Meta-learning Loss Functions of Parametric Partial Differential Equations Using Physics-Informed Neural Networks

TL;DR

This paper introduces a meta-learning approach to automatically learn loss functions for parametric PDEs using physics-informed neural networks, enhancing efficiency and convergence in solving these equations.

Contribution

It presents a novel method to meta-learn loss functions for parametric PDEs with physics-informed neural networks, replacing traditional data loss.

Findings

Improved convergence in solving parametric PDEs

Effective meta-learning of loss functions for PDEs

Enhanced performance on Burger's and 2D Heat Equations

Abstract

This paper proposes a new way to learn Physics-Informed Neural Network loss functions using Generalized Additive Models. We apply our method by meta-learning parametric partial differential equations, PDEs, on Burger's and 2D Heat Equations. The goal is to learn a new loss function for each parametric PDE using meta-learning. The derived loss function replaces the traditional data loss, allowing us to learn each parametric PDE more efficiently, improving the meta-learner's performance and convergence.