Using a library of chemical reactions to fit systems of ordinary differential equations to agent-based models: a machine learning approach

TL;DR

This paper presents a novel machine learning method that uses a library of chemical reactions to accurately derive ordinary differential equations from agent-based model simulations, improving stability and respecting system coupling.

Contribution

It introduces a new approach that constructs ODE systems from agent-based models using chemical reaction libraries, unlike existing methods that treat components as decoupled.

Findings

Successfully applied to a tumor growth model on a 2D lattice.

Provides a robust and stable way to estimate non-negative rate constants.

Respects coupling between system components in the ODE construction.

Abstract

In this paper we introduce a new method based on a library of chemical reactions for constructing a system of ordinary differential equations from stochastic simulations arising from an agent-based model. The advantage of this approach is that this library respects any coupling between systems components, whereas the SINDy algorithm (introduced by Brunton, Proctor and Kutz) treats the individual components as decoupled from one another. Another advantage of our approach is that we can use a non-negative least squares algorithm to find the non-negative rate constants in a very robust, stable and simple manner. We illustrate our ideas on an agent-based model of tumour growth on a 2D lattice.