Solving system, training method and solving method of integrated circuit device electric field partial differential equation

Abstract

The invention discloses a solving system, a training method and a solving method for an electric field partial differential equation of an integrated circuit device, and belongs to the technical field of integrated circuits. The method comprises the following steps: after respectively extracting global features of geometric parameters, electrical parameters and material attributes of an integrated circuit device, constructing a geometry-electricity-material three-coupling mechanism through a fusion module to fuse the global features of the geometric parameters, the electrical parameters and the physical attributes, and firstly introducing a physical field consistency mapping mechanism; according to the method, the electrical characteristics are mapped to a high-dimensional characteristic space aligned with the geometric characteristics, the spatial consistency and the expression complementarity of the electrical characteristics and the geometric characteristics are ensured, the coupling capability of the electrical characteristics and the geometric characteristics is enhanced, and then the mutual influence degree of the geometric parameters, the electrical parameters and the material attributes in different electric field areas is dynamically evaluated through an attention mechanism. The deep coupling of the three features is dynamically realized, the expression problem of a nonlinear complex region in the electric field solution of an integrated circuit device is solved, and the solution accuracy is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of integrated circuits, and more specifically, relates to a solution system, a training method and a solution method for electric field partial differential equations of integrated circuit devices. Background Art

[0002] With the development of integrated circuit technology, integrated circuit devices have been widely used in high-performance and low-power chip design. In modern chip design, device structures are becoming increasingly complex and geometric dimensions are shrinking, which makes the electric field distribution inside integrated circuit devices more nonlinear and multi-scale. In order to accurately simulate and optimize the electrical performance of integrated circuit devices, the electric field distribution must be accurately modeled and efficiently solved, which relies on partial differential equations (PDEs) as the basic mathematical description.

[0003] Traditional partial differential equation solution methods, such as finite difference method and finite element method, usually require high-density mesh discretization of complex geometric shapes and boundary conditions of integrated circuit devices, and rely on a large number of iterative calculations to complete the solution. This high computational complexity seriously affects the speed and efficiency of design iterations, especially when facing multi-dimensional and multi-scale electric field modeling of integrated circuit devices, showing obvious shortcomings.

[0004] In recent years, machine learning technology has been gradually applied to solving partial differential equations, and has shown good prospects in accelerating computing. For example, an existing method for solving partial differential equations based on machine learning technology learns the mapping relationship between the computational domain and boundary conditions of the partial differential equations and the solution results by training a machine learning model. However, this method is only applicable to solving simple partial differential equations, while the structure of the integrated circuit device concerned in the present invention has nonlinear boundary conditions, and the structure of the electric field partial differential equation is relatively complex, and the solution accuracy of the existing method is not high. Summary of the invention

[0005] In view of the above defects or improvement needs of the prior art, the present invention provides a solution system, training method and solution method for the electric field partial differential equation of integrated circuit devices, so as to solve the technical problem that the prior art cannot accurately solve the electric field partial differential equation of integrated circuit devices.

[0006] In order to achieve the above-mentioned object, in a first aspect, the present invention provides a system for solving electric field partial differential equations of integrated circuit devices, comprising: A geometric feature extraction module is used to extract the features of the geometric parameters of the integrated circuit device to obtain a first global geometric feature; an electrical feature extraction module is used to extract the features of the electrical parameters of the integrated circuit device to obtain a first global electrical feature; a material feature extraction module is used to extract the features of the material properties of the integrated circuit device to obtain a first global material feature; A fusion module, used for fusing the first global geometric feature, the first global electrical feature and the first global material feature to obtain a fusion feature; An encoding module, used for encoding the fused features to obtain encoded features; A decoding module, used to decode the coding feature to obtain the electric field distribution of the integrated circuit device; The fusion module includes: A first feature extractor is used to perform spatial grid division on the first global geometric feature according to the structure of the integrated circuit device to obtain local geometric features of each grid unit; perform feature extraction on each local geometric feature to obtain geometric parameter features of each grid unit; perform embedding processing on the geometric parameter features of each grid unit to obtain geometric embedding features of each grid unit, which together constitute the second global geometric features; A second feature extractor is used to extract features of multiple scales from the first global electrical feature, and to embed the features of each scale obtained to obtain electrical embedding features corresponding to each scale, which together constitute the second global electrical feature; The third feature extractor includes a fully connected layer, which is used to input the feature obtained by adding the second global geometric feature and the second global electrical feature into the fully connected layer for feature extraction, and add the extracted feature to the first global material feature to obtain the second global material feature; The fuser is used to use the second global geometric feature, the second global electrical feature and the second global material feature as a query matrix, a key matrix and a value matrix respectively, and fuse them based on an attention mechanism to obtain a fused feature.

[0007] Further preferably, the encoding module comprises: an embedding layer and an encoder; The embedding layer is used to embed the fused features to obtain fused embedded features; The encoder includes: m cascaded attention modules, which are used to process the fused embedded features based on the attention mechanism to obtain encoded features; m ≥ 2.

[0008] Further preferably, each of the first m1 attention modules in the encoder, in the process of processing the input features based on the attention mechanism, further comprises: after obtaining the attention map matrix, statically pruning the attention map matrix; m1≥1: Among them, in the training phase of the solution system, the attention module statically prunes the attention map matrix in the following manner: copy the attention map matrix to obtain the corresponding copy matrix; after setting the elements in the copy matrix that are less than the first preset threshold to 0, sum the copy matrix by column, and sort the columns of the copy matrix from large to small according to the column summation results, set the non-zero elements in the copy matrix to 1, and obtain a mask matrix; save the obtained mask matrix, and record the mapping relationship between the original column number and the sorted column number of each column in the copy matrix; after sorting the columns of the attention map matrix based on the above mapping relationship, perform dot multiplication with the mask matrix to complete the static pruning of the attention map matrix; In the solution phase, the attention module statically prunes the attention map matrix in the following way: after sorting the columns of the attention map matrix based on the corresponding mapping relationship obtained in the training phase, it performs a dot multiplication with the corresponding mask matrix obtained in the training phase to complete the static pruning of the attention map matrix.

[0009] Further preferably, each of the last m-m1 attention modules in the encoder, in the process of processing the input features based on the attention mechanism, further comprises: after obtaining the attention map matrix, dynamically pruning the attention map matrix: After setting the elements in the attention map matrix that are less than the second preset threshold to 0, the columns of the attention map matrix are sorted from large to small according to the column sum results to complete the dynamic pruning of the attention map matrix.

[0010] Further preferably, the decoding module comprises: a cascaded feedforward neural network and a decoder; the feedforward neural network comprises: a plurality of cascaded fully connected layers; Among them, the activation function of the fully connected layer is the ReLU function; In the solution phase, the first fully connected layer L in the feedforward neural network is the fully connected layer after removing all inactive neurons; Among them, the inactivated neurons are the neurons whose outputs are always 0 in the fully connected layer L counted during the training phase of the solution system.

[0011] Further preferably, the above decoder is a KAN model.

[0012] In a second aspect, the present invention provides a training method for the above-mentioned solution system, comprising: The training samples in the training set are used as input and the corresponding electric field distribution labels are used as output to train the above-mentioned solution system; The training set is obtained in the following way: Collect the real electric field distribution of different integrated circuit devices under different physical parameters; physical parameters include: geometric parameters, electrical parameters and material properties; Construct a training set with physical parameters as training samples and the corresponding real electric field distribution as the electric field distribution label.

[0013] In a third aspect, the present invention provides a method for solving an electric field partial differential equation of an integrated circuit device, comprising: Inputting the physical parameters of the integrated circuit device to be solved into the solving system provided by the first aspect of the present invention to obtain the electric field distribution of the integrated circuit device; Among them, physical parameters include: geometric parameters, electrical parameters and material properties.

[0014] In a fourth aspect, the present invention provides an electronic device comprising: a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the training method of the solution system provided in the second aspect of the present invention or the solution method provided in the third aspect.

[0015] In a fifth aspect, the present invention further provides a computer-readable storage medium, which includes a stored computer program, wherein when the computer program is executed by a processor, the device where the storage medium is located is controlled to execute the training method of the solution system provided in the second aspect of the present invention or the solution method provided in the third aspect.

[0016] In a sixth aspect, the invention further provides a computer program product, including a computer program / instruction, which, when executed by a processor, implements the training method of the solution system provided in the second aspect or the solution method provided in the third aspect.

[0017] In general, the above technical solutions conceived by the present invention can achieve the following beneficial effects: 1. The present invention provides a solution system for the electric field partial differential equation of an integrated circuit device, which respectively extracts the global features of the geometric parameters, electrical parameters and material properties of the integrated circuit device through different feature extraction modules, and each feature extraction module focuses on extracting a type of physical parameter to ensure that the feature extraction processes of different input parameters are independent and accurate. On this basis, the global features of the geometric parameters, electrical parameters and physical properties are integrated by constructing a geometric-electrical-material three-coupling mechanism through a fusion module. First, a physical field consistency mapping mechanism is introduced to map the electrical features to a high-dimensional feature space aligned with the geometric features to ensure the spatial consistency and complementarity of the two in expression, and enhance the coupling ability of the electrical features and geometric features. Then, through the attention mechanism, the mutual influence of the geometric parameters, electrical parameters and material properties in different electric field regions is dynamically evaluated, and the deep coupling of the three features is dynamically realized, which solves the expression problem of nonlinear complex regions in the electric field solution of the integrated circuit device, can better aggregate the extracted feature information, and improves the accuracy of solving the electric field partial differential equation of the integrated circuit device.

[0018] 2. Furthermore, in the solution system of the electric field partial differential equation of the integrated circuit device provided by the present invention, the encoding module includes: an embedding layer and an encoder; wherein the embedding layer can dynamically aggregate the feature information of the input and add position information to the input data, thereby better expressing the features in different input structures; the encoder includes multiple cascaded attention modules, which can focus on capturing the dependency between the geometric parameters and boundary conditions of the integrated circuit device, express the complex physical properties in the electric field of the integrated circuit, and provide highly structured feature expressions for downstream tasks, so that the solution system can more closely fit the mathematical structure in the operator learning while efficiently learning the operator mapping, thereby further improving the accuracy of solving the electric field partial differential equation.

[0019] 3. Furthermore, in the system for solving the electric field partial differential equations of integrated circuit devices provided by the present invention, each of the first m1 attention modules in the encoder, in the process of processing the input features based on the attention mechanism, also includes: after obtaining the attention map matrix, statically pruning the attention map matrix; by dynamically selecting and focusing on the most representative features in the input data, thereby effectively aggregating global information, thereby greatly reducing the amount of calculation, and helping the computing device to balance the workload and accelerate the entire computing process.

[0020] 4. Furthermore, in the solution system of the electric field partial differential equation of the integrated circuit device provided by the present invention, each of the last m-m1 attention modules in the encoder, in the process of processing the input features based on the attention mechanism, also includes: after obtaining the attention map matrix, dynamically pruning the attention map matrix to effectively retain the key feature information of the input data, so as not to affect the accuracy of the solution result.

[0021] 5. Further, in the solution system of the electric field partial differential equation of the integrated circuit device provided by the present invention, the decoding module includes: a cascaded feedforward neural network and a decoder; the feedforward neural network includes: a plurality of cascaded fully connected layers, which are used to capture the characteristic changes of different scales in the electric field of the integrated circuit device, including the relationship between the local electric field gradient and the global potential distribution; wherein the activation function of the fully connected layer is the ReLU function; in the solution stage, the first fully connected layer L in the feedforward neural network is the fully connected layer after removing all unactivated neurons; since the partial differential equation solution of the integrated circuit device has significant sparsity and diversity, and the activation function of the fully connected layer is the ReLU function, there are a large number of unactivated neurons in the output of the first fully connected layer. Cascaded neuron pruning is introduced in the decoding module, which greatly reduces the amount of forward propagation calculation by marking unactivated neurons during the training process and skipping the relevant calculations of these neurons during the solution process, which not only accelerates the decoding process, but also effectively reduces the demand for computing resources, so that the decoding module can quickly and accurately generate a solution result that is consistent with the electric field characteristics of the integrated circuit device, thereby significantly improving the efficiency and applicability of the entire partial differential equation solution.

[0022] 6. Furthermore, in the solution system of the electric field partial differential equation of the integrated circuit device provided by the present invention, the decoder is a KAN model. The KAN model can effectively capture the influence of sharp potential gradients, strong coupling regions or complex structures in the electric field of the integrated circuit device on the solution characteristics through its high nonlinear representation ability. The decoding module can dynamically adjust the network structure and parameters of KAN to more accurately match the specific physical characteristics of the electric field of the integrated circuit device. Through this flexible adjustment, the decoding module can not only improve the fitting accuracy of complex solutions, but also optimize the processing effect of discontinuous or non-smooth solutions. Through efficient feature processing and precise function matching, the decoding module significantly improves the efficiency and result accuracy of solving the electric field partial differential equation of the integrated circuit device. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 A schematic diagram of the structure of a system for solving electric field partial differential equations of integrated circuit devices provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0024] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0025] In order to achieve the above objectives, in a first aspect, the present invention provides a system for solving electric field partial differential equations of integrated circuit devices, such as Figure 1 As shown, including: A geometric feature extraction module is used to extract the features of the geometric parameters of the integrated circuit device to obtain a first global geometric feature; an electrical feature extraction module is used to extract the features of the electrical parameters of the integrated circuit device to obtain a first global electrical feature; a material feature extraction module is used to extract the features of the material properties of the integrated circuit device to obtain a first global material feature; A fusion module, used for fusing the first global geometric feature, the first global electrical feature and the first global material feature to obtain a fusion feature; An encoding module, used for encoding the fused features to obtain encoded features; The decoding module is used to decode the coding feature to obtain the electric field distribution of the integrated circuit device.

[0026] It should be noted that the input parameters of the partial differential equations of the above-mentioned integrated circuit devices include geometric parameters (such as gate spacing, etc.), electrical parameters (such as gate voltage, source-drain voltage, etc.), material properties (such as dielectric constant, doping concentration distribution, etc.) and grid information. These parameters can be expressed as one-dimensional parameter vectors, two-dimensional grids or high-dimensional tensors to meet the modeling requirements of complex multi-scale characteristics of integrated circuit devices. The above-mentioned integrated circuit devices can be FinFET, FD-SOI, flat CMOS and other devices, which are not limited here. Taking FinFET as an example, the above-mentioned geometric parameters include: fin width, fin height, gate spacing and other parameters; electrical parameters include: gate voltage, source-drain voltage and other parameters; material properties include: dielectric constant, doping concentration distribution and other parameters.

[0027] The above partial differential equations are specifically used to describe the electric field distribution characteristics of integrated circuit devices, including the three-dimensional Poisson equation, the three-dimensional Laplace equation, etc., which are not limited here. These equations are used to accurately model the electric field distribution within integrated circuit devices, including: potential distribution, capacitive coupling effect, carrier concentration gradient and other information, and can reflect the influence of complex geometric structures, electrical parameters and non-uniform material properties on the electric field.

[0028] It should be noted that the above-mentioned geometric feature extraction module, electrical feature extraction module and material feature extraction module can be neural network models such as fully connected neural network, multi-layer perceptron (MLP), convolutional neural network (CNN), residual neural network (ResNet), etc., which are not limited here. Preferably, in an optional implementation, each of the above-mentioned feature extraction modules adopts a convolutional neural network comprising two convolutional layers, wherein the convolution kernel of the convolutional layer is sparsely optimized to achieve adaptive length and weight. This design enables the feature extraction unit to dynamically adjust the size, step size and patch of the convolution kernel according to the local characteristics of the input data, so as to more effectively capture the key information in the input function. Through this adaptive mechanism, the solution system can flexibly respond to the feature extraction requirements of different types of input parameters, improve the accuracy and efficiency of feature extraction, while reducing redundant calculations and enhancing the performance of the overall solution system.

[0029] It should be noted that the fusion module combines the information of different physical parameters (including geometric parameters, electrical parameters and material properties) and constructs a deep coupling model between geometric structure parameters, electrical parameters and material properties through the geometric-electrical-material triple coupling mechanism to ensure that the key characteristics of the electric field are accurately captured.

[0030] Specifically, the fusion module includes: A first feature extractor is used to perform spatial grid division on the first global geometric feature according to the structure of the integrated circuit device to obtain local geometric features of each grid unit; perform feature extraction on each local geometric feature to obtain geometric parameter features of each grid unit; perform embedding processing on the geometric parameter features of each grid unit to obtain geometric embedding features of each grid unit, which together constitute the second global geometric features; A second feature extractor is used to extract features of multiple scales from the first global electrical feature, and to embed the features of each scale obtained to obtain electrical embedding features corresponding to each scale, which together constitute the second global electrical feature; The third feature extractor includes a fully connected layer, which is used to input the feature obtained by adding the second global geometric feature and the second global electrical feature into the fully connected layer for feature extraction, and add the extracted feature to the first global material feature to obtain the second global material feature; The fuser is used to use the second global geometric feature, the second global electrical feature and the second global material feature as a query matrix, a key matrix and a value matrix respectively, and fuse them based on an attention mechanism to obtain a fused feature.

[0031] The first feature extractor and the second feature extractor mentioned above can be neural network models such as a fully connected neural network, a multi-layer perceptron (MLP), a convolutional neural network (CNN), a residual neural network (ResNet), etc., which are not limited here.

[0032] The fusion module provided by the present invention solves the expression problem of nonlinear complex areas in the electric field solution of integrated circuit devices by constructing a geometric-electrical-material three-coupling mechanism to better aggregate the extracted feature information. In a specific implementation, the first global geometric feature input is used to divide the device structure into a spatial grid through a first feature extractor to extract the local geometric features of each grid unit. Subsequently, these local geometric features are further extracted to obtain corresponding geometric parameter features; the geometric parameter features of each grid unit are encoded into a high-dimensional feature vector corresponding to each grid unit through an embedding layer to form a spatial geometric feature representation that can be processed by the fusion module. In the embedding process, a boundary constraint module is added, including: dynamically marking key area features such as sharp corners, surface inflection points and thin layer structures, and assigning different weights to different key area features, thereby providing priority weights in geometric space for subsequent coupling processes. The first global electrical feature extracts the electric field response characteristics of each region of the device at multiple resolution scales through a dynamic weighted convolutional network. In order to enhance the coupling ability between electrical and geometric features, a physical field consistent mapping mechanism is introduced to map electrical features to a high-dimensional feature space aligned with geometric features to ensure the spatial consistency and complementarity of the two in expression. The material properties adopt a regional adaptive decomposition mechanism to dynamically assign different weights to material features for different geometric and electrical feature regions. For example, in high dielectric constant regions, the potential distribution characteristics are given priority, and in regions with drastic changes in conductivity, the carrier concentration changes are given priority. After the geometric, electrical and material features are initially aligned, the geometric-electrical-material joint attention mechanism is used to dynamically achieve deep coupling of the three. First, through the attention mechanism, the mutual influence of geometric structure parameters, electrical parameters and material properties in different electric field regions is dynamically evaluated, especially for complex boundary conditions and non-uniform regions, focusing on capturing the nonlinear modulation effect of material property changes on electric field distribution and carrier concentration, and finally outputting a high-dimensional coupling feature vector to accurately express the electric field distribution in complex regions under multiple physical fields.

[0033] It should be noted that the encoding module is used to encode the fused feature information, focusing on capturing the dependency between the geometric parameters and boundary conditions of the integrated circuit device, expressing the complex physical properties in the electric field of the integrated circuit, and providing a highly structured feature expression for downstream tasks. The encoding module can be an attention mechanism, a convolutional neural network, a residual neural network, etc., which are not limited here. Preferably, in an optional implementation, the encoding module includes: an embedding layer and an encoder; The embedding layer is used to embed the fused features to obtain fused embedded features; The encoder includes: m cascaded attention modules, which are used to process the fused embedded features based on the attention mechanism to obtain encoded features; m ≥ 2.

[0034] Through the above design, the encoding module can dynamically aggregate the input feature information and add position information to the input data, thereby better expressing the features in different input structures; in addition, the encoding module also enables the solution system to more closely fit the mathematical structure in operator learning while efficiently learning operator mapping.

[0035] In an optional implementation, each of the first m1 attention modules in the encoder, in the process of processing the input features based on the attention mechanism, further includes: after obtaining the attention map matrix, statically pruning the attention map matrix; m1≥1: Among them, in the training phase of the solution system, the attention module statically prunes the attention map matrix in the following manner: copy the attention map matrix to obtain the corresponding copy matrix; after setting the elements in the copy matrix that are less than the first preset threshold to 0, sum the copy matrix by column, and sort the columns of the copy matrix from large to small according to the column summation results, set the non-zero elements in the copy matrix to 1, and obtain a mask matrix; save the obtained mask matrix, and record the mapping relationship between the original column number and the sorted column number of each column in the copy matrix; after sorting the columns of the attention map matrix based on the above mapping relationship, perform dot multiplication with the mask matrix to complete the static pruning of the attention map matrix; In the solution phase, the attention module statically prunes the attention map matrix in the following way: after sorting the columns of the attention map matrix based on the corresponding mapping relationship obtained in the training phase, it performs a dot multiplication with the corresponding mask matrix obtained in the training phase to complete the static pruning of the attention map matrix.

[0036] The encoding module introduces a hybrid sparse attention mechanism through the above design, dynamically selecting and focusing on the most representative features in the input data, thereby effectively aggregating global information. During the training process, the encoding module completes efficient pruning and sparse processing according to the numerical size of the attention map, obtains the replica matrix of the attention map matrix, clears the numerical positions that are less than the set threshold, and marks the corresponding position labels. Then, the replica matrix is ​​reordered in the column direction according to the accumulated values ​​of the columns, and the corresponding relationship (mapping relationship) between the original column numbers and the sorted column numbers is recorded, and the non-zero elements in the rearranged replica matrix are set to 1 to obtain a binary mask matrix. In the reasoning process of solving partial differential equations, the columns of the attention map matrix are sorted based on the corresponding mapping relationship obtained in the training phase, and then point multiplied with the corresponding mask matrix obtained in the training phase to complete the static pruning of the attention map matrix, realizing static pruning and sparse processing of the attention map, thereby greatly reducing the amount of calculation, and is conducive to balancing the workload of computing devices and accelerating the entire calculation process.

[0037] In order to ensure the accuracy of solving partial differential equations, the acceleration method dynamically selects the attention map matrices in the attention modules that need static pruning and sparseness, and the attention map matrices in the remaining attention modules adopt a dynamic pruning and sparseness scheme.

[0038] Furthermore, in an optional implementation manner, each of the last m-m1 attention modules in the encoder, in the process of processing the input features based on the attention mechanism, further comprises: after obtaining the attention map matrix, dynamically pruning the attention map matrix: After setting the elements in the attention map matrix that are less than the second preset threshold to 0, the columns of the attention map matrix are sorted from large to small according to the column sum results to complete the dynamic pruning of the attention map matrix, and then the rearranged attention map matrix is ​​output to the next layer. This scheme effectively retains the key feature information of the input data without affecting the accuracy of the solution results.

[0039] It should be noted that the task of the decoding module is to map the encoding features output by the encoding module to the required target output space, that is, to map the high-dimensional features output by the encoding module to the target solution results, including key electric field distribution physical quantities such as potential distribution, carrier concentration and capacitive coupling effect. The decoding module can be a multi-layer perceptron, an attention mechanism module, a convolutional neural network, a residual neural network, etc., which are not limited here. Preferably, in an optional embodiment, the above-mentioned decoding module includes: a cascaded feedforward neural network and a decoder; the feedforward neural network includes: a plurality of cascaded fully connected layers, preferably two cascaded fully connected layers; wherein the activation function of the fully connected layer is a ReLU function; in the solution stage, the first fully connected layer L in the feedforward neural network is a fully connected layer after removing all inactivated neurons; wherein the inactivated neurons are neurons whose outputs are always 0 in the fully connected layer L counted in the training stage of the solution system.

[0040] Feedforward neural networks can capture the characteristic changes of different scales in the electric field of integrated circuit devices, including the relationship between the local electric field gradient and the global electric potential distribution. Since the partial differential equation solutions of integrated circuit devices are significantly sparse and diverse, and the activation function of the fully connected layer is the ReLU function, there are a large number of inactivated neurons in the output of the first fully connected layer. Cascade neuron pruning is introduced in the decoding module, which greatly reduces the amount of forward propagation calculation by marking inactivated neurons during training and skipping the relevant calculations of these neurons during the solution process (inference process). Specifically, during training, the labels of inactivated neurons are determined according to the output of the first layer; during inference, the redundant calculations of the first and subsequent layers are skipped according to these labels, ensuring that the mapping process from features to target physical quantities is more efficient. This optimized design not only speeds up the decoding process, but also effectively reduces the demand for computing resources, enabling the decoding module to quickly and accurately generate solution results that are consistent with the electric field characteristics of integrated circuit devices, thereby significantly improving the efficiency and applicability of the entire partial differential equation solution.

[0041] It should be noted that the decoder can be a KAN model, a convolutional neural network, an attention mechanism module, a residual neural network, etc., which are not limited here. Preferably, the decoder is a KAN model. The decoding module can flexibly activate the KAN model according to the complexity of the solution of the partial differential equation of the electric field of the integrated circuit device to adapt the common non-smooth solutions or solution characteristics under complex geometric boundaries in the integrated circuit device. The KAN model can more accurately match the complex solution characteristics related to the electric field of the integrated circuit device through its high nonlinear representation ability, such as sharp field intensity gradients or discontinuous solutions under gate voltage changes, and can effectively capture the impact of sharp potential gradients, strong coupling regions or complex structures in the electric field of the integrated circuit device on the solution characteristics. The decoding module can dynamically adjust the network structure and parameters of the KAN to more accurately match the specific physical characteristics of the electric field of the integrated circuit device, such as non-uniform electric field distribution and local transition of carrier density under gate voltage. Through this flexible adjustment, the decoding module can not only improve the fitting accuracy of complex solutions, but also optimize the processing effect of discontinuous or non-smooth solutions. Through efficient feature processing and precise function matching, the decoding module significantly improves the efficiency and accuracy of solving the electric field partial differential equations of integrated circuit devices. This design effectively supports the needs of integrated circuit device modeling and performance optimization, and demonstrates important application value in high-precision simulation and high-performance design.

[0042] Based on the above design, the decoding module can adapt to the different smoothness of the electric field solution of integrated circuit devices. By dynamically adjusting the network structure, it can effectively match the influence of sharp gradients or complex geometric boundaries in non-uniform electric fields on the solution characteristics, ensuring the accuracy and stability of the output results.

[0043] In a second aspect, the present invention provides a training method for the above-mentioned solution system, comprising: The training samples in the training set are used as input, and the corresponding electric field distribution labels are used as output to train the solution system provided by the first aspect of the present invention; the related technical solution is the same as the solution system provided by the first aspect of the present invention, and will not be described in detail here; The training set is obtained in the following way: Collect the real electric field distribution of different integrated circuit devices under different physical parameters; physical parameters include: geometric parameters, electrical parameters and material properties; Construct a training set with physical parameters as training samples and the corresponding real electric field distribution as the electric field distribution label.

[0044] It should be noted that there are many methods for collecting the real electric field distribution of different integrated circuit devices under different physical parameters. In one optional implementation, it can be directly measured. In another optional implementation, the finite difference method is used to solve different physical parameters respectively to obtain corresponding high-precision potential distribution, carrier concentration, capacitive coupling effect and other result data to constitute the corresponding real electric field distribution.

[0045] In an optional implementation, after the training is completed, a group of representative random data is generated as a test data set according to the input parameter format of different partial differential equations, and is input into the trained solution system to obtain the corresponding electric field distribution as the data set to be evaluated.

[0046] The finite difference method is used to solve the input parameters of the test data set and obtain the corresponding real electric field distribution as the verification data set.

[0047] The error between the data group to be evaluated and the verification data group is calculated, and when the error exceeds the preset error threshold, the parameters in the solution system are readjusted and training is performed here; when the error does not exceed the preset error threshold, the training is terminated.

[0048] By verifying the performance of the solution system and continuing to return to training when the prediction does not meet the requirements, the accuracy of the solution system can be further improved.

[0049] In order to further illustrate the solution system and training method of the electric field partial differential equation of the integrated circuit device provided by the present invention, a specific embodiment is described in detail below: This embodiment provides a method for constructing a system for solving a three-dimensional Poisson equation for electric field distribution in an integrated circuit device, including: A1: Obtain the geometric parameters, electrical parameters and material properties of integrated circuit devices. Divide the device area into a three-dimensional problem domain, use non-uniform grids for random sampling, and numerically solve the above Poisson equation through the finite difference method to obtain accurate potential distribution data and construct a training sample set.

[0050] A2: Construct a feature extraction module for the solution system and design three feature extraction units. Each feature extraction unit is used to extract the input function features of the corresponding type, namely: geometric feature extraction module, electrical feature extraction module and material feature extraction module. The geometric feature extraction module is used to process the one-dimensional parameter vector of the geometric parameters, extract the features of the geometric parameters, and obtain the first global geometric features. The electrical feature extraction module is used to extract the features of the electrical parameters of the integrated circuit device (such as extracting the three-dimensional boundary conditions of the boundary potential) to obtain the first global electrical features. The material feature extraction module is used for the features of the material properties to obtain the first global material features.

[0051] In this embodiment, each of the feature extraction units is a convolutional neural network comprising two convolutional layers, each of which comprises 9 convolutional kernels. The convolutional neural network dynamically adjusts the size, step size and patch of different convolutional kernels according to the local features of the input data to accurately capture the local features of the electric field distribution of the integrated circuit device.

[0052] A3: Construct a fusion module for solving the system, which is used to combine information from different physical parameters. The model consists of four parts: geometry processing branch, electrical processing branch, material processing branch and coupling module, to ensure accurate capture of the key features of the electric field.

[0053] It should be noted that the first global geometric feature input is used to divide the device structure into spatial grids through the first feature extractor to extract the local geometric features of each grid unit. Subsequently, these local geometric features are further extracted to obtain the corresponding geometric parameter features; the geometric parameter features of each grid unit are encoded into a high-dimensional feature vector corresponding to each grid unit through the embedding layer, while enhancing the characteristics of key areas, such as the expression ability of device boundaries or transition areas.

[0054] The first global electrical feature uses a multi-resolution convolutional network to extract the global electric field trend and local change characteristics, and processes the features of different resolutions through the embedding layer to obtain the electrical embedding features corresponding to different resolutions, which together constitute the second global electrical feature. The third feature extractor extracts material properties through the convolution layer, and uses the attention mechanism to dynamically allocate the weights of material properties in different regions to adapt to the diversity of geometric and electrical properties. Then, the fuser uses a joint attention mechanism and outputs a comprehensive high-dimensional feature tensor, which effectively captures the nonlinear dependencies and interactions between the three by evaluating the mutual influence of geometric structure parameters, electrical parameters and material properties in different regions.

[0055] A4: Construct the encoding module of the solution system, which is used to dynamically aggregate the input feature information and add position information to the input data, thereby better expressing the features in different input structures. This module consists of 5 layers of attention modules.

[0056] During the training process, the attention modules of the first two layers complete efficient pruning and sparse processing according to the element size of the attention map matrix within them, set the elements in the copy matrix of the attention map matrix that are less than the set threshold (set to 0.1 in this embodiment) to 0, and then sort the columns of the attention map matrix from large to small according to the accumulated values ​​of the columns, and then set the non-zero elements in the current copy matrix to 1 to obtain a binary mask matrix; save the obtained mask matrix, and record the mapping relationship between the original column number of each column in the copy matrix and the sorted column number.

[0057] In the reasoning process of solving partial differential equations, each of the first two layers of attention modules statically prunes the attention map matrix in the following way: after sorting the columns of the attention map matrix based on the corresponding mapping relationship obtained in the training phase, they are point-multiplied with the corresponding mask matrix obtained in the training phase to complete the static pruning of the attention map matrix, thereby greatly reducing the amount of computation and helping the computing device to balance the workload.

[0058] It should be noted that in order to ensure the accuracy of solving partial differential equations, this embodiment will dynamically select the attention map matrix in the attention module that needs to be statically pruned and sparse, and the remaining attention map matrices use a dynamic pruning and sparse scheme. In this embodiment, the first two layers are selected to use static pruning, and the last three layers are selected to use dynamic pruning. The dynamic pruning and sparse scheme refers to comparing the attention map with a set threshold (set to 0.1 in this embodiment) during the reasoning and training process. If the value is less than the threshold, it will be directly cleared, and then the columns of the attention map matrix are sorted from large to small according to the cumulative value of the column, and then the rearranged attention map and the corresponding column number label are output to the next layer. This scheme effectively retains the key feature information of the input data without affecting the accuracy of the solution.

[0059] A5: Construct a decoding module of the solution system to map the features output by the encoding module to the required target output space. In this embodiment, the decoding module includes a feedforward neural network consisting of two layers of fully connected network layers and a KAN model. In the feedforward neural network, the output of the first layer of the fully connected network layer has the characteristic of sparse neurons, that is, some neurons are not activated, so a cascade neuron pruning and sparse operation that skips unactivated neurons can be used. The cascade neuron pruning and sparse operation includes: determining the unactivated neurons according to the output of the first layer during the training process and recording their labels; during the inference process, according to the neuron labels obtained during the training process, all forward calculations related to the series of neurons in the first and second layers are skipped, thereby greatly reducing the number of calculations.

[0060] It should be noted that the use of the KAN model is dynamically selected. In order to match the non-smooth solution or the solution of complex shape in this embodiment, the KAN model is used here to significantly improve the solution efficiency and result accuracy through efficient feature processing and precise function matching.

[0061] A6: Under the same initial data conditions as the training sample set, set the same geometric parameters, electrical parameters and material properties, construct a three-dimensional problem domain, perform uniformly distributed random sampling as input data, and form a test data set.

[0062] A7: Use the test data set obtained in step A6 as input data, use the finite difference method to solve the three-dimensional Poisson equation that is the same as the training set, and obtain the solution data as the verification data set.

[0063] A8: The test data set obtained in step A6 is used as input data and input into the trained solution system to complete the inference process and obtain the corresponding solution result data as the data set to be evaluated.

[0064] A9: Calculate the fitting error between the evaluation data set obtained by solving the system in step A8 and the verification data set obtained by solving the system by the finite difference method in step A7, and judge whether the solution result of the solution system meets the expected accuracy requirements; by calculating the solution time of the solution system, evaluate whether the speed of solving the partial differential equation meets the standard.

[0065] In this embodiment, if all indicators of the solution system meet the requirements, the training is stopped and the solution system is output; otherwise, return to step A2, and adjust and optimize the network by modifying the number of training iterations, the number of convolution kernels of the feature extraction unit, the number of neural network layers of the fusion module, and the set threshold of the decoding module, so that the prediction result of the solution system is more accurate. When the number of training iterations is large, it will cause overfitting problems and lead to insufficient generalization ability of the acceleration method. It is necessary to reduce the number of training iterations; when the number of convolution kernels of the feature extraction unit or the number of network layers of the sampling layer is too large, it will lead to a large scale of network parameters, and the prediction and training time will be greatly increased. In this case, the number of convolution kernels and the number of network layers can be adjusted to reduce; when the set threshold of decoding is too large, it will lead to the loss of feature information, affecting the accuracy of the solution result, and it is necessary to appropriately reduce the set threshold.

[0066] In this embodiment, the specific steps of determining whether the obtained solution model meets the accuracy and speed requirements are as follows: Accuracy assessment, comparing the solution obtained by the finite difference method with the solution obtained by the solution system, and calculating the error indicators between them, such as the root mean square error (RMSE) or the mean absolute error (MAE). If the error is within the set accuracy requirement range, it is determined that the acceleration method meets the accuracy requirement. In this embodiment, it is set that the root mean square error of the two sets of solution result data does not exceed 0.5%.

[0067] Speed ​​evaluation, calculate the prediction speed of the solution system, that is, the time required for the solution system to complete the prediction under a given input. If the prediction speed meets the requirements of the actual application, then the solution system is judged to meet the speed requirements. In this embodiment, the maximum solution time is set to no more than 20 ms.

[0068] By evaluating these requirements, we can fully understand the performance of the solution method in terms of accuracy and speed to determine whether it meets the needs of practical applications. If it does not meet the requirements, we need to return to step A2 to further adjust and optimize the solution system to improve its performance.

[0069] In summary, the present invention proposes a solution system for the electric field partial differential equation of integrated circuit devices, aiming to significantly improve the solution efficiency and result accuracy. Based on the geometric parameters, electrical parameters and material properties of integrated circuit devices, an efficient solution system is constructed and trained by obtaining electric field distribution data under different conditions. The solution system includes multiple key modules: the feature extraction module can independently extract the physical parameter features of the input such as geometric parameters, electrical parameters and material properties; the fusion module combines information from different physical parameters to solve the expression problem of nonlinear complex areas in the electric field solution; the encoding module dynamically aggregates global and local information to capture the complex dependency between the electric field coupling effect and multi-scale features in the integrated circuit device. The decoding module maps the encoding result to the target output to adapt to non-smooth potential distribution and complex geometric shapes. In addition, optimization methods such as the geometric-electrical-material three-coupling mechanism and the sparse attention mechanism are introduced to further reduce the computational burden and enhance the model's adaptability to multi-scale characteristics. Through this method, not only the solution process of the electric field-related partial differential equations in integrated circuit devices is significantly accelerated, but also the adaptability to complex geometric shapes and non-smooth solutions is greatly improved, and the solution accuracy is improved. This method has broad application value in integrated circuit device design and performance optimization, and can effectively support the rapid development of high-performance and low-power chips.

[0070] In a third aspect, the present invention provides a method for solving an electric field partial differential equation of an integrated circuit device, comprising: Inputting the physical parameters of the integrated circuit device to be solved into the solving system provided by the first aspect of the present invention to obtain the electric field distribution of the integrated circuit device; Among them, physical parameters include: geometric parameters, electrical parameters and material properties.

[0071] The related technical solution is the same as the solution system provided in the first aspect of the present invention, and will not be described in detail here.

[0072] In a fourth aspect, the present invention provides an electronic device comprising: a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the training method of the solution system provided in the second aspect of the present invention or the solution method provided in the third aspect.

[0073] The related technical solutions are the same as the training method of the solution system provided in the second aspect of the present invention and the solution method provided in the third aspect, and will not be elaborated here.

[0074] In a fifth aspect, the present invention further provides a computer-readable storage medium, which includes a stored computer program, wherein when the computer program is executed by a processor, the device where the storage medium is located is controlled to execute the training method of the solution system provided in the second aspect of the present invention or the solution method provided in the third aspect.

[0075] The related technical solutions are the same as the training method of the solution system provided in the second aspect of the present invention and the solution method provided in the third aspect, and will not be elaborated here.

[0076] In a sixth aspect, the invention further provides a computer program product, including a computer program / instruction, which, when executed by a processor, implements the training method of the solution system provided in the second aspect or the solution method provided in the third aspect.

[0077] The related technical solutions are the same as the training method of the solution system provided in the second aspect of the present invention and the solution method provided in the third aspect, and will not be elaborated here.

[0078] It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A system for solving partial differential equations of electric fields of integrated circuit devices, characterized in that: include: A geometric feature extraction module, used to extract the features of the geometric parameters of the integrated circuit device to obtain a first global geometric feature; An electrical feature extraction module, used to extract features of electrical parameters of integrated circuit devices to obtain a first global electrical feature; A material feature extraction module, used to extract the features of the material properties of the integrated circuit device to obtain a first global material feature; A fusion module, used for fusing the first global geometric feature, the first global electrical feature and the first global material feature to obtain a fusion feature; An encoding module, used for encoding the fused features to obtain encoded features; A decoding module, used to decode the coding feature to obtain the electric field distribution of the integrated circuit device; The fusion module includes: A first feature extractor is used to perform spatial grid division on the first global geometric feature according to the structure of the integrated circuit device to obtain local geometric features of each grid unit; perform feature extraction on each local geometric feature to obtain geometric parameter features of each grid unit; perform embedding processing on the geometric parameter features of each grid unit to obtain geometric embedding features of each grid unit, which together constitute the second global geometric features; A second feature extractor is used to extract features of multiple scales from the first global electrical feature, and to embed the features of each scale obtained to obtain electrical embedding features corresponding to each scale, which together constitute the second global electrical feature; The third feature extractor includes a fully connected layer, which is used to input the feature obtained by adding the second global geometric feature and the second global electrical feature into the fully connected layer for feature extraction, and add the extracted feature to the first global material feature to obtain the second global material feature; The fuser is used to use the second global geometric feature, the second global electrical feature and the second global material feature as a query matrix, a key matrix and a value matrix respectively, and fuse them based on an attention mechanism to obtain a fused feature.

2. The solution system according to claim 1, characterized in that: The encoding module includes: embedding layer and encoder; The embedding layer is used to embed the fused features to obtain fused embedded features; The encoder includes: m cascaded attention modules, which are used to process the fused embedded features based on the attention mechanism to obtain encoded features; m≥2.

3. The solution system according to claim 2, characterized in that: Each of the first m1 attention modules in the encoder also includes the following steps in the process of processing the input features based on the attention mechanism: after obtaining the attention map matrix, static pruning of the attention map matrix; m1 ≥ 1: Among them, in the training stage of the solution system, the attention module statically prunes the attention map matrix in the following manner: copy the attention map matrix to obtain the corresponding copy matrix; after setting the elements in the copy matrix that are less than the first preset threshold to 0, sum the copy matrix by column, and sort the columns of the copy matrix from large to small according to the column summation results, set the non-zero elements in the copy matrix to 1, and obtain a mask matrix; save the obtained mask matrix, and record the mapping relationship between the original column number and the sorted column number of each column in the copy matrix; after sorting the columns of the attention map matrix based on the mapping relationship, perform dot multiplication with the mask matrix to complete the static pruning of the attention map matrix; In the solution phase, the attention module statically prunes the attention map matrix in the following way: after sorting the columns of the attention map matrix based on the corresponding mapping relationship obtained in the training phase, perform dot multiplication with the corresponding mask matrix obtained in the training phase to complete the static pruning of the attention map matrix.

4. The solution system according to claim 3, characterized in that: Each of the last m-m1 attention modules in the encoder also includes the following steps in the process of processing the input features based on the attention mechanism: After obtaining the attention map matrix, the attention map matrix is ​​dynamically pruned: After setting the elements in the attention map matrix that are less than the second preset threshold to 0, the columns of the attention map matrix are sorted from large to small according to the column sum results to complete the dynamic pruning of the attention map matrix.

5. The solution system according to any one of claims 1 to 4, characterized in that: The decoding module includes: a cascaded feedforward neural network and a decoder; the feedforward neural network includes: a plurality of cascaded fully connected layers; The activation function of the fully connected layer is a ReLU function; In the solution stage, the first fully connected layer L in the feedforward neural network is a fully connected layer after removing all inactive neurons; The inactivated neurons are neurons whose outputs are always 0 in the fully connected layer L counted during the training phase of the solution system.

6. The solution system according to claim 5, characterized in that: The decoder is a KAN model.

7. The training method for a solution system according to any one of claims 1 to 6, characterized in that: include: Using training samples in the training set as input and corresponding electric field distribution labels as output, training the solution system; The training set is obtained in the following way: Collecting the real electric field distribution of different integrated circuit devices under different physical parameters; the physical parameters include: geometric parameters, electrical parameters and material properties; The training set is constructed with physical parameters as training samples and the corresponding real electric field distribution as the electric field distribution label.

8. A method for solving electric field partial differential equations of integrated circuit devices, characterized in that: include: Inputting the physical parameters of the integrated circuit device to be solved into the solving system according to any one of claims 1 to 6 to obtain the electric field distribution of the integrated circuit device; The physical parameters include: geometric parameters, electrical parameters and material properties.

9. An electronic device, characterized in that: include: A memory and a processor, wherein the memory stores a computer program, and the processor executes the method according to any one of claims 7 to 8 when executing the computer program.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium includes a stored computer program, wherein when the computer program is executed by a processor, the device where the storage medium is located is controlled to execute the method according to any one of claims 7 to 8.

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