Complexity of Model Testing for Dynamical Systems with Toric Steady States

TL;DR

This paper explores the computational complexity of testing and selecting models for dynamical systems with toric steady states, common in chemical reaction networks, by analyzing the Euclidean distance degree.

Contribution

It provides closed-form formulas for the ED degree of various chemical reaction network families, linking algebraic geometry to model testing complexity.

Findings

Closed-form ED degree formulas for multiple network families

ED degree as a predictor of computational cost

Application to chemical reaction network analysis

Abstract

In this paper we investigate the complexity of model selection and model testing for dynamical systems with toric steady states. Such systems frequently arise in the study of chemical reaction networks. We do this by formulating these tasks as a constrained optimization problem in Euclidean space. This optimization problem is known as a Euclidean distance problem; the complexity of solving this problem is measured by an invariant called the Euclidean distance (ED) degree. We determine closed-form expressions for the ED degree of the steady states of several families of chemical reaction networks with toric steady states and arbitrarily many reactions. To illustrate the utility of this work we show how the ED degree can be used as a tool for estimating the computational cost of solving the model testing and model selection problems.