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.
Investigating the Ability of Physics-Informed Neural Networks (PINNs) to Solve Burgers' Partial Differential Equation Near Finite-Time Blow-Up
Physics-Informed Neural Networks (PINNs) can potentially solve Burgers' partial differential equation near finite-time blow-up, but their stability and performance in such scenarios require rigorous theoretical and experimental investigation.
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