mgjeon/long-time-integration-pi-deeponets

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

Code and data (available upon request) accompanying the manuscript titled "Long-time integration of parametric evolution equations with physics-informed DeepONets", authored by Sifan Wang, and Paris Perdikaris.

Abstract

Partial differential equations (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 PDEs 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.

Citation

@article{wang2021long,
  title={Long-time integration of parametric evolution equations with physics-informed DeepONets},
  author={Wang, Sifan and Perdikaris, Paris},
  journal={arXiv preprint arXiv:2106.05384},
  year={2021}
  }