F cubed NO: Frequency-Decomposed Finite-Time Flow-map Neural Operators with Cross-Scale Conditioning
F3NO introduces a neural operator that improves long-term forecasting of Partial Differential Equations (PDEs) by addressing error accumulation and fine-scale structure resolution issues. It uses a Frequency-Decomposed Spectral Refinement block to update low-frequency features, which then guide the refinement of high-frequency details. This method achieves lower prediction errors across various complex PDE benchmarks compared to existing methods.