@Article{CiCP-33-1240,
author = {Basir , Shamsulhaq},
title = {Investigating and Mitigating Failure Modes in Physics-Informed Neural Networks (PINNs)},
journal = {Communications in Computational Physics},
year = {2023},
volume = {33},
number = {5},
pages = {1240--1269},
abstract = {<p style="text-align: justify;">This paper explores the difficulties in solving partial differential equations
(PDEs) using physics-informed neural networks (PINNs). PINNs use physics as a regularization term in the objective function. However, a drawback of this approach is the
requirement for manual hyperparameter tuning, making it impractical in the absence
of validation data or prior knowledge of the solution. Our investigations of the loss
landscapes and backpropagated gradients in the presence of physics reveal that existing methods produce non-convex loss landscapes that are hard to navigate. Our findings demonstrate that high-order PDEs contaminate backpropagated gradients and
hinder convergence. To address these challenges, we introduce a novel method that
bypasses the calculation of high-order derivative operators and mitigates the contamination of backpropagated gradients. Consequently, we reduce the dimension of the
search space and make learning PDEs with non-smooth solutions feasible. Our method
also provides a mechanism to focus on complex regions of the domain. Besides, we
present a dual unconstrained formulation based on Lagrange multiplier method to enforce equality constraints on the model’s prediction, with adaptive and independent
learning rates inspired by adaptive subgradient methods. We apply our approach to
solve various linear and non-linear PDEs.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2022-0239},
url = {http://global-sci.org/intro/article_detail/cicp/21761.html}
}