SPINN: sparse, physics-based, and partially interpretable neural networks for PDEs

DOI10.1016/j.jcp.2021.110600OpenAlexW3184364599WikidataQ114163429 ScholiaQ114163429MaRDI QIDQ2133032

Prabhu Ramachandran, Amuthan A. Ramabathiran

Publication date: 29 April 2022

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2102.13037

zbMATH Keywords

partial differential equationsmeshless methodsnumerical methods for PDEssparse neural networksinterpretable machine learningphysics-based neural networks

Mathematics Subject Classification ID

Artificial intelligence (68Txx) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Numerical methods for partial differential equations, boundary value problems (65Nxx)

Related Items (10)

Scientific machine learning through physics-informed neural networks: where we are and what's next ⋮ Deep neural networks based temporal-difference methods for high-dimensional parabolic partial differential equations ⋮ Physics and equality constrained artificial neural networks: application to forward and inverse problems with multi-fidelity data fusion ⋮ Physics-informed radial basis network (PIRBN): a local approximating neural network for solving nonlinear partial differential equations ⋮ Stochastic projection based approach for gradient free physics informed learning ⋮ Distributed PINN for Linear Elasticity — A Unified Approach for Smooth, Singular, Compressible and Incompressible Media ⋮ Neural Control of Parametric Solutions for High-Dimensional Evolution PDEs ⋮ Exact imposition of boundary conditions with distance functions in physics-informed deep neural networks ⋮ Theory-guided physics-informed neural networks for boundary layer problems with singular perturbation ⋮ Learning stochastic dynamics with statistics-informed neural network

Uses Software

• Gmsh
• FEniCS
• MayaVi
• NumPy
• Pyclaw
• Matplotlib
• PyWENO
• Mayavi
• FastDer++
• PyTorch
• PySPH
• Adam
• DeepXDE
• PDE-Net
• DGM
• automan
• MscaleDNN

Cites Work

• Automated solution of differential equations by the finite element method. The FEniCS book
• Machine learning from a continuous viewpoint. I
• Automatic finite element formulation and assembly of hyperelastic higher order structural models
• Entropically damped artificial compressibility for SPH
• The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems
• High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method
• Automatic differentiation for solving nonlinear partial differential equations: an efficient operator overloading approach
• DGM: a deep learning algorithm for solving partial differential equations
• Deep least-squares methods: an unsupervised learning-based numerical method for solving elliptic PDEs
• A mesh-free method for interface problems using the deep learning approach
• On the eigenvector bias of Fourier feature networks: from regression to solving multi-scale PDEs with physics-informed neural networks
• An energy approach to the solution of partial differential equations in computational mechanics via machine learning: concepts, implementation and applications
• Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• Numerical Gaussian Processes for Time-Dependent and Nonlinear Partial Differential Equations
• PyClaw: Accessible, Extensible, Scalable Tools for Wave Propagation Problems
• Relu Deep Neural Networks and Linear Finite Elements
• Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities
• Introduction to wavelets in engineering
• Solving high-dimensional partial differential equations using deep learning
• PySPH: A Python-based Framework for Smoothed Particle Hydrodynamics
• DeepXDE: A Deep Learning Library for Solving Differential Equations
• Multi-Scale Deep Neural Network (MscaleDNN) for Solving Poisson-Boltzmann Equation in Complex Domains
• Physics-Informed Neural Networks with Hard Constraints for Inverse Design

This page was built for publication: SPINN: sparse, physics-based, and partially interpretable neural networks for PDEs