Li Z, Matzakos N (2027)
Publication Language: English
Publication Status: Submitted
Publication Type: Unpublished / Preprint
Future Publication Type: Journal article
Publication year: 2027
URI: https://arxiv.org/abs/2608.10738
DOI: 10.48550/arXiv.2608.10738
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. The Floquet strategy addresses autonomous targets with a stable limit cycle and uses no data at deployment: a certified contraction of the learned return map confines the error to linear growth in the number of elapsed periods. For the time-periodic architecture we deploy, the scalar certificate degenerates; we prove instead a uniform-in-time orbital guarantee whose hypotheses are measured on the trained model, and an obstruction showing that, for an exactly periodic learned field, small one-period error and a contracting stroboscopic map cannot hold at once. Numerical experiments on four benchmarks confirm the predicted error laws and measure the hypotheses of every guarantee.
APA:
Li, Z., & Matzakos, N. (2027). Long-Time Trajectory Approximation via SA-NODEs: Model Predictive and Floquet Strategies. (Unpublished, Submitted).
MLA:
Li, Ziqian, and Nikolaos Matzakos. Long-Time Trajectory Approximation via SA-NODEs: Model Predictive and Floquet Strategies. Unpublished, Submitted. 2027.
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