Adversarial Multi-task Learning Enhanced Physics-informed Neural Networks for Solving Partial Differential Equations

04/29/2021
by   Pongpisit Thanasutives, et al.
0

Recently, researchers have utilized neural networks to accurately solve partial differential equations (PDEs), enabling the mesh-free method for scientific computation. Unfortunately, the network performance drops when encountering a high nonlinearity domain. To improve the generalizability, we introduce the novel approach of employing multi-task learning techniques, the uncertainty-weighting loss and the gradients surgery, in the context of learning PDE solutions. The multi-task scheme exploits the benefits of learning shared representations, controlled by cross-stitch modules, between multiple related PDEs, which are obtainable by varying the PDE parameterization coefficients, to generalize better on the original PDE. Encouraging the network pay closer attention to the high nonlinearity domain regions that are more challenging to learn, we also propose adversarial training for generating supplementary high-loss samples, similarly distributed to the original training distribution. In the experiments, our proposed methods are found to be effective and reduce the error on the unseen data points as compared to the previous approaches in various PDE examples, including high-dimensional stochastic PDEs.

READ FULL TEXT

page 1

page 2

page 6

research
04/10/2023

iPINNs: Incremental learning for Physics-informed neural networks

Physics-informed neural networks (PINNs) have recently become a powerful...
research
02/14/2020

Optimally weighted loss functions for solving PDEs with Neural Networks

Recent works have shown that deep neural networks can be employed to sol...
research
01/14/2020

SelectNet: Self-paced Learning for High-dimensional Partial Differential Equations

The residual method with deep neural networks as function parametrizatio...
research
09/01/2022

Physics-informed MTA-UNet: Prediction of Thermal Stress and Thermal Deformation of Satellites

The rapid analysis of thermal stress and deformation plays a pivotal rol...
research
10/15/2021

Towards fast weak adversarial training to solve high dimensional parabolic partial differential equations using XNODE-WAN

Due to the curse of dimensionality, solving high dimensional parabolic p...
research
09/07/2020

Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanism

Physics-Informed Neural Networks (PINNs) have emerged recently as a prom...
research
08/18/2022

CP-PINNs: Changepoints Detection in PDEs using Physics Informed Neural Networks with Total-Variation Penalty

We consider the inverse problem for the Partial Differential Equations (...

Please sign up or login with your details

Forgot password? Click here to reset