TF-SNO: Time-Frequency Gated Spectral Neural Operators for Learning Non-Stationary Partial Differential Equations

The article introduces the Time-Frequency Gated Spectral Neural Operator (TF-SNO), designed to address the limitations of spectral neural operators in solving non-stationary partial differential equations (PDEs) by incorporating learnable time-frequency gating within spectral blocks. TF-SNO dynamically adapts its spectral response based on the current state, enabling it to effectively capture temporal variations without increasing modeling complexity. Experimental results on six 1D and 2D non-stationary PDE benchmarks show significant reductions in prediction errors and improved robustness, particularly for long-horizon predictions, highlighting its potential for practitioners dealing with time-varying physical systems.