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

Joshua Newey; Jared P. Whitehead

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arXiv · 2610.02686

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 $L^2$ 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.

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BibTeX RIS

Joshua Newey, Jared P. Whitehead. 2026-10-02. Asymptotic approximation of sensitivities in finite dimensional continuous data assimilation with application to parameter estimation. https://arxiv.org/abs/2610.02686

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