Differential elimination for dynamical models via projections with applications to structural identifiability

TL;DR

This paper introduces a new algorithm for differential elimination in dynamical systems that improves efficiency and enables structural identifiability analysis of complex models, with practical implementation in a Julia package.

Contribution

The paper presents a novel differential elimination algorithm that outperforms existing methods and a randomized approach for structural identifiability analysis of complex models.

Findings

Algorithm outperforms general-purpose software on benchmark models.

Enables identifiability analysis of previously intractable models.

Implementation available as a Julia package.

Abstract

Elimination of unknowns in a system of differential equations is often required when analysing (possibly nonlinear) dynamical systems models, where only a subset of variables are observable. One such analysis, identifiability, often relies on computing input-output relations via differential algebraic elimination. Determining identifiability, a natural prerequisite for meaningful parameter estimation, is often prohibitively expensive for medium to large systems due to the computationally expensive task of elimination. We propose an algorithm that computes a description of the set of differential-algebraic relations between the input and output variables of a dynamical system model. The resulting algorithm outperforms general-purpose software for differential elimination on a set of benchmark models from literature. We use the designed elimination algorithm to build a new randomized algorithm for assessing structural identifiability of a parameter in a parametric model. A parameter is said to be identifiable if its value can be uniquely determined from input-output data assuming the absence of noise and sufficiently exciting inputs. Our new algorithm allows the identification of models that could not be tackled before. Our implementation is publicly available as a Julia package at https://github.com/SciML/StructuralIdentifiability.jl.