Nonlinear Continuous Data Assimilation

TL;DR

This paper introduces three nonlinear continuous data assimilation algorithms, demonstrating they converge faster and more accurately than existing linear methods in a 1D PDE context.

Contribution

The paper presents novel nonlinear data assimilation algorithms and compares their performance to the established linear AOT method, showing superior convergence speed.

Findings

Nonlinear models exhibit super-exponential convergence.

Nonlinear models reach machine precision faster.

Outperform linear AOT algorithm in tests.

Abstract

We introduce three new nonlinear continuous data assimilation algorithms. These models are compared with the linear continuous data assimilation algorithm introduced by Azouani, Olson, and Titi (AOT). As a proof-of-concept for these models, we computationally investigate these algorithms in the context of the 1D Kuramoto-Sivashinsky equation. We observe that the nonlinear models experience super-exponential convergence in time, and converge to machine precision significantly faster than the linear AOT algorithm in our tests.