Conjugate heat transfer (CHT) models are vital for the design of many
engineering systems. However, high-fidelity CHT models are computationally
intensive, which limits their use in applications such as design optimization,
where hundreds to thousands of model evaluations are required. In this work, we
develop a modular deep convolutional encoder-decoder hierarchical (DeepEDH)
neural network, a novel deep-learning-based surrogate modeling methodology for
computationally intensive CHT models. Leveraging convective temperature
dependencies, we propose a two-stage temperature prediction architecture that
couples velocity and temperature models. 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 model of the cold plate is developed and
solved using the finite element method (FEM), generating a dataset of 1,500
simulations. The FEM results are transformed and scaled from unstructured to
structured, image-like meshes to create training and test datasets. The DeepEDH
methodology's performance is examined in relation to data scaling, training
dataset size, and network depth. Our performance analysis covers the impact of
the novel architecture, separate field models, output geometry masks,
multi-stage temperature models, and optimizations of the hyperparameters and
architecture. Furthermore, we quantify the influence of the CHT thermal
boundary condition 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 methodology for CHT models exhibits up to a 65% enhancement in
the coefficient of determination ($R^{2}$).

该论文介绍了一种基于深度学习的代理建模方法，DeepEDH 方法，用于计算量大的共轭热传递模型，并通过建立计算模型和使用有限元法进行求解，对冷却板冷却的电池热管理系统中的压力、速度和温度场进行建模和预测，从而验证了 DeepEDH 方法的有效性。

深度卷积编码器 - 解码器层次神经网络在共轭传热代理建模中的应用

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

In this research, we developed a graph-based framework to represent various
aspects of optimal thermal management system design, with the aim of rapidly
and efficiently identifying optimal design candidates. Initially, the
graph-based framework is utilized to generate diverse thermal management system
architectures. The dynamics of these system architectures are modeled under
various loading conditions, and an open-loop optimal controller is employed to
determine each system's optimal performance. These modeled cases constitute the
dataset, with the corresponding optimal performance values serving as the
labels for the data. In the subsequent step, a Graph Neural Network (GNN) model
is trained on 30% of the labeled data to predict the systems' performance,
effectively addressing a regression problem. Utilizing this trained model, we
estimate the performance values for the remaining 70% of the data, which serves
as the test set. In the third step, the predicted performance values are
employed to rank the test data, facilitating prioritized evaluation of the
design scenarios. Specifically, a small subset of the test data with the
highest estimated ranks undergoes evaluation via the open-loop optimal control
solver. This targeted approach concentrates on evaluating higher-ranked designs
identified by the GNN, replacing the exhaustive search (enumeration-based) of
all design cases. The results demonstrate a significant average reduction of
over 92% in the number of system dynamic modeling and optimal control analyses
required to identify optimal design scenarios.

我们开发了一个基于图形的框架来表示最佳热管理系统设计的各个方面，旨在快速高效地识别最佳设计方案。通过图形框架，我们生成多样的热管理系统体系结构，对这些系统体系结构在各种负载条件下建模，并利用开环最优控制器确定每个系统的最佳性能。利用图神经网络模型训练预测性能，我们对剩余数据集进行性能估计，并利用估计值对测试数据进行排序，提供优先评估设计方案的能力。结果显示，通过此方法能够显著降低 92% 以上的系统动态建模和最优控制分析所需的工作量，以识别最佳设计方案。