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Gaussian process learning with flow map refinement for parameter estimation in dynamical systems — arXiv:2608.22324

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.22324
License (as archived): CC0-1.0
Archived: 2026-10-18T08:28:04.751Z
SHA-256 of the archived text: 8469ec3f7a6349d27e1806823a452c6a7740df74750a157749258383524e80ca
Stable URL of this page: https://metraipolis.com/documento/dc_4e6742a49aaa

How to cite

Gaussian process learning with flow map refinement for parameter estimation in dynamical systems — arXiv:2608.22324 — arXiv (en), https://arxiv.org/abs/2608.22324 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_4e6742a49aaa (Metraipolis archive dc_4e6742a49aaa, sha256 8469ec3f7a6349d27e1806823a452c6a7740df74750a157749258383524e80ca)

BibTeX

@misc{dc4e6742a49aaa,
  title = {Gaussian process learning with flow map refinement for parameter estimation in dynamical systems — arXiv:2608.22324},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.22324},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_4e6742a49aaa; sha256 8469ec3f7a6349d27e1806823a452c6a7740df74750a157749258383524e80ca},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.22324. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Parameter estimation is a central task in data-driven learning of dynamical systems. It aims to recover the underlying physical parameters from observed time-series data, thereby providing interpretable insights into the physical mechanisms governing the system. Gradient/derivative matching methods based on Gaussian process provide an efficient way to perform parameter estimation. Those methods avoid repeated numerical integration and enforce local derivative consistency. However, such local matching may result in global inconsistency with the governing flow map, particularly under scarce and noisy observations. To address this limitation, we propose a framework based on Gaussian process learning with flow map refinement (GPL-FMR), a two-stage parameter estimation framework. The first stage is based on Gaussian process learning algorithm and the posterior obtained from which is transferred as an informative prior to the second stage based on flow-map refinement. The second stage further improves the parameter estimation via optimisation based on global dynamical constraints. We demonstrate and analyse its performance on multiple numerical examples, including the Van der Pol oscillator, the Lotka-Volterra model, and the Lorenz-63 system. The results show that the proposed framework consistently improves parameter estimation accuracy, particularly under scarce and noisy observations.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-08-25 in math.NA).
Categorie arXiv: Machine Learning (cs.LG) ; Computational Engineering, Finance, and Science (cs.CE); Numerical Analysis (math.NA).
Pagina del lavoro: https://arxiv.org/abs/2608.22324 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-18T08:27:23.864Z dalla pagina https://arxiv.org/catchup/math.NA/2026-08-25?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).