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PreprintCC BY 4.0arXiv

Asymptotic approximation of sensitivities in finite dimensional continuous data assimilation with application to parameter estimation

  • Joshua Newey
  • Jared P. Whitehead
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Abstract

We develop a rigorous justification for a parameter estimation algorithm which couples continuous data assimilation to generic optimization. For finite dimensional systems, we provide a rigorous justification of an asymptotic approximation of the sensitivity for the underlying modeled dynamical system, prove that the L2 loss function satisfies an approximate Polyak-Lojasiewicz inequality, and use that result to justify convergence of gradient descent for the proposed algorithm. Numerical examples are provided that demonstrate the precision of the rigorous results.

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Cite

BibTeXRIS
BibTeX
@misc{newey2026asymptotic,
  title = {{Asymptotic approximation of sensitivities in finite dimensional continuous data assimilation with application to parameter estimation}},
  author = {Joshua Newey and Jared P. Whitehead},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.02686},
  eprint = {2610.02686},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.02686},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Asymptotic approximation of sensitivities in finite dimensional continuous data assimilation with application to parameter estimation
AU  - Joshua Newey
AU  - Jared P. Whitehead
PY  - 2026
DA  - 2026/10/02
PB  - arXiv
DO  - 10.48550/arxiv.2610.02686
UR  - https://arxiv.org/abs/2610.02686
AB  - We develop a rigorous justification for a parameter estimation algorithm which couples continuous data assimilation to generic optimization. For finite dimensional systems, we provide a rigorous justification of an asymptotic approximation of the sensitivity for the underlying modeled dynamical system, prove that the L^2 loss function satisfies an approximate Polyak-Lojasiewicz inequality, and use that result to justify convergence of gradient descent for the proposed algorithm. Numerical examples are provided that demonstrate the precision of the rigorous results.
ER  -