This paper addresses the problem of learning the dynamics of partial differential equations (PDEs) with unknown physical properties using limited data. We aim to overcome the limitations of existing neural network-based PDE solvers, which require large datasets or rely on known physical laws, such as PDE residuals or hand-crafted stencils. To this end, we propose the Spectral-Inspired Neural Operator (SINO), which can model complex systems with only 2-5 trajectories. SINO does not require explicit PDE terms and automatically captures local and global spatial derivatives through frequency indices, providing a concise representation of the basic differential operator in a physics-independent environment. We employ Pi-blocks, which perform multiplication operations on spectral features to model nonlinear effects, and apply a low-pass filter to suppress aliasing. Extensive experiments on 2D and 3D PDE benchmarks demonstrate that SINO achieves state-of-the-art performance, achieving one to two orders of magnitude performance improvement in accuracy. Notably, with only five training trajectories, SINO outperforms data-driven methods trained on 1,000 trajectories, and maintains its predictive performance even in challenging out-of-distribution cases where other methods fail.
