An online parameter identification method for time dependent partial differential equations

TL;DR

This paper introduces a flexible online parameter identification method for time-dependent PDEs that accommodates partial observations and noisy data, with demonstrated effectiveness through numerical experiments.

Contribution

It presents a novel online identification approach that relaxes model assumptions and handles partial, noisy data for infinite-dimensional systems.

Findings

Method successfully identifies parameters with partial observations.

Approach is robust to noisy data.

Numerical experiments validate effectiveness.

Abstract

Online parameter identification is of importance, e.g., for model predictive control. Since the parameters have to be identified simultaneously to the process of the modeled system, dynamical update laws are used for state and parameter estimates. Most of the existing methods for infinite dimensional systems either impose strong assumptions on the model or cannot handle partial observations. Therefore we propose and analyze an online parameter identification method that is less restrictive concerning the underlying model and allows for partial observations and noisy data. The performance of our approach is illustrated by some numerical experiments.