@Article{EAJAM-14-1,
author = {Yufeng, Wang and Xu, Cong and Yang, Min and Zhang, Jin},
title = {Less Emphasis on Hard Regions: Curriculum Learning of PINNs for Singularly Perturbed Convection-Diffusion-Reaction Problems},
journal = {East Asian Journal on Applied Mathematics},
year = {2024},
volume = {14},
number = {1},
pages = {104--123},
abstract = {<p style="text-align: justify;">Although physics-informed neural networks (PINNs) have been successfully
applied in a wide variety of science and engineering fields, they can fail to accurately predict the underlying solution in slightly challenging convection-diffusion-reaction problems. In this paper, we investigate the reason of this failure from a domain distribution perspective, and identify that learning multi-scale fields simultaneously makes the
network unable to advance its training and easily get stuck in poor local minima. We
show that the widespread experience of sampling more collocation points in high-loss
regions hardly help optimize and may even worsen the results. These findings motivate
the development of a novel curriculum learning method that encourages neural networks to prioritize learning on easier non-layer regions while downplaying learning on
harder regions. The proposed method helps PINNs automatically adjust the learning emphasis and thereby facilitates the optimization procedure. Numerical results on typical
benchmark equations show that the proposed curriculum learning approach mitigates
the failure modes of PINNs and can produce accurate results for very sharp boundary
and interior layers. Our work reveals that for equations whose solutions have large
scale differences, paying less attention to high-loss regions can be an effective strategy
for learning them accurately.</p>},
issn = {2079-7370},
doi = {https://doi.org/10.4208/eajam.2023-062.170523},
url = {https://global-sci.com/article/82400/less-emphasis-on-hard-regions-curriculum-learning-of-pinns-for-singularly-perturbed-convection-diffusion-reaction-problems}
}