A Solving System, Training Method and Solving Method for Electric Field Partial Differential Equation of an Integrated Circuit Device

Abstract

The present invention discloses a solution system, a training method and a solution method for the electric field partial differential equation of an integrated circuit device, belonging to the technical field of integrated circuits; after respectively extracting the global features of the geometric parameters, electrical parameters and material properties of the integrated circuit device, a geometric-electrical-material three-coupling mechanism is constructed through a fusion module to fuse the global features of the geometric parameters, electrical parameters and physical properties. 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, ensuring the spatial consistency and complementary expression between the two, enhancing the coupling ability between the electrical features and the geometric features. Then, through the attention mechanism, the mutual influence degree 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, solving the problem of the expression of non-linear complex regions in the electric field solution of integrated circuit devices and improving the accuracy of the solution.

Description

Technical Field

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

[0002] With the development of integrated circuit technology, integrated circuit devices have been widely used in the design of high-performance and low-power chips. In modern chip design, the device structure is becoming increasingly complex and the geometric size is continuously shrinking, which makes the electric field distribution inside the integrated circuit device more non-linear and multi-scale. In order to achieve accurate simulation and optimization of the electrical performance of integrated circuit devices, it is necessary to accurately model and efficiently solve the electric field distribution, which depends on the mathematical description based on partial differential equations (PDEs).

[0003] Traditional methods for solving partial differential equations, such as the finite difference method and the finite element method, usually require high-density grid discretization of the complex geometry 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 iteration, especially when facing the multi-dimensional and multi-scale electric field modeling of integrated circuit devices, showing obvious deficiencies.

[0004] In recent years, machine learning technology has gradually been applied to the solution of partial differential equations, especially showing good prospects in accelerating calculations. 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 equation and the solution result by training a machine learning model. However, this method is only applicable to the solution of simple partial differential equations, and the structure of the integrated circuit device concerned in the present invention has non-linear 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 requirements of the prior art, the present invention provides a system for solving the electric field partial differential equation of an integrated circuit device, a training method, and a solving method, so as to solve the technical problem that the prior art cannot accurately solve the electric field partial differential equation of an integrated circuit device.

[0006] To achieve the above object, in a first aspect, the present invention provides a system for solving the electric field partial differential equation of an integrated circuit device, including:

[0007] A geometric feature extraction module for extracting the features of the geometric parameters of an integrated circuit device to obtain a first global geometric feature; an electrical feature extraction module for extracting the features of the electrical parameters of the integrated circuit device to obtain a first global electrical feature; a material feature extraction module for extracting the features of the material properties of the integrated circuit device to obtain a first global material feature;

[0008] A fusion module for fusing the first global geometric feature, the first global electrical feature, and the first global material feature to obtain a fused feature;

[0009] An encoding module for encoding the fused feature to obtain an encoded feature;

[0010] A decoding module for decoding the encoded feature to obtain the electric field distribution of the integrated circuit device;

[0011] Among them, the fusion module includes:

[0012] A first feature extractor for spatially partitioning the first global geometric feature according to the structure of the integrated circuit device to obtain the local geometric features of each grid cell; respectively extracting the features of each local geometric feature to obtain the geometric parameter features of each grid cell; performing an embedding process on the geometric parameter features of each grid cell to obtain the geometric embedding features of each grid cell, which together constitute a second global geometric feature;

[0013] A second feature extractor for extracting features of multiple scales from the first global electrical feature and performing an embedding process on the obtained features of each scale to obtain the electrical embedding features corresponding to each scale, which together constitute a second global electrical feature;

[0014] The third feature extractor includes a fully connected layer for inputting 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 adding the extracted feature to the first global material feature to obtain a second global material feature;

[0015] A fuser for using the second global geometric feature, the second global electrical feature, and the second global material feature as the query matrix, key matrix, and value matrix respectively, and performing fusion based on the attention mechanism to obtain a fused feature.

[0016] Further preferably, the encoding module includes: an embedding layer and an encoder;

[0017] The embedding layer is used for performing an embedding process on the fused feature to obtain a fused embedding feature;

[0018] The encoder includes: m cascaded attention modules for processing the fused embedding feature based on the attention mechanism to obtain an encoded feature; m≥2.

[0019] Further preferably, in each of the first m attention modules in the encoder, the process of processing the input features based on the attention mechanism further includes: after obtaining the attention map matrix, performing static pruning on the attention map matrix; m 1 ≥ 1: 1

[0020] Wherein, in the training stage of the solution system, the attention module performs static pruning on the attention map matrix in the following manner: copying the attention map matrix to obtain a corresponding copy matrix; after setting the elements in the copy matrix that are less than the first preset threshold to 0, performing column-wise summation on the copy matrix, and sorting the columns of the copy matrix from largest to smallest according to the column summation results, setting the non-zero elements in the copy matrix to 1 to obtain a mask matrix; saving the obtained mask matrix, and recording the mapping relationship between the original column numbers and the sorted column numbers of each column in the copy matrix; after sorting the columns of the attention map matrix based on the above mapping relationship, performing a dot product with the mask matrix to complete the static pruning of the attention map matrix;

[0021] In the solution stage, the attention module performs static pruning on the attention map matrix in the following manner: after sorting the columns of the attention map matrix based on the corresponding mapping relationship obtained in the training stage, performing a dot product with the corresponding mask matrix obtained in the training stage to complete the static pruning of the attention map matrix.

[0022] Further preferably, in each of the last m - m attention modules in the encoder, the process of processing the input features based on the attention mechanism further includes: after obtaining the attention map matrix, performing dynamic pruning on the attention map matrix: 1

[0023] After setting the elements in the attention map matrix that are less than the second preset threshold to 0, and sorting the columns of the attention map matrix from largest to smallest according to the column summation results to complete the dynamic pruning of the attention map matrix.

[0024] Further preferably, the above decoding module includes: a cascaded feed-forward neural network and a decoder; the feed-forward neural network includes: a plurality of cascaded fully-connected layers;

[0025] Wherein, the activation function of the fully-connected layer is the ReLU function;

[0026] In the solution stage, the first fully-connected layer L in the feed-forward neural network is a fully-connected layer after removing all unactivated neurons;

[0027] Wherein, the unactivated neurons are the neurons in the fully-connected layer L whose outputs are always 0 during the training stage of the solution system.

[0028] ​​Further preferably, the above decoder is a KAN model.

[0029] In a second aspect, the present invention provides a training method for the above solution system, including:

[0030] Using the training samples in the training set as inputs and the corresponding electric field distribution labels as outputs to train the above solution system;

[0031] wherein, the training set is obtained through the following method:

[0032] Collecting the real electric field distributions of different integrated circuit devices under different physical parameters; the physical parameters include: geometric parameters, electrical parameters, and material properties;

[0033] Constructing a training set with physical parameters as training samples and the corresponding real electric field distributions as electric field distribution labels.

[0034] In a third aspect, the present invention provides a method for solving the partial differential equation of the electric field of an integrated circuit device, including:

[0035] Inputting the physical parameters of the integrated circuit device to be solved into the solution system provided in the first aspect of the present invention to obtain the electric field distribution of the integrated circuit device;

[0036] wherein, the physical parameters include: geometric parameters, electrical parameters, and material properties.

[0037] In a fourth aspect, the present invention provides an electronic device, including: a memory and a processor, the memory stores a computer program, and when the processor executes the computer program, it executes 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.

[0038] In a fifth aspect, the present invention further provides a computer-readable storage medium, the computer-readable storage medium includes a stored computer program, wherein when the computer program is run by a processor, it controls the device where the storage medium is located 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.

[0039] In a sixth aspect, the invention further provides a computer program product, including computer program / instructions, when the computer program / instructions are executed by a processor, they implement the training method of the solution system provided in the second aspect or the solution method provided in the third aspect.

[0040] Generally speaking, through the above technical solutions conceived by the present invention, the following beneficial effects can be achieved:

[0041] 1. The present invention provides a system for solving the electric field partial differential equation of an integrated circuit device. Global features of the geometric parameters, electrical parameters, and material properties of the integrated circuit device are extracted by different feature extraction modules respectively. Each feature extraction module focuses on extracting one type of physical parameter to ensure that the feature extraction processes of different input parameters are independent and accurate from each other. On this basis, a geometric-electrical-material three-coupling mechanism is constructed by a fusion module to fuse the global features of geometric parameters, electrical parameters, and physical properties. First, a physical field consistency mapping mechanism is introduced to map electrical features to a high-dimensional feature space aligned with geometric features, ensuring the spatial consistency and complementary expression between the two, enhancing the coupling ability between electrical features and geometric features. Then, through an attention mechanism, the mutual influence degree of 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, solving the expression problem of non-linear complex regions in the electric field solution of integrated circuit devices, being able to better aggregate the extracted feature information, and improving the accuracy of solving the electric field partial differential equation of integrated circuit devices.

[0042] 2. Further, in the system for solving 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 input feature information, add position information to the input data, thereby better expressing the features in different input structures; the encoder includes a plurality of cascaded attention modules, which can focus on capturing the dependency relationship between the geometric parameters of the integrated circuit device and the boundary conditions, representing the complex physical characteristics in the integrated circuit electric field, providing a highly structured feature expression for downstream tasks, enabling the solution system to more closely fit the mathematical structure in operator learning while efficiently learning the operator mapping, and further improving the accuracy of solving the electric field partial differential equation.

[0043] 3. Further, in the system for solving the electric field partial differential equation of the integrated circuit device provided by the present invention, each of the first m attention modules in the encoder, in the process of processing the input features based on the attention mechanism, further includes: when the attention map matrix is obtained, performing static pruning on the attention map matrix; by dynamically selecting and focusing on the most representative features in the input data, thereby effectively aggregating the global information, thus greatly reducing the amount of calculation, and being beneficial for the computing device to balance the workload and accelerate the entire computing process. 1

[0044] 4. Further, in the system for solving the electric field partial differential equation of the integrated circuit device provided by the present invention, the latter m - m in the encoder 1 ​Each attention module in the attention modules further includes, during the process of processing the input features based on the attention mechanism: 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.

[0045] 5. Further, in the solution system of the partial differential equation of the electric field 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 for capturing feature changes at 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 a fully connected layer after removing all unactivated neurons; due to the significant sparsity and diversity of the solution of the partial differential equation of the integrated circuit device, 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. By marking unactivated neurons during the training process and skipping the relevant calculations of these neurons during the solution process, the computational amount of the forward propagation is greatly reduced, which not only accelerates the decoding process, but also effectively reduces the demand for computing resources, enabling the decoding module to quickly and accurately generate a solution result that conforms to the electric field characteristics of the integrated circuit device, thereby significantly improving the efficiency and applicability of the entire partial differential equation solution.

[0046] 6. Further, in the solution system of the partial differential equation of the electric field of the integrated circuit device provided by the present invention, the decoder is a KAN model. Through its high non-linear representation ability, the KAN model can effectively capture the influence of sharp potential gradients, strongly coupled 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 precisely 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 the solution of the partial differential equation of the electric field of the integrated circuit device. Description of the Drawings

[0047] Figure 1 It is a schematic structural diagram of the solution system of the partial differential equation of the electric field of the integrated circuit device provided by the embodiment of the present invention. Detailed Embodiments

[0048] To make the objectives, technical solutions and advantages of the present invention more clear and understandable, the present invention will be further described in detail below with reference to 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 used 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.

[0049] To achieve the above objective, in a first aspect, the present invention provides a solution system for the partial differential equation of the electric field of an integrated circuit device, as Figure 1 shown, including:

[0050] A geometric feature extraction module, configured to extract the features of the geometric parameters of the integrated circuit device to obtain the first global geometric feature; an electrical feature extraction module, configured to extract the features of the electrical parameters of the integrated circuit device to obtain the first global electrical feature; a material feature extraction module, configured to extract the features of the material properties of the integrated circuit device to obtain the first global material feature;

[0051] A fusion module, configured to fuse the first global geometric feature, the first global electrical feature, and the first global material feature to obtain a fusion feature;

[0052] An encoding module, configured to encode the fusion feature to obtain an encoded feature;

[0053] A decoding module, configured to decode the encoded feature to obtain the electric field distribution of the integrated circuit device.

[0054] It should be noted that the input parameters of the partial differential equation of the above integrated circuit device include geometric parameters (such as gate pitch, 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 represented as one-dimensional parameter vectors, two-dimensional grids, or high-dimensional tensors to meet the modeling requirements of the complex multi-scale characteristics of integrated circuit devices. The above integrated circuit device can be a FinFET, FD-SOI, planar CMOS, etc. device, which is not limited here. Taking the FinFET as an example, the above geometric parameters include: fin width, fin height, gate pitch 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.

[0055] The above partial differential equation is specifically used to describe the electric field distribution characteristics of the integrated circuit device, including three-dimensional Poisson equation, three-dimensional Laplace equation, etc., which is not limited here. These equations are used to accurately model the electric field distribution inside the integrated circuit device, specifically including: potential distribution, capacitance 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.

[0056] It should be noted that the above geometric feature extraction module, electrical feature extraction module, and material feature extraction module can be neural network models such as fully connected neural networks, multi-layer perceptrons (MLPs), convolutional neural networks (CNNs), and residual neural networks (ResNets), which are not limited here. Preferably, in an alternative embodiment, each of the above feature extraction modules employs a convolutional neural network comprising two convolutional layers, where the convolutional kernels of the convolutional layers are sparsely optimized to achieve adaptive lengths and weights. This design enables the feature extraction unit to dynamically adjust the size, stride, and patch of the convolutional kernel according to the local features of the input data, thereby more effectively capturing the key information in the input function. Through this adaptive mechanism, the solution system can flexibly handle the feature extraction requirements of different types of input parameters, improving the accuracy and efficiency of feature extraction, reducing redundant calculations, and enhancing the performance of the overall solution system.

[0057] 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 the geometric structure parameters, electrical parameters, and material properties through a geometric-electrical-material three-coupling mechanism to ensure accurately capturing the key features of the electric field.

[0058] Specifically, the fusion module includes:

[0059] The first feature extractor is used to perform spatial grid division on the first global geometric feature according to the integrated circuit device structure to obtain the local geometric features of each grid unit; perform feature extraction on each local geometric feature respectively to obtain the geometric parameter features of each grid unit; perform embedding processing on the geometric parameter features of each grid unit to obtain the geometric embedding features of each grid unit, which together constitute the second global geometric feature;

[0060] The second feature extractor is used to perform feature extraction on the first global electrical feature at multiple scales, and perform embedding processing on the obtained features at each scale to obtain the electrical embedding features corresponding to each scale, which together constitute the second global electrical feature;

[0061] 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;

[0062] The fuser is used to use the second global geometric feature, the second global electrical feature, and the second global material feature as the query matrix, key matrix, and value matrix respectively, and perform fusion based on the attention mechanism to obtain the fusion feature.

[0063] The above-mentioned first feature extractor and second feature extractor can be neural network models such as fully-connected neural networks, multi-layer perceptrons (MLP), convolutional neural networks (CNN), residual neural networks (ResNet), etc., which are not limited here.

[0064] The fusion module provided by the present invention solves the problem of expressing non-linear complex regions in the electric field solution of integrated circuit devices by constructing a geometric-electrical-material three-coupling mechanism, so as to better aggregate the extracted feature information. In a specific embodiment, the input first global geometric feature performs spatial grid division on the device structure through the first feature extractor, and extracts the local geometric features of each grid unit. Subsequently, further feature extraction is performed on these local geometric features respectively to obtain the corresponding geometric parameter features; the geometric parameter features of each grid unit are encoded into high-dimensional feature vectors corresponding to each grid unit through an embedding layer, forming a spatial geometric feature representation that can be processed by the fusion module. Among them, during the embedding process, a boundary constraint module is added, including: dynamically marking key region features such as sharp corners, surface inflection points, and thin layer structures, and assigning different weights to different key region features, so as to provide a priority weight in the geometric space for the subsequent coupling process. The first global electrical feature extracts the electric field response features of each region of the device at multiple resolution scales through a dynamic weighted convolutional network. In order to enhance the coupling ability between the electrical feature and the geometric feature, a physical field consistency mapping mechanism is introduced to map the electrical feature to a high-dimensional feature space aligned with the geometric feature, ensuring the spatial consistency and complementary expression between the two. The material properties adopt a region adaptive decomposition mechanism, and different weights are dynamically assigned to the material features for different geometric and electrical feature regions. For example, in regions with high dielectric constants, the potential distribution features are given priority attention, and in regions where the conductivity changes violently, the changes in carrier concentration are given priority focus. After the geometric feature, electrical feature, and material feature are initially aligned, a geometric-electrical-material joint attention mechanism is adopted to dynamically realize the deep coupling of the three. First, through the attention mechanism, the mutual influence degree 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, the non-linear modulation effect of material property changes on the electric field distribution and carrier concentration is mainly captured, and finally a high-dimensional coupled feature vector is output to accurately express the electric field distribution in complex regions under multi-physical fields.

[0065] It should be noted that the encoding module is used to encode the fused feature information, mainly capture the dependence relationship between the geometric parameters and boundary conditions of the integrated circuit device, represent the complex physical characteristics in the integrated circuit electric field, and provide 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 alternative embodiment, the encoding module includes: an embedding layer and an encoder;

[0066] The embedding layer is used to perform embedding processing on the fused features to obtain fused embedding features;

[0067] The encoder includes: m cascaded attention modules, which are used to process the fused embedding features based on the attention mechanism to obtain encoded features; m ≥ 2.

[0068] Through the above design, the encoding module can dynamically aggregate the input feature information, add position information to the input data, and thus better express the features in different input structures; in addition, the encoding module also enables the solution system to be more in line with the mathematical structure in operator learning while efficiently learning the operator mapping.

[0069] In an alternative embodiment, each of the first m 1 attention modules in the encoder further includes, during the process of processing the input features based on the attention mechanism: when the attention map matrix is obtained, performing static pruning on the attention map matrix; m 1 ≥ 1:

[0070] Wherein, during the training stage of the solution system, the attention module performs static pruning on the attention map matrix in the following manner: copying the attention map matrix to obtain a corresponding copy matrix; setting the elements in the copy matrix that are less than the first preset threshold to 0, then performing column-wise summation on the copy matrix, sorting the columns of the copy matrix from largest to smallest according to the column summation results, setting the non-zero elements in the copy matrix to 1 to obtain a mask matrix; saving the obtained mask matrix and recording the mapping relationship between the original column numbers and the sorted column numbers of each column in the copy matrix; after sorting the columns of the attention map matrix based on the above mapping relationship, performing a dot product with the mask matrix to complete the static pruning of the attention map matrix;

[0071] During the solution stage, the attention module performs static pruning on the attention map matrix in the following manner: after sorting the columns of the attention map matrix based on the corresponding mapping relationship obtained during the training stage, performing a dot product with the corresponding mask matrix obtained during the training stage to complete the static pruning of the attention map matrix.

[0072] The encoding module introduces a hybrid sparse attention mechanism through the above design, dynamically selects and focuses on the most representative features in the input data, thereby effectively aggregating global information. During the training process, the encoding module performs efficient pruning and sparse processing according to the numerical values of the attention map, obtains a copy matrix of the attention map matrix, clears the numerical positions smaller than the set threshold, and marks their corresponding position labels. Subsequently, the copy matrix is re-sorted in the column direction according to the cumulative numerical values of each column, and the corresponding relationship (mapping relationship) between the original column numbers and the sorted column numbers is recorded. The non-zero elements in the re-sorted copy matrix are set to 1 to obtain a binary mask matrix. During the inference process of solving the partial differential equation, after sorting each column of the attention map matrix based on the corresponding mapping relationship obtained in the training stage, it is multiplied point by point with the corresponding mask matrix obtained in the training stage to complete the static pruning of the attention map matrix, realizing the static pruning and sparse processing of the attention map. Thereby, the amount of calculation is greatly reduced, and it is beneficial for the computing device to balance the workload and accelerate the entire computing process.

[0073] To ensure the solution accuracy of the partial differential equation, the acceleration method dynamically selects the attention map matrix in the attention module that needs to be statically pruned and sparse, and the attention map matrices in the remaining attention modules adopt the dynamic pruning and sparse scheme.

[0074] Further, in an alternative embodiment, each of the last m - m 1 attention modules in the encoder, during the process of processing the input features based on the attention mechanism, further includes: when the attention map matrix is obtained, performing dynamic pruning on the attention map matrix:

[0075] After setting the elements in the attention map matrix that are smaller than the second preset threshold to 0, the columns of the attention map matrix are sorted from largest to smallest according to the column sum results to complete the dynamic pruning of the attention map matrix, and then the re-sorted 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 result.

[0076] It should be noted that the task of the decoding module is to map the encoded 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 physical quantities of the electric field distribution such as the electric potential distribution, carrier concentration, and capacitance 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 is not limited here. Preferably, in an alternative embodiment, the above 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 the 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 unactivated neurons; wherein, the unactivated neurons are the neurons with an output of always 0 in the fully connected layer L statistically during the training stage of the solution system.

[0077] The feedforward neural network can capture the feature changes at 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 solutions of the partial differential equations of integrated circuit devices have 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. By marking the unactivated neurons during the training process and skipping the relevant calculations of these neurons during the solution process (inference process), the computational amount of the forward propagation is greatly reduced. Specifically, the labels of the unactivated neurons are determined according to the output of the first layer during training; during inference, the redundant calculations of the first layer 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 accelerates the decoding process but also effectively reduces the demand for computing resources, enabling the decoding module to quickly and accurately generate solution results consistent with the electric field characteristics of integrated circuit devices, thus significantly improving the efficiency and applicability of the entire partial differential equation solution.

[0078] It should be noted that the above 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 above 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, so as to adapt to the solution characteristics of common non-smooth solutions or complex geometric boundaries in the integrated circuit device. Through its high non-linear representation ability, the KAN model can more accurately match the complex solution characteristics related to the electric field of the integrated circuit device, such as the sharp field strength gradient or discontinuous solution under the change of gate voltage, and can effectively capture the influence of sharp potential gradients, strongly coupled 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 the non-uniform electric field distribution under the gate voltage and the local transition of the carrier density. 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 accurate function matching, the decoding module significantly improves the efficiency and result accuracy of solving the partial differential equation of the electric field of the integrated circuit device. This design effectively supports the device modeling and performance optimization requirements of the integrated circuit device, and demonstrates important application value in high-precision simulation and high-performance design.

[0079] Based on the above design, the decoding module can adapt to different smoothness of the solution of the electric field of the integrated circuit device. By dynamically adjusting the network structure, it can effectively match the influence of sharp gradients or complex geometric boundaries in the non-uniform electric field on the solution characteristics, ensuring the accuracy and stability of the output results.

[0080] In a second aspect, the present invention provides a training method for the above-mentioned solving system, including:

[0081] Taking the training samples in the training set as inputs and the corresponding electric field distribution labels as outputs, training the solving system provided in the first aspect of the present invention; the related technical solutions are the same as those of the solving system provided in the first aspect of the present invention, which will not be elaborated here;

[0082] Among them, the training set is obtained through the following methods:

[0083] Collect the real electric field distributions of different integrated circuit devices under different physical parameters; the physical parameters include: geometric parameters, electrical parameters, and material properties;

[0084] Construct a training set with physical parameters as training samples and the corresponding real electric field distributions as electric field distribution labels.

[0085] It should be noted that there are various methods for collecting the true electric field distribution of different integrated circuit devices under different physical parameters. In an alternative implementation, it can be directly measured. In another alternative implementation, the finite difference method is used to solve different physical parameters respectively to obtain corresponding result data such as high-precision potential distribution, carrier concentration, and capacitive coupling effect, which constitute the corresponding true electric field distribution.

[0086] In an alternative implementation, after the training is completed, according to the input parameter formats of different partial differential equations, a set of representative random data is generated as the test data set, and it is input into the trained solution system to obtain the corresponding electric field distribution as the data set to be evaluated.

[0087] The input parameters of the test data set are solved using the finite difference method to obtain the corresponding true electric field distribution as the verification data set.

[0088] Calculate the error between the data set to be evaluated and the verification data set. When the error exceeds the preset error threshold, readjust the parameters in the solution system and perform training here; when the error does not exceed the preset error threshold, end the training.

[0089] By verifying the performance of the solution system, when the prediction does not meet the requirements, continue to return for training, which can further improve the accuracy of the solution system.

[0090] To further illustrate the solution system and its training method for the electric field partial differential equation of the integrated circuit device provided by the present invention, a specific embodiment will be described in detail below:

[0091] This embodiment provides a method for constructing a solution system for a three-dimensional Poisson equation of the electric field distribution in an integrated circuit device, including:

[0092] A1: Obtain the geometric parameters, electrical parameters, and material properties of the integrated circuit device. Divide the device area into a three-dimensional problem domain, perform random sampling using a non-uniform grid, and numerically solve the above Poisson equation using the finite difference method to obtain accurate potential distribution data and construct a training sample set.

[0093] A2: Construct a feature extraction module for the solution system, design 3 feature extraction units, and 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 feature. 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 feature. The material feature extraction module is used for the features of the material properties to obtain the first global material feature.

[0094] In this embodiment, each of the above-mentioned feature extraction units is a convolutional neural network including two convolutional layers, and each convolutional layer includes 9 convolutional kernels. The convolutional neural network dynamically adjusts the sizes, strides, and patches 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.

[0095] A3: Construct a fusion module for the solution system to combine information from different physical parameters. This model consists of four parts: a geometric processing branch, an electrical processing branch, a material processing branch, and a coupling module, ensuring accurate capture of the key features of the electric field.

[0096] It should be noted that the first global geometric feature of the input performs spatial grid division on the device structure through the first feature extractor to extract the local geometric features of each grid cell. Subsequently, further feature extraction is performed on these local geometric features respectively to obtain the corresponding geometric parameter features; the geometric parameter features of each grid cell are encoded into high-dimensional feature vectors corresponding to each grid cell through the embedding layer, while enhancing the characteristics of key regions, such as the expression ability of the device boundary or transition region.

[0097] The first global electrical feature uses a multi-resolution convolutional network to extract the global electric field trend and local change features, and processes the features of different resolutions through the embedding layer to obtain the electrical embedding features corresponding to different resolutions, jointly constituting the second global electrical feature. The third feature extractor extracts the material characteristics through the convolutional layer, and at the same time uses the attention mechanism to dynamically allocate the weights of the material characteristics in different regions, so as to adapt to the diversity of geometric and electrical characteristics. Then, the fuser uses the joint attention mechanism and outputs a comprehensive high-dimensional feature tensor, and effectively captures the non-linear dependence relationship and interaction among the three by evaluating the mutual influence degree of the geometric structure parameters, electrical parameters, and material properties in different regions.

[0098] A4: Construct an encoding module for the solution system to dynamically aggregate the input feature information, add position information to the input data, and thus better express the features in different input structures. This module consists of 5 attention modules.

[0099] During the training process, the first two attention modules complete efficient pruning and sparse processing according to the element sizes of their internal attention map matrices. 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) are set to 0. Subsequently, the columns of the attention map matrix are sorted from large to small according to the cumulative values by column. Then, the non-zero elements in the current copy matrix are set to 1 to obtain a binary mask matrix; the obtained mask matrix is saved, and the mapping relationship between the original column numbers and the sorted column numbers of each column in the copy matrix is recorded.

[0100] In the reasoning process of solving partial differential equations, each layer of the attention module in the first two layers 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 stage, it multiplies with the corresponding mask matrix obtained in the training stage to complete the static pruning of the attention map matrix, thereby greatly reducing the computational amount and facilitating the computing device to balance the workload.

[0101] It should be noted that in order to ensure the solution accuracy of partial differential equations, this embodiment dynamically selects the attention map matrix in the attention module that needs to be statically pruned and sparsified, and the remaining attention map matrices adopt the dynamic pruning and sparsification scheme. In this embodiment, the first two layers are selected to use static pruning, and the last three layers use dynamic pruning. The dynamic pruning and sparsification scheme means that during the reasoning and training processes, the attention map is compared with a set threshold (set to 0.1 in this embodiment). If the value is less than the threshold, it will be directly cleared. Subsequently, the columns of the attention map matrix are sorted from large to small according to the cumulative values of the columns, and then the rearranged attention map and the corresponding column sequence number labels 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 result.

[0102] A5: Construct the 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 consists of a feed-forward neural network composed of two fully connected network layers and a KAN model. In the feed-forward neural network, the output of the first fully connected network layer has the characteristic of neuron sparsity, that is, some neurons are not activated. Therefore, the cascade neuron pruning and sparsification operation of skipping the unactivated neurons can be adopted. The cascade neuron pruning and sparsification operation includes: determining the unactivated neurons according to the output of the first layer during the training process and recording their labels; during the reasoning process, according to the neuron labels obtained during the training process, all the forward calculations related to this series of neurons in the first and second layers are skipped, thereby greatly reducing the number of calculations.

[0103] It should be noted that the use of the KAN model is dynamically selected. In order to match the non-smooth solutions or solutions with complex shapes in this embodiment, the KAN model is adopted here, which significantly improves the solution efficiency and result accuracy through efficient feature processing and precise function matching.

[0104] 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, and perform uniformly distributed random sampling as input data to form a test data group.

[0105] A7: Use the test data set obtained in step A6 as input data, and use the finite difference method to solve the same three-dimensional Poisson equation as the training set to obtain the solution result data as the verification data set.

[0106] A8: Use the test data set obtained in step A6 as input data, input it into the trained solution system, complete the inference process, and obtain the corresponding solution result data as the data set to be evaluated.

[0107] A9: Calculate the fitting error between the data set to be evaluated obtained by the solution system in step A8 and the verification data set obtained by the finite difference method in step A7, and determine whether the solution result of the obtained solution system meets the expected set accuracy requirements; by calculating the solution time of this solution system, evaluate whether the speed of solving the partial differential equation meets the standard.

[0108] In this embodiment, if all indicators of the solution system meet the requirements, stop training and output the solution system; otherwise, return to step A2, and adjust and optimize the network by modifying the training iteration times, 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 training iteration times are relatively large, it will lead to overfitting problems and insufficient generalization ability of the acceleration method, and the training iteration times need to be reduced; 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 network parameter scale, and both the prediction and training times will increase significantly, then the number of convolution kernels and network layers can be adjusted and reduced; when the set threshold of decoding is too large, it will lead to loss of feature information and affect the accuracy of the solution result, and the set threshold needs to be appropriately reduced.

[0109] In this embodiment, the specific steps for determining whether the obtained solution model meets the accuracy and speed requirements are as follows:

[0110] Accuracy evaluation: Compare the solution result implemented by the finite difference method with the solution result obtained by the solution system, and calculate the error index between them, such as root mean square error (RMSE) or mean absolute error (MAE), etc. If the error is within the set accuracy requirement range, it is determined that the acceleration method meets the accuracy requirements. In this embodiment, it is set that the root mean square error of the two groups of solution result data does not exceed 0.5%.

[0111] 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, it is determined that the solution system meets the speed requirements. In this embodiment, it is set that the maximum solution time does not exceed 20 ms.

[0112] By evaluating these requirements, the performance of the solution method in terms of accuracy and speed can be comprehensively understood to determine whether it meets the needs of practical applications. If the requirements are not met, it is necessary to return to step A2 to further adjust and optimize the solution system to improve its performance.

[0113] In summary, the present invention proposes a solution system for the partial differential equation of the electric field of an integrated circuit device, aiming to significantly improve the solution efficiency and result accuracy. Based on the geometric parameters, electrical parameters, and material properties of the integrated circuit device, by obtaining the electric field distribution data under different conditions, an efficient solution system is constructed and trained. 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 the information from different physical parameters to solve the expression problem of the non-linear complex region in the electric field solution; the encoding module dynamically aggregates global and local information to capture the complex dependence relationship 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 the non-smooth potential distribution and complex geometry. In addition, optimization means 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 partial differential equation related to the electric field in the integrated circuit device is significantly accelerated, but also the adaptability to complex geometry and non-smooth solutions is greatly improved, and the solution accuracy is enhanced. In the design and performance optimization of integrated circuit devices, this method has broad application value and can effectively support the rapid development of high-performance and low-power chips.

[0114] In a third aspect, the present invention provides a method for solving the partial differential equation of the electric field of an integrated circuit device, including:

[0115] Input the physical parameters of the integrated circuit device to be solved into the solution system provided in the first aspect of the present invention to obtain the electric field distribution of the integrated circuit device;

[0116] wherein the physical parameters include: geometric parameters, electrical parameters, and material properties.

[0117] The related technical solutions are the same as those of the solution system provided in the first aspect of the present invention and will not be elaborated here.

[0118] In a fourth aspect, the present invention provides an electronic device, including: a memory and a processor, the memory stores a computer program, and when the processor executes the computer program, it executes 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 of the present invention.

[0119] 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, which will not be elaborated here.

[0120] In a fifth aspect, the present invention further provides a computer-readable storage medium, which includes a stored computer program. When the computer program is run by a processor, it controls the device where the storage medium is located 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.

[0121] 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, which will not be elaborated here.

[0122] In a sixth aspect, the invention further provides a computer program product, including a computer program / instructions. When the computer program / instructions are executed by a processor, they implement the training method of the solution system provided in the second aspect or the solution method provided in the third aspect.

[0123] 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, which will not be elaborated here.

[0124] Those skilled in the art can easily understand that the above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principles of the present invention shall 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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