Spectral-Inspired Neural Operator for PDE Learning with Limited Data

Researchers propose the Spectral-Inspired Neural Operator (SINO), a machine learning model that can learn partial differential equation (PDE) dynamics from as few as 2-5 trajectories without requiring explicit knowledge of the underlying physics. SINO automatically captures local and global spatial derivatives from frequency indices, enabling compact representation of differential operators. It uses a Pi-block for multiplicative operations on spectral features and a low-pass filter to suppress aliasing. Experiments on 2D and 3D PDE benchmarks show state-of-the-art performance with improvements of 1-2 orders of magnitude over existing methods. The approach addresses the challenge of modeling complex systems with limited data and unknown physics.