@Article{CiCP-34-869,
author = {Wang , HonghuiLu , LuSong , Shiji and Huang , Gao},
title = {Learning Specialized Activation Functions for Physics-Informed Neural Networks},
journal = {Communications in Computational Physics},
year = {2023},
volume = {34},
number = {4},
pages = {869--906},
abstract = {<p style="text-align: justify;">Physics-informed neural networks (PINNs) are known to suffer from optimization difficulty. In this work, we reveal the connection between the optimization
difficulty of PINNs and activation functions. Specifically, we show that PINNs exhibit
high sensitivity to activation functions when solving PDEs with distinct properties.
Existing works usually choose activation functions by inefficient trial-and-error. To
avoid the inefficient manual selection and to alleviate the optimization difficulty of
PINNs, we introduce adaptive activation functions to search for the optimal function
when solving different problems. We compare different adaptive activation functions
and discuss their limitations in the context of PINNs. Furthermore, we propose to tailor the idea of learning combinations of candidate activation functions to the PINNs
optimization, which has a higher requirement for the smoothness and diversity on
learned functions. This is achieved by removing activation functions which cannot
provide higher-order derivatives from the candidate set and incorporating elementary
functions with different properties according to our prior knowledge about the PDE at
hand. We further enhance the search space with adaptive slopes. The proposed adaptive activation function can be used to solve different PDE systems in an interpretable
way. Its effectiveness is demonstrated on a series of benchmarks. Code is available at
https://github.com/LeapLabTHU/AdaAFforPINNs.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2023-0058},
url = {http://global-sci.org/intro/article_detail/cicp/22125.html}
}