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标题: "Long-Time Trajectory Approximation via SA-NODEs: Model Predictive and Floquet Strategies"
原文链接: "https://arxiv.org/abs/2608.10738"
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去重键: "https://arxiv.org/abs/2608.10738"
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## Computer Science > Machine Learning

## Title:Long-Time Trajectory Approximation via SA-NODEs: Model Predictive and Floquet Strategies

Authors:[Ziqian Li](https://arxiv.org/search/cs?searchtype=author&query=Li,+Z), [Nikolaos M. Matzakos](https://arxiv.org/search/cs?searchtype=author&query=Matzakos,+N+M)

[View PDF](https://arxiv.org/pdf/2608.10738) [HTML (experimental)](https://arxiv.org/html/2608.10738v1)

> Abstract: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.

| Subjects: | Machine Learning (cs.LG); Numerical Analysis (math.NA) |
| --- | --- |
| MSC classes: | 68T07, 93B45, 34C25, 65L05, 41A30 |
| Cite as: | [arXiv:2608.10738](https://arxiv.org/abs/2608.10738) \[cs.LG\] |
|  | (or [arXiv:2608.10738v1](https://arxiv.org/abs/2608.10738v1) \[cs.LG\] for this version) |
|  | [https://doi.org/10.48550/arXiv.2608.10738](https://doi.org/10.48550/arXiv.2608.10738) |

## Submission history

From: Ziqian Li \[[view email](https://arxiv.org/show-email/abba4373/2608.10738)\]  
**\[v1\]** Tue, 11 Aug 2026 09:55:54 UTC (229 KB)

[Which authors of this paper are endorsers?](https://arxiv.org/auth/show-endorsers/2608.10738) | Disable MathJax ([What is MathJax?](https://info.arxiv.org/help/mathjax.html))
