@Article{NMTMA-18-521,
author = {Wang , LinYang , MinGao , Ruisong and Chen , Chuanjun},
title = {Noise Robust Physics-Informed Generative Adversarial Networks for Solving Stochastic Differential Equations},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2025},
volume = {18},
number = {2},
pages = {521--543},
abstract = {<p style="text-align: justify;">This paper proposes a class of physics-informed neural networks called
noise robust physics-informed generative adversarial networks (NR-PIGANs) to solve
stochastic differential equations in the presence of noisy measurements. In these
scenarios, while the governing equations are known, only a limited number of sensor measurements of the system parameters are available, and some may contain
significant measurement errors. To address this, NR-PIGAN incorporates an additional noise generator with specific distribution constraints into a physics-informed
generative adversarial network framework. The noise generator is trained alongside the clean data generators in an end-to-end manner, enabling the model to effectively capture both clean and noisy data distributions under the given physical
constraints. Numerical experiments demonstrate that NR-PIGAN excels in handling
forward and inverse problems under diverse noise perturbations, and its advantage
becomes more pronounced as the noise level increases.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.OA-2024-0123},
url = {http://global-sci.org/intro/article_detail/nmtma/24074.html}
}