Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

Pamela M. Burrage, Hasitha N. Weerasinghe, Kevin Burrage

TL;DR

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 of tumour growth on a 2D lattice is introduced.

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.

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

TL;DR

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 of tumour growth on a 2D lattice is introduced.

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.
Paper Structure (5 sections, 45 equations, 5 figures)

This paper contains 5 sections, 45 equations, 5 figures.

Table of Contents

  1. Introduction
  2. A library of chemical reactions
  3. The tumour agent-based model
  4. Implementation and numerical results
  5. Conclusions

Figures (5)

  • Figure 1: Cartoon showing the tumour microenvironment
  • Figure 2: Simulation set up for the agent-based model
  • Figure 3: Sample outputs from the agent-based model in terms of effects on cell stickiness (top) and jump radius (bottom) in terms of initial healthy cell and ECM protein densities
  • Figure 4: Data from tumour and healthy cell densities along with fitted ODE, using MATLAB routine lsqr
  • Figure 5: Data from tumour and healthy cell densities along with fitted ODE, using the library of chemical reactions and MATLAB routine lsqnonneg