Parameter estimation in ODEs: assessing the potential of local and global solvers

TL;DR

This paper evaluates the effectiveness of local and global solvers in parameter estimation for ODE-based dynamic systems, highlighting current limitations and potential for handling more complex, realistic problems.

Contribution

It provides a comparative assessment of state-of-the-art solvers' capabilities to address nonconvex parameter estimation problems in realistic scenarios.

Findings

Global solvers struggle with problems larger than five variables.

Local solvers are faster but may get trapped in local minima.

Current methods have limited scalability for practical applications.

Abstract

We consider the problem of parameter estimation in dynamic systems described by ordinary differential equations. A review of the existing literature emphasizes the need for deterministic global optimization methods due to the nonconvex nature of these problems. Recent works have focused on expanding the capabilities of specialized deterministic global optimization algorithms to handle more complex problems. Despite advancements, current deterministic methods are limited to problems with a maximum of around five state and five decision variables, prompting ongoing efforts to enhance their applicability to practical problems. Our study seeks to assess the effectiveness of state-of-the-art general-purpose global and local solvers in handling realistic-sized problems efficiently, and evaluating their capabilities to cope with the nonconvex nature of the underlying estimation problems.