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[2602.18801] SGNO: Spectral Generator Neural Operators for Stable Long Horizon PDE Rollouts
Summary
The paper introduces the Spectral Generator Neural Operator (SGNO), a novel approach to enhance the stability of long horizon rollouts in PDE simulations, addressing common issues of error accumulation and high-frequency feedback.
Why It Matters
This research is significant as it tackles the challenges of stability in predictive models for partial differential equations (PDEs), which are widely used in various scientific and engineering applications. By improving the reliability of long-term predictions, SGNO could enhance simulations in fields such as fluid dynamics, climate modeling, and more.
Key Takeaways
- SGNO effectively mitigates error accumulation in long horizon PDE rollouts.
- The method employs a learned diagonal generator constrained to prevent amplification of linear dynamics.
- Incorporates a gated forcing term to control nonlinear updates and limit high-frequency feedback.
- Demonstrates superior performance over existing neural operator baselines on APEBench.
- Provides theoretical bounds for error amplification and stability in rollouts.
Computer Science > Machine Learning arXiv:2602.18801 (cs) [Submitted on 21 Feb 2026] Title:SGNO: Spectral Generator Neural Operators for Stable Long Horizon PDE Rollouts Authors:Jiayi Li, Zhaonan Wang, Flora D. Salim View a PDF of the paper titled SGNO: Spectral Generator Neural Operators for Stable Long Horizon PDE Rollouts, by Jiayi Li and 2 other authors View PDF HTML (experimental) Abstract:Neural operators provide fast PDE surrogates and often generalize across parameters and resolutions. However, in the short train long test setting, autoregressive rollouts can become unstable. This typically happens for two reasons: one step errors accumulate over time, and high frequency components feed back and grow. We introduce the Spectral Generator Neural Operator (SGNO), a residual time stepper that targets both effects. For the linear part, SGNO uses an exponential time differencing update in Fourier space with a learned diagonal generator. We constrain the real part of this generator to be nonpositive, so iterating the step does not amplify the linear dynamics. For nonlinear dynamics, SGNO adds a gated forcing term with channel mixing within each Fourier mode, which keeps the nonlinear update controlled. To further limit high frequency feedback, SGNO applies spectral truncation and an optional smooth mask on the forcing pathway. We derive a one step amplification bound and a finite horizon rollout error bound. The bound separates generator approximation error from nonlinear...
