One-Step Evolution for Long-Time Extrapolation: An Error-Bound-Informed and Prior-Guided Neural Residual Framework for Autonomous PDEs
Accurate simulation of the long-time evolution of systems governed by partial differential equations (PDEs) is central to scientific computing. Among existing deep learning?based approaches for solving PDEs, neural operators typically rely on extensive trajectory data, whereas physics-informed meth?ods often exhibit limited stability during long-time extrapolation. For a well-posed autonomous PDE, long-time trajectories can be generated by repeated composition of a fixed-step evolution operator; hence, long-time extrapolation depends on controlling the approximation error of this operator and the propagation of that error under recursive composition. Accordingly, we propose a numerical-pr...
| Authors | Maqun Zhang, Feng Gao, Wankun Chen et al. |
|---|---|
| Primary category | cs.AI |
| Published | 22 August 2026 |
| Last updated at source | 22 August 2026 |
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