A Finite Element Mesh Generation Method for Core Thermal Simulation Based on Neural Networks

Abstract

This invention relates to a neural network-based finite element mesh generation method for chip thermal simulation. The method includes a geometric and thermal feature extraction module, a temperature distribution prediction module, and an intelligent mesh optimization module. The geometric and thermal feature extraction module uses tensor construction combined with multi-scale convolution, pyramid pooling, and deformable convolution to achieve accurate prediction of chip temperature distribution. The intelligent mesh optimization module adaptively optimizes the finite element mesh by coupling thermal gradients and geometric constraints, reducing the number of mesh cells and improving computational efficiency. This invention is the first to combine deep learning with finite element mesh generation, using neural network prediction of thermal distribution to replace the traditional iterative mesh refinement process, significantly improving mesh generation speed while maintaining thermal simulation accuracy within 0.8%. This method is particularly suitable for complex 2.5D / 3D chip packaging structures, effectively addressing the thermal management challenges in modern integrated circuit design and providing a fast and accurate thermal simulation tool for chip design.

Description

Technical Field

[0001] This invention relates to the field of integrated circuit thermal management technology, and more specifically to a finite element mesh generation method for chip thermal simulation based on neural networks. Background Technology

[0002] With the continuous development of semiconductor technology, integrated circuit (IC) systems are gradually approaching their physical limits in the post-Moore's Law era. To address this challenge, chip-scale packaging technology has emerged. This technology integrates multiple independently manufactured functional chips into a single system through advanced 2.5D / 3D packaging, overcoming the limitations of single manufacturing processes while reducing defect rates and manufacturing costs. However, as the power density of modern chip-scale packaging designs continues to increase and feature sizes continue to shrink, thermal analysis problems are becoming increasingly severe. Traditional thermal simulation methods such as the finite element method (FEM) and the finite difference method (FDM), while highly accurate, consume significant computational resources and cannot meet the needs of repeated thermal simulations in the design optimization process of complex tasks.

[0003] In recent years, researchers have attempted to accelerate the solution of thermal equations using neural networks. However, these deep learning methods exhibit poor generalization ability when dealing with different chip structures, and their end-to-end thermal predictions often fail to meet simulation accuracy requirements. Traditional FEM mesh optimization relies on an iterative refinement process based on posterior error analysis, resulting in significant computational overhead. While some active optimization strategies based on graph convolutional networks (GCNs), machine learning, and reinforcement learning have shown potential in improving efficiency, these methods primarily focus on two-dimensional mesh optimization and fail to effectively handle high-temperature regions and regions with large thermal gradients in integrated circuit thermal simulations.

[0004] Therefore, there is an urgent need for a method that can significantly accelerate mesh generation and optimization without sacrificing simulation accuracy, in order to address the increasingly complex thermal management challenges in modern integrated circuit design. Summary of the Invention

[0005] Purpose of the invention: This invention aims to provide a finite element mesh generation method for chip thermal simulation based on neural networks, in order to solve the problem of low efficiency in mesh generation and optimization in existing technologies for 2.5D / 3D chip thermal simulation, achieve fast and high-precision thermal simulation, and provide an efficient thermal management solution for modern integrated circuit design.

[0006] To achieve the above objectives, this invention provides a finite element mesh generation method for core particle thermal simulation based on neural networks, comprising the following steps:

[0007] S1: Convert the geometric boundaries and physical properties of the 2.5D / 3D chip into structured tensor inputs. The geometric boundary is defined as the edge set E = {e...} i (p i ,pi ′)}, containing component volume V={v i (comp) (e.g., TSV, chip, substrate, etc.). Critical boundaries are defined using formulas. Screening. Simultaneously, the 3D structure is decomposed into multiple planar P layers. i Each layer of feature tensors encodes material properties (thermal conductivity k). p Density ρ p Heat source H sp (etc.) and thickness information to form the input tensor.

[0008] S2: Parallel multi-scale convolutional kernels (1×1×1, 3×3×3, 5×5×5) are used to extract local details and global thermal features. Pyramid pooling is combined to enhance spatial awareness, and deformable convolution is used to adapt to material heterogeneity. Subsequently, a multi-attention head mechanism is used to fuse encoder and decoder features. Spatial features are mapped to the frequency domain through 3D Discrete Cosine Transform (3D-DCT), and the weights of high-frequency thermal gradient regions are dynamically adjusted. Spatial features are then reconstructed through 3D Inverse Discrete Cosine Transform (3D-IDCT). Afterward, transposed convolution (TrConv) is used to progressively upsample the feature map, and the high-temperature gradient region is weighted and refined using an attention fusion module. Finally, a high-resolution temperature prediction map is output.

[0009] S3: Based on the predicted planar temperature distribution, a continuous 3D temperature field is reconstructed using a physical information interpolation scheme. The interpolation formula is:

[0010]

[0011] Ensure that the temperature field satisfies the steady-state thermal equation And maintain the continuity of material boundaries.

[0012] Where, x p ,y p ,z p Let n be the node coordinates. R This is the z-axis resolution.

[0013] A refinement parameter σ(x,y,z) is generated by combining temperature gradient and geometric features to control the mesh density. The formula for the normalized heat contribution parameter is:

[0014]

[0015] Where T is temperature, and a geometric weighting function is introduced. Integrating thermal and geometric information:

[0016]

[0017] Final refined parameters:

[0018]

[0019] Ensure improved mesh resolution at the high-temperature gradient region and material interface.

[0020] S4: Based on the refinement parameter σ, the initial coarse mesh is locally refined. A hybrid loss function is used to jointly optimize the prediction and simulation accuracy, specifically including thermal prediction loss and physical consistency loss. The mean square error (MSE) constrains the spatial domain temperature error, and the physical consistency loss is calculated using the residual R(T) of the steady-state thermal equation. h ) and gradient jump term J(T h Strengthen the understanding of physical laws. The specific formula is as follows:

[0021]

[0022] The joint optimization objective is the total loss L total =L s +αL physics , where α is the weight hyperparameter.

[0023] A finite element mesh generation system for core particle thermal simulation based on neural networks, the system comprising:

[0024] The geometric and thermal feature extraction module is used to perform dimensionality reduction and feature fusion on the input geometric parameters, material parameters, and heat source parameters;

[0025] Temperature distribution prediction module, used to extract and predict the chip's temperature distribution based on the enhanced U-Net architecture;

[0026] The intelligent mesh optimization module is used to generate thermal-geometry coupled mesh optimization parameters based on the predicted temperature distribution and geometric constraints.

[0027] The adaptive mesh refinement module is used to adaptively refine the initial coarse mesh according to the optimization parameters to generate the final finite element mesh.

[0028] An electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the aforementioned neural network-based finite element mesh generation method for core particle thermal simulation.

[0029] A computer-readable storage medium storing computer instructions that, when executed by a processor, implement the aforementioned neural network-based finite element mesh generation method for core particle thermal simulation.

[0030] Beneficial Effects: This invention achieves, for the first time, highly efficient finite element mesh optimization without iterative refinement by fusing deep learning-driven thermal distribution prediction with geometric features. Key technological innovations include: an enhanced U-Net architecture that accurately captures high-frequency thermal gradients through multi-scale convolution and attention mechanisms; dynamic balancing of temperature gradient and geometric complexity in thermal-geometric refinement parameters to achieve local adaptive optimization; and physics-guided interpolation that ensures the continuity and physical rationality of the 3D temperature field, avoiding the accumulation of numerical errors. This method provides a fast and high-precision thermal management solution for complex 2.5D / 3D chip design. Attached Figure Description

[0031] Figure 1 This is a diagram of the grid optimization algorithm architecture of the present invention, showing the connection relationship between input features, predicted temperature, and feature fusion.

[0032] Figure 2 : This describes the detailed structure of the deep learning network in this invention.

[0033] Figure 3-4 This section compares the experimental results of the present invention under different test cases. Detailed Implementation

[0034] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0035] Example 1, see Figure 1 , Figure 2 A finite element mesh generation method for core thermal simulation based on neural networks, the method comprising the following steps:

[0036] S1: Input the geometric parameters, material parameters, heat source parameters and boundary conditions of the chip. The geometric and thermal feature extraction module performs tensor construction to generate an input tensor containing geometric boundaries, material properties, power distribution, boundary conditions and thermal distribution features.

[0037] S2: The input tensor is processed by the temperature distribution prediction module. Based on the enhanced U-Net architecture, multi-scale convolution, pyramid pooling and deformable convolution are combined to extract the temperature distribution features of the chip and generate preliminary temperature distribution prediction results.

[0038] S3: Through the intelligent mesh optimization module, combined with the temperature distribution prediction results and geometric constraints, thermal-geometric coupling mesh optimization parameters are generated to guide the adaptive refinement of the finite element mesh;

[0039] S4: Based on the mesh optimization parameters, the initial coarse mesh is adaptively refined to generate an optimized finite element mesh, reducing the number of mesh elements, improving simulation efficiency, and maintaining thermal simulation accuracy.

[0040] By combining the temperature prediction method of the deep neural network segmentation model with key geometric information, the finite element mesh is optimized. In step S2, the temperature distribution prediction module includes the following steps:

[0041] 2-1: Data Preprocessing: The input tensors are processed through multi-scale convolutional layers. Convolutional kernels of different sizes (1×1×1, 3×3×3, 5×5×5) are used in parallel to extract local details and global heat distribution features, generating multi-scale feature maps.

[0042] 2-2: Feature Extraction: Pyramid pooling is performed on the multi-scale feature map. Pooling windows of different sizes are used to enhance spatial feature capture capabilities and extract more global heat distribution information.

[0043] 2-3: Apply deformable convolution operations to the feature maps after multi-scale convolution and pyramid pooling to enhance the network's adaptability to chip material heterogeneity and generate more representative thermal distribution features.

[0044] 2-4: By using attention-based skip connections, the features extracted by the encoder are fused with the upsampled features from the decoder. Combining 3D Discrete Cosine Transform (3D-DCT) and 3D Inverse Discrete Cosine Transform (3D-IDCT), the feature reconstruction capability for regions with large temperature gradient changes is enhanced, generating accurate temperature distribution prediction results. (This mainly utilizes a deep learning segmentation model for prediction.)

[0045] 2-5: Subsequently, based on the temperature gradient information from the temperature prediction results and combined with the key geometric boundary information, the coarse finite element mesh of the heterogeneous integrated chip is refined to obtain the optimized mesh.

[0046] In step S3, the steps of the smart grid optimization module include:

[0047] 3-1: Based on the temperature distribution results output by the temperature distribution prediction module, and combined with the chip's geometric boundary information, thermal-geometric coupling mesh optimization parameters are generated. These parameters are calculated using normalized temperature gradients and geometric features, and the formula is as follows:

[0048]

[0049] 3-2: Based on the aforementioned mesh optimization parameters, the initial coarse mesh is adaptively refined using an edge-based refinement strategy to determine the number and position of new vertices. The formula is as follows:

[0050]

[0051] 3-3: Using a physics-driven interpolation method, the discrete temperature distribution prediction results are reconstructed into a continuous three-dimensional temperature field, ensuring the continuity of the temperature field at the material interface. The formula is:

[0052]

[0053] 3-4: Based on the reconstructed 3D temperature field and mesh optimization parameters, the final optimized finite element mesh is generated to ensure higher mesh density in high-temperature gradient regions and geometric boundaries, while reducing the number of mesh elements in non-critical regions, thereby improving the computational efficiency of subsequent thermal simulations.

[0054] Step 3 follows the sequence described above, where x p ,y p ,z p Let n be the node coordinates. R This is the z-axis resolution.

[0055] In step S4, the mesh optimization process specifically includes:

[0056] 4-1: Using the mesh optimization parameters obtained in step S3, determine the optimization nodes for the generated preliminary coarse mesh;

[0057] 4-2: Connect the mesh refinement nodes to construct a more refined optimized finite element mesh.

[0058] In step S2, the decoder part of the temperature distribution prediction module includes:

[0059] The features extracted by the encoder are upsampled by multiple residual blocks, and the feature resolution is gradually restored by transposed convolution (TrConv) in each layer.

[0060] After upsampling at each layer, the corresponding scale features of the encoder and the features of the decoder are concatenated through attention-based skip connections to enhance the reconstruction capability of regions with large temperature gradient changes.

[0061] Example 2: As Figure 1 As shown, the overall process of the NeuralMesh framework of this invention includes four main stages: geometric and thermal feature tensor construction, temperature distribution prediction based on enhanced U-Net, and intelligent mesh optimization. The specific implementation steps are as follows:

[0062] S1: A training dataset containing 2.5D / 3D chip structures was generated using COMSOL Multiphysics, covering the substrate layer, TSV array, microbumps, chip layer, and heat dissipation layer. The chip size was set to 10mm × 10mm × 1.2mm (3D stacking), and the mesh resolution was 512 × 512 × 64. The heat source power density follows a log-normal distribution (mean 5W / mm²). 3 Variance 2.5 2The TSV diameter is randomly distributed between 5-25 μm, and the thermal conductivity of the material is set to a range of 0.1-400 W / m·K (covering silicon, copper, epoxy resin, etc.). Input parameters include geometric features (boundary coordinates, layer thickness, TSV distribution), material properties (thermal conductivity, specific heat capacity), and power distribution (3D heat source mapping).

[0063] The 3D structure is decomposed into material interface layers, and a planar feature tensor is constructed for each layer, as shown in the following formula:

[0064]

[0065] Where M p For material type, k p For thermal conductivity, Th p The thickness is denoted by Z. Feature dimensionality reduction is performed using a 3D convolutional layer (kernel size 3×3×3, stride 2×2×1), increasing the number of output channels to 64. The original resolution is then restored using bilinear interpolation.

[0066] S2: The encoder employs a multi-scale parallel convolutional structure, executing 1×1, 3×3, and 5×5 convolutions in parallel, with output channels of 32 / 64 / 128 respectively. Multi-granularity features are fused through channel concatenation. A 3×3 deformable convolution (offset learning rate 0.1) is used to dynamically adapt to local heat conduction characteristics. The encoder and decoder use 3D-DCT / IDCT frequency domain transformation to calculate multi-head attention weights (8 heads) to focus on high-gradient regions. The decoder uses transposed convolutions (kernel size 4×4, stride 2) for progressive upsampling and fuses with encoder features through a gated attention mechanism. Specific details are as follows... Figure 2 As shown, the decoder consists of four residual blocks. Each layer is upsampled by a factor of 2 using trilinear interpolation, then fed into a 3×3×3 convolution (channel count changes from 512 to 256), and undergoes instance normalization and SiLU activation to enhance nonlinear expressiveness. The upsampled features are concatenated with the thermal gradient features output by the intelligent grid optimization module, and information at different scales is fused using a 3×3×3 convolution. The final layer uses a 1×1×1 convolution (channel count changes from 256 to 1), and the output range is normalized to match the range of the true temperature distribution, ultimately generating the predicted temperature field distribution.

[0067] S3: Based on the predicted interlayer temperature distribution, physical constraint interpolation is used. The adaptive refinement parameters are defined as follows:

[0068]

[0069] Discrete parameters are mapped to continuous space by trilinear interpolation to generate a refined field σ∈[0,1].

[0070] Apply an edge splitting strategy to the initial coarse mesh. For edge e... ij Number of splits Where σ avg The endpoint σ is the mean. The new vertex positions are distributed exponentially according to the σ gradient. By controlling the vertex positions, the aspect ratio Q of the tetrahedron is ensured. e <3.0, and maintain the smoothness of the mesh size transition to prevent numerical artifacts.

[0071] S4: Based on the refinement parameter σ, the initial coarse mesh is locally refined.

[0072] To evaluate the effectiveness of this invention, we compared it with traditional thermal simulation methods (such as COMSOL). Experimental results show that, compared with COMSOL simulation, mesh generation time is accelerated by 45 times, and prediction error is controlled within 0.8%. This indicates that this method significantly improves computational efficiency while maintaining high accuracy, providing an efficient and accurate solution for thermal simulation of 2.5D / 3D packaged chips.

[0073] It should be noted that the above embodiments are not intended to limit the scope of protection of the present invention. Equivalent transformations or substitutions made based on the above technical solutions all fall within the scope of protection of the claims of the present invention.

Claims

1. A neural network-based core-particle thermal simulation finite element mesh generation method, characterized in that, The method comprises the following steps: S1: input the geometric parameters, material parameters, heat source parameters and boundary conditions of the chip, construct a tensor through a geometric and thermal feature extraction module, and generate an input tensor containing geometric boundaries, material properties, power distribution, boundary conditions and thermal distribution features; S2: process the input tensor through a temperature distribution prediction module, extract the temperature distribution features of the chip based on an enhanced U-Net architecture, combine multi-scale convolution, pyramid pooling and deformable convolution, and generate a preliminary temperature distribution prediction result; S3: combine the temperature distribution prediction result and geometric constraints through an intelligent grid optimization module to generate grid optimization parameters coupled with heat and geometry, and guide the adaptive refinement of the finite element grid; S4: refine the initial coarse grid adaptively according to the grid optimization parameters, generate an optimized finite element grid, reduce the number of grid elements, improve the simulation calculation efficiency, and maintain the thermal simulation accuracy; By combining the temperature prediction method of the deep neural network segmentation model and the key geometric information, the finite element grid is optimized, and in step S2, the temperature distribution prediction module comprises the following steps: 2-1: data preprocessing: process the input tensor through a multi-scale convolution layer, use convolution kernels of different sizes (1x1x1, 3x3x3, 5x5x5) to extract local details and global thermal distribution features in parallel, and generate multi-scale feature maps, 2-2: feature extraction: perform a pyramid pooling operation on the multi-scale feature maps, enhance the spatial feature capture capability through different size pooling windows, and extract more global thermal distribution information, 2-3: apply deformable convolution operation to the feature maps after multi-scale convolution and pyramid pooling, enhance the adaptability of the network to chip material heterogeneity, and generate more representative thermal distribution features, 2-4: fuse the features extracted by the encoder with the features after upsampling of the decoder through the attention mechanism-based skip connection, combine 3D discrete cosine transform (3D-DCT) and 3D inverse discrete cosine transform (3D-IDCT), enhance the feature reconstruction capability of the area with large temperature gradient changes, and generate accurate temperature distribution prediction results, 2-5: then, according to the temperature gradient information of the temperature prediction result, combine the key geometric boundary information, refine the finite element coarse grid of the heterogeneous integrated chip, and finally obtain the optimized grid.

2. The neural network-based core-pel thermal simulation finite element mesh generation method according to claim 1, characterized in that, In step S3, the intelligent grid optimization module comprises the following steps: 3-1: based on the temperature distribution result output by the temperature distribution prediction module, combine the geometric boundary information of the chip to generate grid optimization parameters coupled with heat and geometry, the parameters are calculated by normalizing the temperature gradient and geometric features, and the formula is: 3-2: refine the initial coarse grid adaptively according to the grid optimization parameters, determine the number and position of new vertices by using an edge-based refinement strategy, and the formula is: 3-3: reconstruct the discrete temperature distribution prediction result into a continuous three-dimensional temperature field through a physically driven interpolation method, ensure the continuity of the temperature field at the material interface, and the formula is: 3-4: According to the reconstructed three-dimensional temperature field and the grid optimization parameters, the final optimized finite element grid is generated, ensuring higher grid density in high temperature gradient areas and geometric boundaries, while reducing the number of grid elements in non-critical areas, improving the computational efficiency of subsequent thermal simulation, The sequence of Step 3 is the above step, wherein is the node coordinate, is the z-axis resolution.

3. The neural network-based core-pel thermal simulation finite element mesh generation method according to claim 1, wherein, In step S4, the grid optimization process specifically includes: 4-1: Determine the optimized nodes for the generated preliminary coarse grid through the grid optimization parameters obtained in step S3; 4-2: Connect the grid refinement nodes to build a more refined optimized finite element grid.

4. The neural network-based core-particle thermal simulation finite element mesh generation method according to claim 1, characterized in that, In step S2, the decoder part of the temperature distribution prediction module includes: Up-sample the features extracted by the encoder through multi-layer residual blocks, and use transpose convolution (TrConv) at each layer to gradually restore the feature resolution; After each upsampling, the corresponding scale features of the encoder are spliced with the decoder features through the attention mechanism-based skip connection to enhance the reconstruction ability of the area with large temperature gradient changes.

5. A neural network based core thermal simulation finite element mesh generation system, characterized by, The finite element grid generation method of any one of claims 1-4, The system comprises: A geometric and thermal feature extraction module for dimensionality reduction and feature fusion of input geometric parameters, material parameters and heat source parameters; A temperature distribution prediction module for extracting and predicting the temperature distribution of the chip based on the enhanced U-Net architecture; An intelligent grid optimization module for generating thermal-geometric coupled grid optimization parameters according to the predicted temperature distribution and geometric constraints; An adaptive grid refinement module for adaptive refinement of the initial coarse grid according to the optimization parameters to generate the final finite element grid.

6. An electronic device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that: The processor executes the program to realize the neural network-based chip thermal simulation finite element grid generation method of any one of claims 1-4.

7. A computer readable storage medium having stored thereon computer instructions, characterized in that: The computer instructions are executed by the processor to realize the neural network-based chip thermal simulation finite element grid generation method of any one of claims 1-4. The computer instructions are executed by the processor to realize the neural network-based chip thermal simulation finite element grid generation method of any one of claims 1-4.

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