Title:
Model Discovery on the Fly Using Continuous Data Assimilation
Abstract:
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) [1]. This derivation relies on the same assumptions as the previous derivation but frames the problem as a finite dimensional root-finding or optimization problem. Within the approach we develop, the algorithm from [1] is simply a realization of Newton’s Root-finding method. We implement other derivative based optimization algorithms; we show that the Gauss Newton and Levenberg Marquardt algorithms have similar performance to the CHL algorithm in the single parameter estimation case and generalize 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.