物理启发的深度学习模型及其在热端部件散热中的应用

热端部件散热是众多空天设备的关键技术。表面温度分布是散热设计中用到的重要信息,常规的解析建模手段和机器学习方法均无法有效地表达此类高维信息。近年来兴起的图像深度学习算法是解决表面温度信息预测的有效手段。然而,现有的基于大数据的深度学习方法往往对于物理数据和小样本数据不适用,体现为泛化精度差、数据兼容性差、可解释性差。因此,有必要结合传热的先验知识发展物理启发的新型深度学习算法,以增强高自由度、高复杂度散热对象上的设计能力。本文基于卷积算子和有限差分求解方式的类比关系,提出了一种物理启发式的循环卷积神经网络。以横向出流的冲击冷却为例,开展了变计算域大小、变工况、变尺寸的批量数值模拟,获取了冲击冷却关键特征的小样本图像数据。进一步通过神经网络的训练,构建了多参数、大范围内有较好拟合能力的温度、传热系数、压力代理模型。研究结果表明,本文提出的物理启发神经网络模型,对于计算域大小没有限制,可以统一表达不同空间范围内获取的物理数据的共性规律。模型的各类超参设定均具有明确的物理意义,且与经典的微分方程求解理论有一定的类比关系,增强了神经网络调参的方向性。通过传热物理规律与黑箱模型的融合,本文实现了小样本多参数物理数据的共性建模。该方法可以迅速重构热端部件的高维分布信息,可服务于热端部件的快速分析设计以及优化。

A Physics-Informed Deep Learning Model and Its Application in Heat Dissipation for Hot Section Components

The heat dissipation design of hot section components is a key technology for many aerospace equipment. While surface temperature distribution is important for heat dissipation, such high-dimensional information could hardly be regressed by traditional analytical modeling methods and machine learning methods. Recent progress in the deep learning domain provided capabilities for image prediction and could be properly used for reconstructing temperature distributions. However, data-driven deep learning methods were often not compatible with physics data and small datasets, which included poor generalization accuracy, poor data compatibility, and poor interpretability. Therefore, it is necessary to integrate the prior knowledge of heat transfer with data and develop physics-informed deep learning algorithms to enhance the capability of models. Based on the analogy between the convolution operators and the derivatives, a physics-informed recurrent convolutional neural network was proposed in this study. Taking the impingement cooling with cross-flow effect as an example task, a batch of numerical simulations with variable computational domain, working conditions, and sizes were conducted, and image datasets of key heat transfer features were obtained. The dataset was used to train a neural network to predict heat transfer coefficients and pressure, which had a high accuracy within a large parameter range. The research results indicated that the physics-informed neural network model proposed had no limitation on the size of the computational domain and could efficiently express the commonness of physical data acquired in different spatial ranges. The hyper-parameters of the model had clear physical meanings and had an analogy with the classic partial differential equation numerical solution theory. Through the integration of the heat transfer physics law with the black box model, this study realized a universal commonness modeling for physical data. The proposed method quickly reconstructed the high-dimensional distribution information of hot section components, and could be applied to the rapid analysis, design and optimization of hot section components.