Data-driven identification of reaction-diffusion dynamics from finitely many non-local noisy measurements by exponential fitting
arxiv(2024)
摘要
Given a reaction-diffusion equation with unknown right-hand side, we consider
a nonlinear inverse problem of estimating the associated leading eigenvalues
and initial condition modes from a finite number of non-local noisy
measurements. We define a reconstruction criterion and, for a small enough
noise, we prove the existence and uniqueness of the desired approximation and
derive closed-form expressions for the first-order condition numbers, as well
as bounds for their asymptotic behavior in a regime when the number of measured
samples is fixed and the inter-sampling interval length tends to infinity. When
computing the sought estimates numerically, our simulations show that the
exponential fitting algorithm ESPRIT is first-order optimal, as its first-order
condition numbers have the same asymptotic behavior as the analytic condition
numbers in the considered regime.
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