Long-Time Trajectory Approximation via SA-NODEs: Model Predictive and Floquet Strategies
We study the approximation of dynamical systems by semi-autonomous neural ordinary differential equations (SA-NODEs) over long time horizons. For a single network trained on the whole horizon, the available error bound deteriorates double exponentially in the horizon length. We develop two training strategies that avoid this barrier, each built on a reset of the state. The model predictive strategy partitions the horizon adaptively and restarts every window from observed data: when training meets a prescribed tolerance on every window, the composite model meets it uniformly in time, with a parameter budget linear in the horizon for targets with a bounded, uniformly regular reachable tube....
| Authors | Ziqian Li, Nikolaos M. Matzakos |
|---|---|
| Primary category | cs.LG |
| Published | 11 August 2026 |
| Last updated at source | 11 August 2026 |
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