Core particle thermal simulation finite element mesh generation method based on neural network

Abstract

The invention relates to a core particle thermal simulation finite element mesh generation method based on a neural network. The method comprises a geometric and thermal feature extraction module, a temperature distribution prediction module and an intelligent grid optimization module. The geometric and thermal feature extraction module realizes accurate prediction of chip temperature distribution through tensor construction in combination with multi-scale convolution, pyramid pooling and deformable convolution; the intelligent grid optimization module adaptively optimizes a finite element grid through coupling of thermal gradient and geometric constraint, reduces the number of grid units and improves calculation efficiency. According to the method, deep learning and finite element mesh generation are combined for the first time, a traditional iterative mesh refinement process is replaced by predicting heat distribution through a neural network, the mesh generation speed is remarkably increased, and meanwhile, the thermal simulation precision is kept within 0.8%. The method is particularly suitable for a complicated 2.5 D / 3D chip packaging structure, can effectively cope with thermal management challenges in modern integrated circuit design, and provides a rapid and accurate thermal simulation tool for chip design.

Description

Technical Field

[0001] The present invention relates to the technical field of integrated circuit thermal management, and particularly relates to a method for generating a finite element mesh for die thermal simulation based on a neural network. Background Art

[0002] With the continuous development of semiconductor technology, integrated circuit (IC) systems are gradually approaching the physical limit in the post-Moore's Law era. To address this challenge, chip-level packaging technology has emerged. This technology integrates multiple independently manufactured functional chips into a system through advanced 2.5D / 3D packaging, overcoming the limitations of single manufacturing processes while reducing defect rates and manufacturing costs. However, with the increasing power density and shrinking feature sizes in modern chip-level packaging designs, the problem of thermal analysis has become increasingly severe. Although traditional thermal simulation methods such as the finite element method (FEM) and the finite difference method (FDM) have high accuracy, they consume a large amount of computing resources and are difficult to meet the requirements of repeated thermal simulations during the design optimization process of complex tasks.

[0003] In recent years, researchers have attempted to use neural networks to accelerate the solution of discrete heat equations. However, these deep learning methods have poor generalization ability when dealing with different chip structures, and their end-to-end thermal predictions often cannot meet the simulation accuracy requirements. Traditional FEM mesh optimization relies on an iterative refinement process based on posterior error analysis, which has a large computational overhead. Although some active optimization strategies based on graph convolutional networks (GCNs), machine learning, and reinforcement learning show potential in improving efficiency, these methods mainly focus on two-dimensional mesh optimization and fail to effectively handle high-temperature regions and large thermal gradient regions 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 to address the increasingly complex thermal management challenges in modern integrated circuit designs. Summary of the Invention

[0005] Object of the Invention: The present invention aims to provide a method for generating a finite element mesh for die thermal simulation based on a neural network to solve the problem of low efficiency in mesh generation and optimization in 2.5D / 3D chip thermal simulations in the prior art, and to achieve fast and high-precision thermal simulation, providing an efficient thermal management solution for modern integrated circuit designs.

[0006] To achieve the above object, the present invention provides a method for generating a finite element mesh for die thermal simulation based on a neural network, including the following steps:

[0007] S1: Convert the geometric boundaries and physical properties of a 2.5D / 3D chip into a structured tensor input. The geometric boundary is defined as an edge set E = {e i (p i ,pi ')}, including component volume V = {v i (comp)}(such as TSV, chips, substrates, etc.). The critical boundaries are screened by the formula At the same time, the 3D structure is decomposed into multiple layers of planes P i , and the feature tensor of each layer encodes material properties (thermal conductivity k p , density ρ p , heat source H sp , etc.) and thickness information to form an input tensor.

[0008] S2: Use parallel multi-scale convolutional kernels (1×1×1, 3×3×3, 5×5×5) to extract local details and global thermal features, combine pyramid pooling to enhance spatial perception ability, and adapt to material heterogeneity through deformable convolution. Subsequently, use the multi-attention head mechanism to fuse the encoder and decoder features, map the spatial features to the frequency domain through 3D discrete cosine transform (3D-DCT), dynamically adjust the weights of the high-frequency thermal gradient regions, and then reconstruct the spatial features through 3D inverse discrete cosine transform (3D-IDCT). After that, use transposed convolution (TrConv) to gradually upsample the feature map, combine the attention fusion module to weight and refine the high-temperature gradient regions, and finally output a high-resolution temperature prediction map.

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

[0010]

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

[0012] where x p , y p , z p are the node coordinates, and n R is the z-axis resolution.

[0013] Combine the temperature gradient and geometric features to generate the refinement parameter σ(x, y, z) to control the grid density. The formula for the normalized heat contribution parameter is:

[0014]

[0015] where T is the temperature, and the geometric weight function is introduced to fuse the thermal and geometric information:

[0016]

[0017] The final refinement parameter:

[0018]

[0019] Ensure to improve the grid resolution at the interface between the high-temperature gradient region and the material.

[0020] S4: Locally refine the initial coarse grid based on the refinement parameter σ. Use a hybrid loss function to jointly optimize the prediction and simulation accuracy, specifically including the thermal prediction loss and the physical consistency loss. The mean square error (MSE) constrains the temperature error in the spatial domain, and the physical consistency loss strengthens the physical laws through the steady-state heat equation residual R(T h ) and the gradient jump term J(T h ). 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 die thermal simulation based on neural network, the system includes:

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

[0025] A temperature distribution prediction module, which is used to extract and predict the temperature distribution of the chip based on the enhanced U-Net architecture;

[0026] An intelligent grid optimization module, which is used to generate thermal-geometric coupling grid optimization parameters according to the predicted temperature distribution and geometric constraints;

[0027] An adaptive grid refinement module, which is used to adaptively refine the initial coarse grid according to the optimization parameters to generate the final finite element grid.

[0028] An electronic device, including a memory, a processor, and a computer program stored on the memory and executable on the processor, where when the processor executes the program, it implements the above-mentioned finite element mesh generation method for die thermal simulation based on neural network.

[0029] A computer-readable storage medium, on which computer instructions are stored, and when the computer instructions are executed by a processor, they implement the above-mentioned finite element mesh generation method for die thermal simulation based on neural network.

[0030] Beneficial effects: Through the fusion of deep learning-driven heat distribution prediction and geometric features, the present invention realizes for the first time the efficient finite element mesh optimization without iterative refinement. The key technological innovations include: the enhanced U-Net architecture accurately captures high-frequency heat gradients through multi-scale convolution and attention mechanisms; the heat-geometry refinement parameter dynamically balances the temperature gradient and geometric complexity to achieve local adaptive optimization; the physics-guided interpolation 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 designs. Description of the Drawings

[0031] Figure 1 : It is the architecture diagram of the mesh optimization algorithm of the present invention, showing the connection relationships of input features, predicted temperature, and feature fusion.

[0032] Figure 2 : It is the detailed structure of the deep learning network in the present invention.

[0033] Figures 3-4 : It is the comparison of experimental results of the present invention under different test cases. Detailed Implementation Manner

[0034] The present invention will be elaborated in detail below in conjunction with the drawings and specific embodiments.

[0035] Example 1, refer to Figure 1 、 Figure 2 , a method for generating a finite element mesh for die thermal simulation based on a neural network, the method comprising the following steps:

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

[0037] S2: Process the input tensor through a temperature distribution prediction module, and based on the enhanced U-Net architecture, combine multi-scale convolution, pyramid pooling, and deformable convolution to extract the temperature distribution features of the chip and generate a preliminary temperature distribution prediction result;

[0038] S3: Through an intelligent mesh optimization module, combine the temperature distribution prediction result and geometric constraints to generate heat-geometry coupled mesh optimization parameters to guide the adaptive refinement of the finite element mesh;

[0039] S4: According to the mesh optimization parameters, adaptively refine the initial coarse mesh to generate an optimized finite element mesh, reduce the number of mesh elements, improve the simulation calculation efficiency, and at the same time maintain the thermal simulation accuracy.

[0040] Optimize the finite element mesh by combining the temperature prediction method of the deep neural network segmentation model and the key geometric information. In step S2, the steps of the temperature distribution prediction module include:

[0041] 2-1: Data preprocessing: Process the input tensor through multi-scale convolutional layers, and use convolutional kernels of different sizes (1×1×1, 3×3×3, 5×5×5) to extract local details and global heat distribution features in parallel, generating multi-scale feature maps.

[0042] 2-2: Feature extraction: Perform pyramid pooling operations on the multi-scale feature maps, enhance the spatial feature capture ability through pooling windows of different sizes, 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 the heterogeneity of chip materials and generate more representative heat distribution features.

[0044] 2-4: Through skip connections based on the attention mechanism, fuse the features extracted by the encoder with the upsampled features of the decoder, and combine 3D discrete cosine transform (3D-DCT) and 3D inverse discrete cosine transform (3D-IDCT) to enhance the feature reconstruction ability in areas with large temperature gradient changes, generating accurate temperature distribution prediction results. (Here, mainly use the segmentation model of deep learning for prediction).

[0045] 2-5: Subsequently, according to the temperature gradient information of the temperature prediction results, combined with the key geometric boundary information, refine the finite element coarse mesh of the heterogeneous integrated chip to finally obtain the optimized mesh.

[0046] In step S3, the steps of the intelligent mesh optimization module include:

[0047] 3-1: Based on the temperature distribution results output by the temperature distribution prediction module, combined with the geometric boundary information of the chip, generate thermo-geometric coupled mesh optimization parameters, which are calculated through the normalized temperature gradient and geometric features. The formula is:

[0048]

[0049] 3-2: According to the mesh optimization parameters, adaptively refine the initial coarse mesh, adopt an edge-based refinement strategy, and determine the number and position of new vertices. The formula is:

[0050]

[0051] 3-3: Through a physically driven interpolation method, reconstruct the discrete temperature distribution prediction results into a continuous three-dimensional temperature field to ensure the continuity of the temperature field at the material interface. The formula is:

[0052]

[0053] 3 - 4: Generate the final optimized finite element mesh according to the reconstructed three - dimensional temperature field and mesh optimization parameters, ensuring a higher mesh density in the high - temperature gradient region and geometric boundaries, while reducing the number of mesh elements in non - critical regions to improve the computational efficiency of subsequent thermal simulations.

[0054] The order of step 3 is the above steps, where x p , y p , z p are the node coordinates, and n R is the z - axis resolution.

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

[0056] 4 - 1: Determine the optimized nodes for the initially generated coarse mesh through the mesh optimization parameters obtained in step S3;

[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] Upsample the features extracted by the encoder through multiple layers of residual blocks, and use transposed convolution (TrConv) layer by layer to gradually restore the feature resolution;

[0060] After each layer of upsampling, splice the corresponding scale features of the encoder and the decoder features through skip connections based on the attention mechanism to enhance the reconstruction ability for regions with large temperature gradient changes.

[0061] Embodiment 2: As Figure 1 shown, the overall process of the NeuralMesh framework of the present 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: Generate a training dataset containing 2.5D / 3D chip structures based on COMSOL Multiphysics, covering the base layer, TSV array, micro - bumps, chip layer, and heat dissipation layer. The chip size is set to 10mm × 10mm × 1.2mm (3D stack), and the mesh resolution is 512 × 512 × 64. The heat source power density follows a log - normal distribution (mean 5W / mm 3 , variance 2.5 2) The diameter of the TSVs is randomly distributed between 5 - 25 μm, and the range of the material thermal conductivity is set to 0.1 - 400 W / m·K (covering silicon, copper, epoxy resin, etc.). The 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 three-dimensional structure is decomposed into material interface layers, and a planar feature tensor is constructed for each layer. The formula is as follows:

[0064]

[0065] Where M p is the material type, k p is the thermal conductivity, and Th p is the thickness along the Z-axis. Feature dimensionality reduction is performed through a 3D convolutional layer (kernel size 3×3×3, stride 2×2×1), and the number of output channels is increased to 64. Subsequently, it is restored to the original resolution through bilinear interpolation.

[0066] S2: The encoder adopts a multi-scale parallel convolutional structure, performing 1×1, 3×3, and 5×5 convolutions in parallel. The number of output channels is 32 / 64 / 128 respectively, and 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; a 3D-DCT / IDCT frequency domain conversion is performed between the encoder and the decoder to calculate the multi-head attention weights (number of heads 8), focusing on high-gradient regions. The decoder uses transposed convolution (kernel size 4×4, stride 2) for progressive upsampling and fuses with the encoder features through a gated attention mechanism. The specific details are as Figure Two shown. The decoder contains 4 residual blocks. Each layer performs 2-fold upsampling through trilinear interpolation, then connects to a 3×3×3 convolution (number of channels 512→256), and undergoes instance normalization and SiLU activation function to enhance the non-linear expression ability. The upsampled features are concatenated with the thermal gradient features output by the intelligent grid optimization module, and different-scale information is fused through a 3×3×3 convolution. The final layer uses a 1×1×1 convolution (number of channels 256→1), and the output range is normalized and adjusted to match the range of the true temperature distribution, finally generating the predicted temperature field distribution.

[0067] S3: Based on the predicted interlayer temperature distribution, physical constraint interpolation is adopted. Define the adaptive refinement parameter, and the formula is as follows:

[0068]

[0069] The discrete parameters are mapped to the continuous space through trilinear interpolation to generate the refinement field σ ∈ [0,1].

[0070] Execute the edge splitting strategy on the initial coarse mesh. For edge e ij , the number of splits where σ avg is the mean value of the endpoints σ. The positions of the new vertices are exponentially distributed according to the σ gradient. By controlling the vertex positions, ensure that the tetrahedron aspect ratio Q e < 3.0, and maintain the smoothness of the mesh size transition to prevent numerical artifacts.

[0071] S4: Based on the refinement parameter σ, perform local refinement on the initial coarse mesh.

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

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

Claims

1. A finite element mesh generation method for core particle thermal simulation based on neural network, characterized in that: The method comprises the following steps: S1: Input the chip's geometric parameters, material parameters, heat source parameters and boundary conditions, and construct tensors through the geometric and thermal feature extraction module to generate input tensors containing geometric boundaries, material properties, power distribution, boundary conditions and thermal distribution features; S2: The temperature distribution prediction module processes the input tensor and extracts the temperature distribution characteristics of the chip based on the enhanced U-Net architecture, combining multi-scale convolution, pyramid pooling and deformable convolution to generate preliminary temperature distribution prediction results. S3: through the intelligent mesh optimization module, combining the temperature distribution prediction results with the geometric constraints, generating the mesh optimization parameters of thermal-geometry coupling to guide the adaptive refinement of the finite element mesh; S4: According to the mesh optimization parameters, the initial coarse mesh is adaptively refined to generate an optimized finite element mesh, which reduces the number of mesh elements and improves the simulation calculation efficiency while maintaining the thermal simulation accuracy.

2. The method for generating finite element mesh for core particle thermal simulation based on neural network according to claim 1, characterized in that: By combining the temperature prediction method and key geometric information of the deep neural network segmentation model, the finite element mesh is optimized. In step S2, the temperature distribution prediction module step includes: 2-1: Data preprocessing: The input tensor is processed through a multi-scale convolution layer, and convolution kernels of different sizes (1×1×1, 3×3×3, 5×5×5) are used to extract local details and global thermal distribution features in parallel to generate a multi-scale feature map. 2-2: Feature extraction: Perform pyramid pooling on the multi-scale feature map, enhance the spatial feature capture capability through pooling windows of different sizes, and extract more global thermal distribution information. 2-3: Apply deformable convolution operation to the feature map after multi-scale convolution and pyramid pooling to enhance the adaptability of the network to the heterogeneity of chip materials and generate more representative thermal distribution features. 2-4: Through the skip connection based on the attention mechanism, the features extracted by the encoder are fused with the features after upsampling by the decoder, combined with 3D discrete cosine transform (3D-DCT) and 3D inverse discrete cosine transform (3D-IDCT), the feature reconstruction capability of the area with large temperature gradient changes is enhanced, and accurate temperature distribution prediction results are generated. 2-5: Then, based on the temperature gradient information of the temperature prediction results and combined with the key geometric boundary information, the finite element coarse grid of the heterogeneous integrated chip is refined to finally obtain the optimized grid.

3. The method for generating finite element mesh for core particle thermal simulation based on neural network according to claim 1, characterized in that: In step S3, the smart grid optimization module steps include: 3-1: Based on the temperature distribution results output by the temperature distribution prediction module and combined with the geometric boundary information of the chip, the mesh optimization parameters of thermal-geometric coupling are generated. The parameters are calculated by normalizing the temperature gradient and geometric features. The formula is: 3-2: According to the mesh optimization parameters, the initial coarse mesh is adaptively refined, and the number and position of new vertices are determined using an edge-based refinement strategy. The formula is: 3-3: Through the physically driven interpolation method, the discrete temperature distribution prediction results are reconstructed into a continuous three-dimensional temperature field to ensure the continuity of the temperature field at the material interface. The formula is: 3-4: Generate the final optimized finite element mesh based on the reconstructed 3D temperature field and mesh optimization parameters to ensure a higher mesh density in high temperature gradient areas and geometric boundaries, while reducing the number of mesh elements in non-critical areas to improve the computational efficiency of subsequent thermal simulations. The order of step 3 is the above steps, where x p ,y p ,z p is the node coordinate, n R is the z-axis resolution.

4. The method for generating finite element mesh for core particle thermal simulation based on neural network according to claim 1, characterized in that: In step S4, the grid optimization process specifically includes: 4-1: Determine the optimization nodes for the generated preliminary coarse grid using the grid optimization parameters obtained in step S3; 4-2: Connect mesh refinement nodes to build a finer optimized finite element mesh.

5. The method for generating finite element mesh for core particle thermal simulation based on neural network according to claim 1, characterized in that: In step S2, the decoder part of the temperature distribution prediction module includes: The features extracted by the encoder are upsampled through multiple layers of residual blocks, and the feature resolution is gradually restored using transposed convolution (TrConv) in each layer; After upsampling each layer, the corresponding scale features of the encoder are concatenated with the decoder features through a jump connection based on the attention mechanism to enhance the reconstruction capability of areas with large temperature gradient changes.

6. A core particle thermal simulation finite element mesh generation system based on neural network, characterized in that: Implementing the finite element mesh generation method according to any one of claims 1 to 5, The system comprises: The geometric and thermal feature extraction module is used to reduce the dimension and fuse the features of the input geometric parameters, material parameters and heat source parameters; Temperature distribution prediction module, used to extract and predict the temperature distribution of the chip based on the enhanced U-Net architecture; Intelligent mesh optimization module, used to generate mesh optimization parameters for thermal-geometry coupling based on predicted temperature distribution and geometric constraints; 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.

7. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the neural network-based core particle thermal simulation finite element mesh generation method as described in any one of claims 1 to 5 is implemented.

8. A computer-readable storage medium having computer instructions stored thereon, characterized in that: When the computer instructions are executed by the processor, the neural network-based finite element mesh generation method for core particle thermal simulation as described in any one of claims 1 to 5 is implemented.

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