Physics-Informed Neural Networks for Heat Transfer Problems
Physics-Informed Neural Networks for Heat Transfer Problems
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DOI：
10.1115/1.4050542
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发表时间：
2021-06-01
影响因子：
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通讯作者：
Karniadakis, George E. M.
中科院分区：
文献类型：
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作者：
Cai, Shengze;Wang, Zhicheng;Karniadakis, George E. M.
物理信息神经网络(PINN)由于能够有效地解决含有噪声数据和部分丢失物理信息的实际问题，在不同的工程领域得到了广泛的应用。在PINN中，利用自动微分来计算没有离散化误差的微分算子，定义了一个多任务学习问题，以便同时拟合观测数据，同时尊重潜在的物理支配规律。在这里，我们介绍了PINN在各种原型热传导问题中的应用，特别是针对传统计算方法不容易处理的现实条件。为此，我们首先考虑了受热表面上具有未知热边界条件的强迫对流和混合对流，目的是在给定稀疏温度测量的情况下，得到区域内包括边界在内的各处的温度和速度场。我们还考虑了两相流的原型Stefan问题，目的是在给定区域内的一些温度测量的情况下，推导出运动界面、到处的速度场和温度场以及固体和液体的不同导热系数。最后，我们给出了一些与电力电子相关的实际工业应用，以突出PINN的实用性以及神经网络在解决工业复杂的一般热传递问题中的有效应用。综上所述，本文的结果表明，PINN不仅可以解决传统计算方法无法解决的病态问题，而且还可以弥合计算和实验热传递之间的差距。
Physics-informed neural networks (PINNs) have gained popularity across different engineering fields due to their effectiveness in solving realistic problems with noisy data and often partially missing physics. In PINNs, automatic differentiation is leveraged to evaluate differential operators without discretization errors, and a multitask learning problem is defined in order to simultaneously fit observed data while respecting the underlying governing laws of physics. Here, we present applications of PINNs to various prototype heat transfer problems, targeting in particular realistic conditions not readily tackled with traditional computational methods. To this end, we first consider forced and mixed convection with unknown thermal boundary conditions on the heated surfaces and aim to obtain the temperature and velocity fields everywhere in the domain, including the boundaries, given some sparse temperature measurements. We also consider the prototype Stefan problem for two-phase flow, aiming to infer the moving interface, the velocity and temperature fields everywhere as well as the different conductivities of a solid and a liquid phase, given a few temperature measurements inside the domain. Finally, we present some realistic industrial applications related to power electronics to highlight the practicality of PINNs as well as the effective use of neural networks in solving general heat transfer problems of industrial complexity. Taken together, the results presented herein demonstrate that PINNs not only can solve ill-posed problems, which are beyond the reach of traditional computational methods, but they can also bridge the gap between computational and experimental heat transfer.