Predictive algorithms in dynamical sampling for burst-like forcing terms

TL;DR

This paper develops predictive algorithms within dynamical sampling to accurately recover burst-like forcing terms in initial value problems, even with measurement errors and background noise.

Contribution

It introduces two novel classes of samplers enabling stable and accurate prediction of burst-like forcing terms in dynamical systems.

Findings

Algorithms effectively recover burst-like forcing terms.

Methods are robust to measurement errors.

Approach accurately predicts solutions over time intervals.

Abstract

In this paper, we consider the problem of recovery of a burst-like forcing term in an initial value problem (IVP) in the framework of dynamical sampling. We introduce an idea of using two particular classes of samplers that allow one to predict the solution of the IVP over a time interval without a burst. This leads to two different algorithms that stably and accurately approximate the burst-like forcing term even in the presence of a measurement acquisition error and a large background source.