Long-time integration of parametric evolution equations with physics-informed DeepONets

06/09/2021
by   Sifan Wang, et al.
0

Ordinary and partial differential equations (ODEs/PDEs) play a paramount role in analyzing and simulating complex dynamic processes across all corners of science and engineering. In recent years machine learning tools are aspiring to introduce new effective ways of simulating PDEs, however existing approaches are not able to reliably return stable and accurate predictions across long temporal horizons. We aim to address this challenge by introducing an effective framework for learning infinite-dimensional operators that map random initial conditions to associated PDE solutions within a short time interval. Such latent operators can be parametrized by deep neural networks that are trained in an entirely self-supervised manner without requiring any paired input-output observations. Global long-time predictions across a range of initial conditions can be then obtained by iteratively evaluating the trained model using each prediction as the initial condition for the next evaluation step. This introduces a new approach to temporal domain decomposition that is shown to be effective in performing accurate long-time simulations for a wide range of parametric ODE and PDE systems, from wave propagation, to reaction-diffusion dynamics and stiff chemical kinetics, all at a fraction of the computational cost needed by classical numerical solvers.

READ FULL TEXT

page 13

page 14

page 16

page 24

page 28

research
12/20/2022

Learning Subgrid-scale Models with Neural Ordinary Differential Equations

We propose a new approach to learning the subgrid-scale model when simul...
research
03/19/2021

Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets

Deep operator networks (DeepONets) are receiving increased attention tha...
research
04/04/2022

Towards Large-Scale Learned Solvers for Parametric PDEs with Model-Parallel Fourier Neural Operators

Fourier neural operators (FNOs) are a recently introduced neural network...
research
08/10/2023

PDE-Refiner: Achieving Accurate Long Rollouts with Neural PDE Solvers

Time-dependent partial differential equations (PDEs) are ubiquitous in s...
research
02/27/2022

DeepPropNet – A Recursive Deep Propagator Neural Network for Learning Evolution PDE Operators

In this paper, we propose a deep neural network approximation to the evo...
research
12/13/2022

Reliable extrapolation of deep neural operators informed by physics or sparse observations

Deep neural operators can learn nonlinear mappings between infinite-dime...

Please sign up or login with your details

Forgot password? Click here to reset