Online estimation of Hilbert-Schmidt operators and application to kernel reconstruction of neural fields

TL;DR

This paper introduces an adaptive observer for real-time estimation of Hilbert-Schmidt operators in nonlinear infinite-dimensional systems, with applications to neural field kernel reconstruction, validated through numerical simulations.

Contribution

It presents a novel online estimation method for Hilbert-Schmidt operators tailored for neural field applications, ensuring convergence under specific conditions.

Findings

Successful real-time estimation demonstrated in simulations

Applicable to neural activity modeling

Convergence guaranteed under detectability and excitation conditions

Abstract

An adaptive observer is designed for online estimation of Hilbert-Schmidt operators from online measurement of the state for some class of nonlinear infinite-dimensional dynamical systems. Convergence is ensured under detectability and persistency of excitation assumptions. The class of systems considered is motivated by an application to kernel reconstruction of neural fields, commonly used to model spatiotemporal activity of neuronal populations. Numerical simulations confirm the relevance of the approach.