Concurrent multi-parameter learning demonstrated on the Kuramoto-Sivashinsky equation

TL;DR

This paper introduces a nudging data assimilation algorithm for real-time concurrent estimation of multiple scalar parameters in dissipative PDE systems, demonstrated on the Kuramoto-Sivashinsky equation.

Contribution

The paper presents a novel, intuitive algorithm capable of simultaneously recovering multiple parameters in PDE systems during ongoing simulations.

Findings

Effective parameter recovery demonstrated on the Kuramoto-Sivashinsky equation

Algorithm handles multiple parameters simultaneously

Applicable to various dissipative PDE systems

Abstract

We develop an algorithm based on the nudging data assimilation scheme for the concurrent (on-the-fly) estimation of scalar parameters for a system of evolutionary dissipative partial differential equations in which the state is partially observed. The algorithm takes advantage of the error that results from nudging a system with incorrect parameters with data from the true system. The intuitive nature of the algorithm makes its extension to several different systems immediate, and it allows for recovery of multiple parameters simultaneously. We test the method on the Kuramoto-Sivashinsky equation in one dimension and demonstrate its efficacy in this context.