Lightweight Fourier Neural Operator for Time-Dependent Partial Differential Equations

Fourier Neural Operators (FNOs) have shown strong performance in solving time-dependent partial differential equations (PDEs). However, accurately modeling complex spatio-temporal dynamics remains challenging and is typically addressed in one of two ways: (i) by applying spectral convolutions over the spatial domain with temporal dynamics handled autoregressively, or (ii) by applying spectral convolutions over the entire spatio-temporal domain. While the former is more computationally efficient, it fails to capture true spatio-temporal interactions. The latter, though more accurate, becomes computationally prohibitive when scaling to larger datasets.We propose \method, a novel FNO framework that achieves both numerical accuracy and computational efficiency for time-dependent PDEs. Specifically, we first model spatial dynamics by learning a low-rank spatial basis of spectral convolutional weights space. We then incorporate temporal dynamics by learning a new temporal basis through transduction. This factorized formulation enables efficient learning of full spatio-temporal dynamics with significantly fewer parameters (99.9% reduction) and superior performance (44% improvement in VRMSE) compared to the variants of FNO models. The source code and the dataset are available at https://anonymous.4open.science/r/LFNO.