Physics-aware deep neural networks for surrogate modeling of turbulent natural convection
Didier Lucor(a,⋆), Atul Agrawal(b,a) and Anne Sergent(a,c) (a) Université Paris-Saclay, CNRS, Laboratoire Interdisciplinaire des Sciences du Numérique (LISN), Orsay, France (b)Department of Mechanical Engineering, Technical University of Munich, Garching b. München, Germany (c)Sorbonne Université, Faculté des Sciences et Ingénierie, UFR Ingénierie, Paris, France
Abstract
Recent works have explored the potential of machine learning as data-driven turbulence closures for RANS and LES techniques. Beyond these advances, the high expressivity and agility of physics-informed neural networks (PINNs) make them promising candidates for full fluid flow PDE modeling. An important question is whether this new paradigm, exempt from the traditional notion of discretization of the underlying operators very much connected to the flow scales resolution, is capable of sustaining high levels of turbulence characterized by multi-scale features? We investigate the use of PINNs surrogate modeling for turbulent Rayleigh-Bénard (RB) convection flows in rough and smooth rectangular cavities, mainly relying on DNS temperature data from the fluid bulk. We carefully quantify the computational requirements under which the formulation is capable of accurately recovering the flow hidden quantities. We then propose a new padding technique to distribute some of the scattered coordinates - at which PDE residuals are minimized - around the region of labeled data acquisition. We show how it comes to play as a regularization close to the training boundaries which are zones of poor acc
中文速览
物理信息神经网络（Physics-Informed Neural Networks，PINNs）虽已被证明能求解多种偏微分方程，但能否在高度湍流、多尺度的三维流场中胜任完整的流体模拟，仍是一个悬而未决的问题。为此，研究者将PINNs应用于光滑与粗糙矩形腔体内的湍流瑞利-贝纳德（Rayleigh-Bénard）对流，仅用直接数值模拟（DNS）中流体内部1.6%的温度数据作为训练输入，让网络同时满足纳维-斯托克斯方程的物理约束，从而反推出速度、压力等隐藏流场变量。研究中提出了两项关键改进：一是"填充"技术，在标注数据区域周围额外布置残差配点，以消除训练边界附近精度差的顽疾；二是适度放宽不可压缩条件，显著改善了复合损失函数的收敛性。在高瑞利数Ra=2×10⁹的强湍流工况下，模型对全部约5亿个DNS坐标点的预测误差仅在0.3%–4%之间（相对L₂范数），这一结果表明PINNs有望成为昂贵DNS计算的高效替代工具，对湍流传热的实时分析与控制具有重要意义。
原文 arXiv:2103.03565;中英对照 + 大白话阅读 https://aha.fim.ai/paper/2103.03565v1