Designing Machine Learning Tools to Characterize Multistationarity of Fully Open Reaction Networks

Aug 4, 2026

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The work introduces machine learning methods for predicting multistationarity in reaction networks. Chemical Reaction Networks model how species quantities evolve over time through mutual interactions, and multistationarity describes networks that admit multiple steady states instead of converging to a single one. Existing multistationarity detection approaches are computationally demanding or limited by the network classes they support, motivating a data-driven alternative. The study develops a graph representation for variable-length CRN inputs, builds a labeled dataset of fully open CRNs, trains and evaluates a graph attention network, and confirms generalizability via independently produced validation data.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages39

Reading Time1 h 38 min

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Introduction

From the life sciences to CRNs

Detecting multistationary

arXiv :2407 .01760v1 [ q-bio .MN] 1 Jul 2024 Designing Machine Learning Tools to Characterize Multistationarity of Fully Open Reaction Networks Shenghao Yao∗†, AmirHosein Sadeghimanesh∗‡§ and Matthew England∗¶ July 3, 2024 Abstract We present the first use of machine learning tools to predict multistationarity of reaction networks. Chemical Reaction Networks (CRNs) are the mathematical formulation of how the quantities associated to a set of species (molecules, proteins, cells, or animals) vary as time passes with respect to their interactions with each other. Their mathematics does not describe just chemical reactions but many other areas of the life sciences such as ecology, epidemiology, and population dynamics. We say a CRN is at a steady state when the concentration (or number) of species do not vary anymore. Some CRNs do not attain a steady state while some others may have more than one possible steady state. The CRNs in the later group are called multistationary. Multistationarity isan important property, e.g. switch-like behaviour in cells needs multistationarity to occur. Existing algorithms to detect whether a CRN is multistationary or not are either extremely expensive or restricted in the type of CRNs they can be used on, motivating a new machine learning approach. We address the problem of representing variable-length CRN data to machine learning models by developing a new graph representation of CRNs for use with graph learning algorithms. We contribute a large dataset of labelled fully open CRNs whose production necessitated the development of new CRN theory. Then we present experimental results on the training and testing of a graph attention network model on this dataset, showing excellent levels of performance. We finish by testing the model predictions on validation data produced independently, demonstrating generalisability of the model to different types of CRN. Keywords: Chemical Reaction Network, Multistationarity, Machine Learning, Graph Attention Network 1 Introduction 1.1 From the life sciences to CRNs Many phenomena in the life sciences involve a group of species, such as chemical molecules, proteins or cells, depending on the context; and some interactions among them. Each interaction causes some of these species to be destroyed / consumed and some others tobe created / produced. Thus the quantities of these species, which can be a concentration ∗ Research Centre for Computational Sciences and Mathematical Modelling, Coventry University, Coventry, United Kingdom. †[yaos10@uni.coventry.ac.uk](yaos10@uni.coventry.ac.uk) ‡[amirhossein.sadeghimanesh@coventry.ac.uk](amirhossein.sadeghimanesh@coventry.ac.uk). § Corresponding author. ¶ [matthew.england@coventry.ac.uk](matthew.england@coventry.ac.uk), [https://www](https://www.matthewengland.coventry.domains/)[.](https://www.matthewengland.coventry.domains/)[matthewengland](https://www.matthewengland.coventry.domains/)[.](https://www.matthewengland.coventry.domains/)[coventry](https://www.matthewengland.coventry.domains/)[.](https://www.matthewengland.coventry.domains/)[domains/](https://www.matthewengland.coventry.domains/) . (a real number) or a count (an integer), are changing over time. This means that the quantity of each species is a variable (function) of time. Then the changes over time because of the interactions give us derivatives. Writing the equations describing how these variables change, gives us equations for these derivatives, called ordinary differential equations (ODEs), and the set of these equations defines an ODE system. To predict behaviour of the original experiments in chemistry or biology, one can study their corresponding ODE system mathematically. For example, consider identifying an equilibrium of the experiment. Equilibria, also known as the steady states of the ODE system, are reached after waiting for sufficient time for the concentrations of the species to not vary any more. The values of co

FAQs

What problem does the document address?

It addresses how to predict whether a chemical reaction network is multistationary using machine learning instead of existing expensive or limited algorithms.

What is multistationarity in chemical reaction networks?

A network is multistationary if it has more than one possible steady state, meaning species concentrations can settle to multiple distinct long-term equilibria.

How does the proposed method handle variable-length CRN data?

It introduces a new graph representation of chemical reaction networks so that graph learning algorithms can process variable-length inputs effectively.

Aug 4, 2026

Upload by Liam