Embedding Hard Physical Constraints in Neural Network Coarse-Graining of 3D Turbulence

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.

arXiv commentv2: modified illustration in Eqn. 8 for clarity

References in corpus (16)

• DeepXDE: A deep learning library for solving differential equations
• Deep learning for universal linear embeddings of nonlinear dynamics
• Super-resolution reconstruction of turbulent flows with machine learning
• PDE-Net 2.0: Learning PDEs from Data with A Numeric-Symbolic Hybrid Deep Network
• Nonlinear mode decomposition with convolutional neural networks for fluid dynamics
• Dynamic Graph CNN for Learning on Point Clouds
• PDE-Net: Learning PDEs from Data
• Enforcing Statistical Constraints in Generative Adversarial Networks for Modeling Chaotic Dynamical Systems
• A Deep Learning based Approach to Reduced Order Modeling for Turbulent Flow Control using LSTM Neural Networks
• Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems
• Physics-informed Autoencoders for Lyapunov-stable Fluid Flow Prediction
• Lat-Net: Compressing Lattice Boltzmann Flow Simulations using Deep Neural Networks
• Compressed Convolutional LSTM: An Efficient Deep Learning framework to Model High Fidelity 3D Turbulence
• The Effects of Hyperparameters on SGD Training of Neural Networks
• Inductive Bias of Deep Convolutional Networks through Pooling Geometry
• From Deep to Physics-Informed Learning of Turbulence: Diagnostics

Cited by in corpus (18)

• PhyGeoNet: Physics-Informed Geometry-Adaptive Convolutional Neural Networks for Solving Parameterized Steady-State PDEs on Irregular Domain
• Theory-guided hard constraint projection (HCP): a knowledge-based data-driven scientific machine learning method
• The Neural Particle Method -- An Updated Lagrangian Physics Informed Neural Network for Computational Fluid Dynamics
• On closures for reduced order models $-$ A spectrum of first-principle to machine-learned avenues
• Physics guided machine learning using simplified theories
• Latent Space Data Assimilation by using Deep Learning
• Teaching the Incompressible Navier-Stokes Equations to Fast Neural Surrogate Models in 3D
• Model fusion with physics-guided machine learning
• Nonlinear proper orthogonal decomposition for convection-dominated flows
• Training neural networks under physical constraints using a stochastic augmented Lagrangian approach
• A Tailored Convolutional Neural Network for Nonlinear Manifold Learning of Computational Physics Data using Unstructured Spatial Discretizations
• Physics-Integrated Variational Autoencoders for Robust and Interpretable Generative Modeling
• Data assimilation empowered neural network parameterizations for subgrid processes in geophysical flows
• Validation and parameterization of a novel physics-constrained neural dynamics model applied to turbulent fluid flow
• PCE-PINNs: Physics-Informed Neural Networks for Uncertainty Propagation in Ocean Modeling
• Learning Incompressible Fluid Dynamics from Scratch -- Towards Fast, Differentiable Fluid Models that Generalize
• A Parallel Integrated Computational-Statistical Platform for Turbulent Transport Phenomena
• Teaching Solid Mechanics to Artificial Intelligence: a fast solver for heterogeneous solids