Model discovery on the fly using continuous data assimilation

Fuente: arXiv
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Main Authors: Newey, Joshua, Whitehead, Jared P, Carlson, Elizabeth
Format: Preprint
Published: 2024
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author Newey, Joshua
Whitehead, Jared P
Carlson, Elizabeth
author_facet Newey, Joshua
Whitehead, Jared P
Carlson, Elizabeth
contents We review an algorithm developed for parameter estimation within the Continuous Data Assimilation (CDA) approach. We present an alternative derivation for the algorithm presented in a paper by Carlson, Hudson, and Larios (CHL, 2021). This derivation relies on the same assumptions as the previous derivation but frames the problem as a finite dimensional root-finding problem. Within the approach we develop, the algorithm developed in (CHL, 2021) is simply a realization of Newton's method. We then consider implementing other derivative based optimization algorithms; we show that the Levenberg Maqrquardt algorithm has similar performance to the CHL algorithm in the single parameter estimation case and generalizes much better to fitting multiple parameters. We then implement these methods in three example systems: the Lorenz '63 model, the two-layer Lorenz '96 model, and the Kuramoto-Sivashinsky equation.
format Preprint
id arxiv_https___arxiv_org_abs_2411_13561
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Model discovery on the fly using continuous data assimilation
Newey, Joshua
Whitehead, Jared P
Carlson, Elizabeth
Numerical Analysis
Dynamical Systems
Data Analysis, Statistics and Probability
We review an algorithm developed for parameter estimation within the Continuous Data Assimilation (CDA) approach. We present an alternative derivation for the algorithm presented in a paper by Carlson, Hudson, and Larios (CHL, 2021). This derivation relies on the same assumptions as the previous derivation but frames the problem as a finite dimensional root-finding problem. Within the approach we develop, the algorithm developed in (CHL, 2021) is simply a realization of Newton's method. We then consider implementing other derivative based optimization algorithms; we show that the Levenberg Maqrquardt algorithm has similar performance to the CHL algorithm in the single parameter estimation case and generalizes much better to fitting multiple parameters. We then implement these methods in three example systems: the Lorenz '63 model, the two-layer Lorenz '96 model, and the Kuramoto-Sivashinsky equation.
title Model discovery on the fly using continuous data assimilation
topic Numerical Analysis
Dynamical Systems
Data Analysis, Statistics and Probability
url https://arxiv.org/abs/2411.13561