Deep encoder-decoder hierarchical convolutional neural networks for conjugate heat transfer surrogate modeling

TL;DR

This work introduces DeepEDH, a modular encoder–decoder CNN architecture for conjugate heat transfer surrogate modeling. By translating unstructured FEM data into structured images and applying output geometry masks plus a two-stage temperature predictor that leverages velocity information, DeepEDH reconstructs full pressure, velocity, and temperature fields with high accuracy and efficiency. The method demonstrates superior performance compared with U‑Net and DenseED, requiring far fewer parameters and enabling rapid evaluations critical for design optimization and real-time applications. Comprehensive hyperparameter optimization, dataset characterization, and a concrete battery-thermal-management case illustrate practical feasibility, revealing significant speedups and memory reductions that enable scalable surrogate modeling of coupled multiphysics problems.

Abstract

Conjugate heat transfer (CHT) analyses are vital for the design of many energy systems. However, high-fidelity CHT numerical simulations are computationally intensive, which limits their applications such as design optimization, where hundreds to thousands of evaluations are required. In this work, we develop a modular deep encoder-decoder hierarchical (DeepEDH) convolutional neural network, a novel deep-learning-based surrogate modeling methodology for computationally intensive CHT analyses. Leveraging convective temperature dependencies, we propose a two-stage temperature prediction architecture that couples velocity and temperature fields. The proposed DeepEDH methodology is demonstrated by modeling the pressure, velocity, and temperature fields for a liquid-cooled cold-plate-based battery thermal management system with variable channel geometry. A computational mesh and CHT formulation of the cold plate is created and solved using the finite element method (FEM), generating a dataset of 1,500 simulations. Our performance analysis covers the impact of the novel architecture, separate DeepEDH models for each field, output geometry masks, multi-stage temperature field predictions, and optimizations of the hyperparameters and architecture. Furthermore, we quantify the influence of the CHT analysis' thermal boundary conditions on surrogate model performance, highlighting improved temperature model performance with higher heat fluxes. Compared to other deep learning neural network surrogate models, such as U-Net and DenseED, the proposed DeepEDH architecture for CHT analyses exhibits up to a 65% enhancement in the coefficient of determination $R^{2}$. (*Due to the notification of arXiv "The Abstract field cannot be longer than 1,920 characters", the appeared Abstract is shortened. For the full Abstract, please download the Article.)

Figures (18)

• Figure 1: Illustration of the application of \ref{['eqn:struct_grid']} to temperature, velocity, or pressure field results, transforming (\ref{['sub@fig:unstruct_grid']}) an unstructured mesh onto (\ref{['sub@fig:struct_grid']}) an image-like structured mesh where each cell is representative of an image pixel.
• Figure 2: Dense block based on the DenseNet Huang_Liu_Maaten_Weinberger_2016 architecture with 3 layers ($L=3$) and a growth rate of 8 ($K=8$). The previous feature maps, represented as blue-hued planes in the figure, are appended to the output from each block of batch normalization, ReLU activations, and convolution using a kernel with kernel size (K) of 3, stride (S) of 1, and padding (P) of 1. The feature map sizes remain constant through the dense block, while the number of feature maps grows by $K$ through each layer.
• Figure 3: (\ref{['sub@fig:encode_layer']}) Encoding layer with convolution and (\ref{['sub@fig:decode_layer']}) decoding layer with convolution and transpose convolution. The first combination of batch normalization, ReLU activations, and convolution for both encoding and decoding layers reduce the number of feature maps, represented as blue-hued planes in the figure, by half using a kernel with kernel size (K) of 1, stride (S) of 1, and padding (P) of 0. The second combination uses a kernel with K=3, S=2, and P=1 to reduce the feature map sizes by half for encoding with convolution layers and doubles the feature map sizes for decoding with transpose convolution layers.
• Figure 4: Network architecture: DeepEDH with $L_{\text{dense}} = [3, 4, 3]$ and $K=2$. This example includes 1 encoding dense block with 3 layers, a bottleneck dense block with 4 layers, and 1 decoding dense block with 3 layers. The number of feature maps, represented as blue-hued planes in the figure, grows by two through each dense block layer as defined by the growth rate.
• Figure 5: Pin-fin cold plate (\ref{['sub@fig:case_study_geo_3d']}) three-dimensional geometry and (\ref{['sub@fig:case_study_geo_2d']}) channel cross-sectional view with the solid metal region shown in black and the flow region shown in white. Symmetry was applied across the width of the cold plate with (\ref{['sub@fig:case_study_geo_2d']}) showing half of the plate.