Data-driven identification of reaction-diffusion dynamics from finitely many non-local noisy measurements by exponential fitting
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866915711646957568 |
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| author | Katz, Rami Giordano, Giulia Batenkov, Dmitry |
| author_facet | Katz, Rami Giordano, Giulia Batenkov, Dmitry |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_09503 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Data-driven identification of reaction-diffusion dynamics from finitely many non-local noisy measurements by exponential fitting Katz, Rami Giordano, Giulia Batenkov, Dmitry Optimization and Control 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. |
| title | Data-driven identification of reaction-diffusion dynamics from finitely many non-local noisy measurements by exponential fitting |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2404.09503 |