Fourier Neural Operators for Accelerating Newton's Method Convergence in Nonlinear Elliptic PDEs
Fourier neural operators accelerate Newton's method convergence for nonlinear elliptic PDEs.
Neural Operators for Solving Large-Scale PDEs: Incremental Spatial and Spectral Learning
Incremental Fourier Neural Operator (iFNO) improves training efficiency and generalization performance for solving PDEs.
Enhancing Fourier Neural Operators: Spectral Analysis and Ensemble Learning for Improved High-Frequency Capture
Fourier Neural Operators (FNOs) exhibit superior performance over Convolutional Neural Networks (CNNs) in solving partial differential equations (PDEs) due to their exceptional ability to capture low-frequency information. However, FNOs face challenges in effectively learning high-frequency information, leading to a notable low-frequency bias. To address this limitation, the paper introduces SpecBoost, an ensemble learning framework that leverages multiple FNOs to better capture high-frequency details overlooked by a solo FNO.
