edges extracted from the first discrete mesh graph, a second discrete mesh graph of the conductor structure is constructed; wherein the mesh granularity of the first discrete mesh graph is larger than that of the second discrete mesh graph. Based on the partial equivalent circuit algorithm, the equivalent circuit operator corresponding to the second discrete mesh diagram is determined; wherein, the equivalent circuit operator includes an inductance matrix and a capacitance matrix; The equivalent circuit operator is optimized by a structured matrix network to obtain the target equivalent circuit operator; wherein the structured matrix network is constructed based on the preset circuit physical constraints and the circuit topology relationship of the conductor structure.

2. The optimization method for the equivalent circuit operator as described in claim 1, characterized in that, The step of constructing a second discrete mesh graph of the conductor structure based on multiple key nodes and multiple key edges extracted from the first discrete mesh graph includes: Based on prior physical knowledge, the multiple key nodes and multiple key edges are extracted from the first discrete mesh graph; wherein, the key nodes are used to characterize the charge degree of freedom of the conductor structure, and the key edges are used to characterize the current degree of freedom of the conductor structure. Based on the multiple key nodes and multiple key edges, the first discrete mesh graph is simplified into multiple rectangular elements using a rectangular mesh; wherein, each rectangular element includes a geometric center point and a branch; the branch connects adjacent geometric center points; each rectangular element includes charge elements and current elements, the geometric center point is equivalent to the charge element, and the branch is equivalent to the current element; The multiple key nodes are mapped to the geometric center points of the multiple rectangular elements, and the multiple key edges are mapped to the branches of the multiple rectangular elements, so as to construct the second discrete mesh graph.

3. The optimization method for the equivalent circuit operator as described in claim 2, characterized in that, The step of determining the equivalent circuit operator corresponding to the second discrete mesh diagram according to the partial element equivalent circuit algorithm includes: Based on the geometric dimensions, relative positions, and dielectric parameters of the multiple rectangular surface elements in the second discrete mesh diagram, an integral equation for the electric field is established. Based on the electric field integral equation, the coupling relationship between the surface charge distribution and potential distribution of the conductor structure is discretized to obtain the potential coefficient matrix; The capacitance matrix is ​​calculated based on the potential coefficient matrix; wherein the capacitance matrix is ​​used to characterize the electrostatic coupling characteristics between each of the rectangular surface elements. Based on the relationship between current continuity and magnetic field integral, the coupling relationship between branch current and magnetic flux of the conductor structure is discretized to obtain the inductance matrix; wherein, the inductance matrix is ​​used to characterize the electromagnetic coupling characteristics between each branch. The capacitor matrix and the inductance matrix are combined to obtain the equivalent circuit operator that characterizes the circuit properties of the second discrete grid diagram.

4. The optimization method for the equivalent circuit operator as described in claim 3, characterized in that, The optimization of the equivalent circuit operator through a structured matrix network to obtain the target equivalent circuit operator includes: Obtain the first state vector obtained by performing a transient simulation of the conductor structure under the first discrete mesh diagram using a partial element equivalent circuit operator, and the second state vector obtained by performing a transient simulation of the conductor structure under the second discrete mesh diagram using a partial element equivalent circuit operator. The structured parameters of the capacitor matrix and the inductor matrix are initialized according to the preset circuit physical constraints to obtain the initial model parameters; wherein, the preset circuit physical constraints include the symmetry of the capacitor matrix, the first physical constraint that the off-diagonal elements of the capacitor matrix are negative and the sum of the rows and columns is positive, and the second physical constraint that the inductor matrix is ​​symmetric and positive definite. Based on the second state vector and the initial model parameters, the state at the next time step is predicted in the discrete time domain using the structured matrix network, resulting in a predicted state vector at the next time step. Based on the training loss value calculated by the next time step state prediction vector and the first state vector, the initial model parameters of the structured matrix network are iteratively updated until the training loss value meets the preset convergence condition, thereby obtaining the target equivalent circuit operator.

5. The optimization method for the equivalent circuit operator as described in claim 4, characterized in that, The initial model parameters are obtained by initializing the structured parameters of the capacitor matrix and the inductor matrix according to the preset circuit physical constraints, including: Based on the first physical constraint, the capacitor matrix is ​​initialized with structured parameters to obtain the initial training parameters of the capacitor. Based on the second physical constraint, the inductance matrix is ​​initialized with structured parameters to obtain the initial training parameters of the inductance. The initial training parameters of the capacitor and the initial training parameters of the inductor are combined to form the initial model parameters.

6. The optimization method for the equivalent circuit operator as described in claim 5, characterized in that, The step of initializing the structured parameters of the capacitance matrix according to the first physical constraint to obtain the initial training parameters of the capacitance includes: Extract the negatives of the off-diagonal terms from the normalized capacitance matrix to obtain the processed capacitance matrix, and perform a soft inverse transformation on the lower triangular part of the extracted processed capacitance matrix to obtain the first initialization training parameters. The difference vector obtained by subtracting the diagonal term vector of the capacitance matrix from the row sum vector of the processed capacitance matrix is ​​subjected to a soft inverse transformation to obtain the second initialization training parameters. The first initial training parameters are subjected to a soft addition transformation to obtain a first transformation matrix, and an initial off-diagonal matrix is ​​constructed based on the first symmetric matrix of the first transformation matrix. The second initialization training parameters are subjected to a soft addition transformation to obtain a second transformation vector. The row sum vector of the first symmetric matrix is ​​added to the second transformation vector to obtain an initial diagonal term vector. Based on the constructed first symmetric matrix and the initial diagonal term vector, the initial training parameters of the capacitor satisfy the first physical constraint are formed.

7. The optimization method for the equivalent circuit operator as described in claim 5, characterized in that, The step of initializing the structured parameters of the inductor matrix according to the second physical constraint to obtain the initial training parameters of the inductor includes: The inductance matrix is ​​subjected to symmetric positive definite processing and normalization processing to obtain the processed inductance matrix; The processed inductance matrix is ​​subjected to Choleski decomposition to obtain the decomposition result; The decomposition result is split into two matrices, which are used as the third initialization training parameter and the fourth initialization training parameter, respectively. The third initialization training parameter is the lower triangular matrix in the decomposition result, and the fourth initialization training parameter is the vector obtained by performing a soft inverse transformation on the diagonal of the decomposition result. After the fourth initialization training parameters are transformed by soft addition, they are combined with the third initialization training parameters to form a lower triangular matrix, thereby obtaining the inductor initial training parameters that satisfy the second physical constraint.

8. The optimization method for the equivalent circuit operator as described in claim 4, characterized in that, The step of predicting the state at the next time step in the discrete time domain using the structured matrix network based on the second state vector and the initial model parameters to obtain the next time step state prediction vector includes: The initial model parameters are embedded into the state space equation of the structured matrix network to obtain the core matrix of the state space equation; The core matrix is ​​discretized using the trapezoidal integral discretization method to obtain an iterative matrix in discrete recursive form; The second state vector is used as input, and implicit time iteration is performed through the iteration matrix; After the implicit time iteration operation is completed, the state prediction vector for the next time step is output.

9. The optimization method for the equivalent circuit operator as described in claim 4, characterized in that, The method of iteratively updating the initial model parameters of the structured matrix network based on the training loss value calculated using the next-time state prediction vector and the first state vector, until the training loss value satisfies a preset convergence condition, to obtain the target equivalent circuit operator, includes: The voltage and current vector and voltage and current change vector in the next moment state prediction vector are compared with the voltage and current vector and voltage and current change vector in the first state vector, respectively, and the voltage and current error and change error are calculated. The data loss value is obtained based on the voltage and current errors and the change error; Obtain the regularization loss value used to maintain the equivalent circuit operator in satisfying the preset circuit physical constraints; The training loss value is obtained by weighting and combining the regularization loss value and the data loss value. The training loss value is backpropagated to obtain the gradient of the initial model parameters, and the initial model parameters are iteratively updated using an adaptive moment estimation optimization algorithm. Repeat the above steps of calculating the training loss value and updating the initial model parameters until the training loss value meets the preset convergence condition and the iteration stops, thus obtaining the target equivalent circuit operator.

10. An optimization device for an equivalent circuit operator, characterized in that, include: The acquisition module is used to acquire the first discrete grid diagram of the conductor structure; A construction module is used to construct a second discrete mesh graph of the conductor structure based on multiple key nodes and multiple key edges extracted from the first discrete mesh graph; wherein the mesh granularity of the first discrete mesh graph is larger than the mesh granularity of the second discrete mesh graph. The determination module is used to determine the equivalent circuit operator corresponding to the second discrete mesh diagram based on the partial element equivalent circuit algorithm; wherein, the equivalent circuit operator includes an inductance matrix and a capacitance matrix; An optimization module is used to optimize the equivalent circuit operator through a structured matrix network to obtain a target equivalent circuit operator; wherein the structured matrix network is constructed based on preset circuit physical constraints and the circuit topology relationship of the conductor structure.

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