Component Fourier Neural Operator for Singularly Perturbed Differential Equations
DOI:
https://doi.org/10.1609/aaai.v38i12.29274Keywords:
ML: Deep Neural Architectures and Foundation Models, ML: Applications, ML: Deep Learning Algorithms, ML: Unsupervised & Self-Supervised LearningAbstract
Solving Singularly Perturbed Differential Equations (SPDEs) poses computational challenges arising from the rapid transitions in their solutions within thin regions. The effectiveness of deep learning in addressing differential equations motivates us to employ these methods for solving SPDEs. In this paper, we introduce Component Fourier Neural Operator (ComFNO), an innovative operator learning method that builds upon Fourier Neural Operator (FNO), while simultaneously incorporating valuable prior knowledge obtained from asymptotic analysis. Our approach is not limited to FNO and can be applied to other neural network frameworks, such as Deep Operator Network (DeepONet), leading to potential similar SPDEs solvers. Experimental results across diverse classes of SPDEs demonstrate that ComFNO significantly improves accuracy compared to vanilla FNO. Furthermore, ComFNO exhibits natural adaptability to diverse data distributions and performs well in few-shot scenarios, showcasing its excellent generalization ability in practical situations.Downloads
Published
2024-03-24
How to Cite
Li, Y., Du, T., Pang, Y., & Huang, Z. (2024). Component Fourier Neural Operator for Singularly Perturbed Differential Equations. Proceedings of the AAAI Conference on Artificial Intelligence, 38(12), 13691-13699. https://doi.org/10.1609/aaai.v38i12.29274
Issue
Section
AAAI Technical Track on Machine Learning III