Exact hierarchical reductions of dynamical models via linear transformations

• Published in: Communications in nonlinear science & numerical simulation Vol. 131; p. 107816
• Main Authors: Demin, Alexander, Demitraki, Elizaveta, Pogudin, Gleb
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.04.2024; Elsevier
• Subjects: Computer Science; Dimensionality reduction; Exact reduction; Lumping; Mathematics; Matrix algebras; Ordinary differential equations; Dimensionality reduction; Exact reduction; Lumping; Matrix algebras; 34C20; 34-04; Ordinary differential equations; 16G10; ordinary differential equations; dimensionality reduction; lumping; exact reduction; matrix algebras; ordinary differential equations exact reduction lumping dimensionality reduction matrix algebras MSC codes. 34C20 34-04 16G10
• ISSN: 1007-5704; 1878-7274
• DOI: 10.1016/j.cnsns.2024.107816

Dynamical models described by ordinary differential equations (ODEs) are a fundamental tool in the sciences and engineering. Exact reduction aims at producing a lower-dimensional model in which each macro-variable can be directly related to the original variables, and it is thus a natural step towards the model’s formal analysis and mechanistic understanding. We present an algorithm which, given a polynomial ODE model, computes a longest possible chain of exact linear reductions of the model such that each reduction refines the previous one, thus giving a user control of the level of detail preserved by the reduction. This significantly generalizes over the existing approaches which compute only the reduction of the lowest dimension subject to an approach-specific constraint. The algorithm reduces finding exact linear reductions to a question about representations of finite-dimensional algebras. We provide an implementation of the algorithm, demonstrate its performance on a set of benchmarks, and illustrate the applicability via case studies. Our implementation is freely available at https://github.com/x3042/ExactODEReduction.jl. •Algorithm for finding a hierarchy of exact linear reductions for ODE models is given.•The hierarchy provides control over the amount of detail preserved in reduction.•We bridge dynamical systems and algebra, linking reductions to representation theory.•Approach is showcased on case-studies and models from the Biomodels repository.•Open-source Julia implementation of our algorithm is available.