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.
@article{arxiv.2412.00225,
title = {Meta-learning Loss Functions of Parametric Partial Differential Equations Using Physics-Informed Neural Networks},
author = {Michail Koumpanakis and Ricardo Vilalta},
journal= {arXiv preprint arXiv:2412.00225},
year = {2024}
}