Identifiability Analysis of Linear Ordinary Differential Equation Systems with a Single Trajectory

TL;DR

This paper develops a quantitative framework for analyzing the identifiability of linear ODE systems from a single trajectory, providing practical scores and insights into high-dimensional cases.

Contribution

It introduces a closed-form representation for non-identifiable systems and proposes new quantitative scores that outperform existing methods, especially under noisy data.

Findings

Proposed scores outperform existing methods in noisy scenarios

Many high-dimensional systems are practically unidentifiable without prior info

Closed-form representation aids in system design and prior selection

Abstract

Ordinary differential equations (ODEs) are widely used to model dynamical behavior of systems. It is important to perform identifiability analysis prior to estimating unknown parameters in ODEs (a.k.a. inverse problem), because if a system is unidentifiable, the estimation procedure may fail or produce erroneous and misleading results. Although several qualitative identifiability measures have been proposed, much less effort has been given to developing \emph{quantitative} (continuous) scores that are robust to uncertainties in the data, especially for those cases in which the data are presented as a single trajectory beginning with one initial value. In this paper, we first derived a closed-form representation of linear ODE systems that are not identifiable based on a single trajectory. This representation helps researchers design practical systems and choose the right prior structural information in practice. Next, we proposed several quantitative scores for identifiability analysis in practice. In simulation studies, the proposed measures outperformed the main competing method significantly, especially when noise was presented in the data. We also discussed the asymptotic properties of practical identifiability for high-dimensional ODE systems and conclude that, without additional prior information, many random ODE systems are practically unidentifiable when the dimension approaches infinity.