Algebraic identifiability of partial differential equation models

TL;DR

This paper develops algebraic theory and algorithms to determine the global identifiability of parameters in polynomial partial differential equation models, addressing a gap in the analysis of complex scientific PDE systems.

Contribution

It introduces a novel algebraic framework and algorithms for testing identifiability in PDE models, extending existing methods from ODEs to PDEs.

Findings

Algorithms successfully tested on scientific PDE models

Provides a theoretical foundation for algebraic identifiability in PDEs

Enables systematic analysis of parameter identifiability in complex models

Abstract

Differential equation models are crucial to scientific processes. The values of model parameters are important for analyzing the behaviour of solutions. A parameter is called globally identifiable if its value can be uniquely determined from the input and output functions. To determine if a parameter estimation problem is well-posed for a given model, one must check if the model parameters are globally identifiable. This problem has been intensively studied for ordinary differential equation models, with theory and several efficient algorithms and software packages developed. A comprehensive theory of algebraic identifiability for PDEs has hitherto not been developed due to the complexity of initial and boundary conditions. Here, we provide theory and algorithms, based on differential algebra, for testing identifiability of polynomial PDE models. We showcase this approach on PDE models arising in the sciences.