Embedding Hard Physical Constraints in Neural Network Coarse-Graining of 3D Turbulence
Authors:
- Arvind T. MohanAMArvind T. Mohan
- Nicholas LubbersNLNicholas Lubbers
- Daniel LivescuDLDaniel Livescu
- Michael ChertkovMCMichael Chertkov
Preprint
Abstract
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.Keywords
All Related Versions
This publication has 21 references indexed in Scilit:
- Enforcing statistical constraints in generative adversarial networks for modeling chaotic dynamical systemsJournal of Computational Physics, 2020
- PDE-Net 2.0: Learning PDEs from data with a numeric-symbolic hybrid deep networkJournal of Computational Physics, 2019
- Prediction of turbulent heat transfer using convolutional neural networksJournal of Fluid Mechanics, 2019
- Nonlinear mode decomposition with convolutional neural networks for fluid dynamicsJournal of Fluid Mechanics, 2019
- Super-resolution reconstruction of turbulent flows with machine learningJournal of Fluid Mechanics, 2019
- Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equationsJournal of Computational Physics, 2019
- Deep learning for universal linear embeddings of nonlinear dynamicsNature Communications, 2018
- Reynolds averaged turbulence modelling using deep neural networks with embedded invarianceJournal of Fluid Mechanics, 2016
- A ghost-cell immersed boundary method for flow in complex geometryJournal of Computational Physics, 2003
- Fully Conservative Higher Order Finite Difference Schemes for Incompressible FlowJournal of Computational Physics, 1998