LOGLO-FNO: Efficient Learning of Local and Global Features in Fourier Neural Operators

Learning local features and high frequencies is an important problem in Scientific Machine Learning. For instance, effectively modeling turbulence (e.g., $Re=3500$ and above) depends on accurately reconstructing moderate to high frequencies. In recent years, Fourier Neural Operators (FNOs) have emerged as a popular class of data-driven models for solving Partial Differential Equations (PDEs) and surrogate modeling in general. Although impressive results have been achieved in several benchmark PDE datasets, FNOs often perform poorly in learning non-dominant frequencies represented by local features, mainly due to the spectral bias of neural networks and the explicit exclusion of high-frequency modes in FNO and its variants. Therefore, to improve the spectral learning capabilities of FNO, we propose two key architectural enhancements to FNO: (i) a parallel branch performing local spectral convolutions, (ii) a high-frequency propagation module, and a frequency-sensitive loss term. Consequently, this introduction of an additional pathway for local convolution results in as much as a 50% reduction in trainable parameters to reach the accuracy of baseline FNO that performs only global convolution. Experiments on two challenging PDE problems in fluid mechanics and biological pattern formation and the qualitative and spectral analysis of predictions show the effectiveness of our method over the state-of-the-art neural operator baselines.