AI RESEARCH
SGNO: Spectral Generator Neural Operators for Stable Long Horizon PDE Rollouts
arXiv CS.LG
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ArXi:2602.18801v2 Announce Type: replace Autoregressive neural PDE surrogates predict future states by repeatedly applying a learned one-step operator. This is a simple and widely used method, but small one-step errors can accumulate during long rollouts. The resulting drift often appears as spectral amplitude distortion, phase misalignment, and nonlinear mode-interaction error. These effects are especially important for time-dependent PDEs with clear Fourier structure. SGNO is designed for periodic linear and semilinear evolution PDEs with Fourier multiplier linear dynamics.