Forward sensitivity analysis of the FitzHugh-Nagumo system: Parameter estimation

TL;DR

This paper introduces a forward sensitivity method for estimating parameters in the FitzHugh-Nagumo model, enhancing understanding of excitable systems through improved data assimilation and parameter inference.

Contribution

The paper develops a variational data assimilation approach using FSM for parameter estimation in the FHN model, with guidelines for optimal observation placement.

Findings

FSM effectively estimates FHN parameters from sparse data

Guidelines improve parameter inference accuracy

Enhanced understanding of bifurcation behavior

Abstract

The FitzHugh-Nagumo (FHN) model, from computational neuroscience, has attracted attention in nonlinear dynamics studies as it describes the behavior of excitable systems and exhibits interesting bifurcation properties. The accurate estimation of the model parameters is vital to understand how the solution trajectory evolves in time. To this end, we provide a forward sensitivity method (FSM) approach to quantify the main model parameters using sparse measurement data. FSM constitutes a variational data assimilation technique which integrates model sensitivities into the process of fitting the model to the observations. We analyse the applicability of FSM to update the FHN model parameters and predict its dynamical characteristics. Furthermore, we highlight a few guidelines for observations placement to control the shape of the cost functional and improve the parameter inference iterations.