硬物理约束在三维Turbulence神经网络粗粒化中的嵌入
Embedding Hard Physical Constraints in Neural Network Coarse-Graining of 3D Turbulence
摘要：
近年来，深度学习方法在物理科学中的复杂系统建模方面表现出了很大的潜力。PDE深度学习的一个主要挑战是强制执行物理约束和边界条件。在这项工作中，我们提出了一个通用的框架，直接嵌入到卷积神经网络的不可压缩流体的概念，并将其应用到粗粒化的湍流。这些物理嵌入式神经网络利用数值方法和计算流体动力学的可解释策略，通过利用基础方程的数学特性来执行物理定律和边界条件。我们展示了三维充分发展的湍流的结果，表明这种技术大大提高了当地的质量守恒，而不牺牲性能根据其他几个指标表征流体流动。
英文摘要：
In the recent years, deep learning approaches have shown much promise in modeling complex systems in the physical sciences. A major challenge in deep learning of PDEs is enforcing physical constraints and boundary conditions. In this work, we propose a general framework to directly embed the notion of an incompressible fluid into Convolutional Neural Networks, and apply this to coarse-graining of turbulent flow. These physics-embedded neural networks leverage interpretable strategies from numerical methods and computational fluid dynamics to enforce physical laws and boundary conditions by taking advantage the mathematical properties of the underlying equations. We demonstrate results on three-dimensional fully-developed turbulence, showing that this technique drastically improves local conservation of mass, without sacrificing performance according to several other metrics characterizing the fluid flow.
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