Efficient and scalable prediction of stochastic reaction–diffusion processes using graph neural networks

Zhixing Cao*, Rui Chen, Libin Xu, Xinyi Zhou, Xiaoming Fu, Weimin Zhong, Ramon Grima*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

The dynamics of locally interacting particles that are distributed in space give rise to a multitude of complex behaviours. However the simulation of reaction–diffusion processes which model such systems is highly computationally expensive, the cost increasing rapidly with the size of space. Here, we devise a graph neural network based approach that uses cheap Monte Carlo simulations of reaction–diffusion processes in a small space to cast predictions of the dynamics of the same processes in a much larger and complex space, including spaces modelled by networks with heterogeneous topology. By applying the method to two biological examples, we show that it leads to accurate results in a small fraction of the computation time of standard stochastic simulation methods. The scalability and accuracy of the method suggest it is a promising approach for studying reaction–diffusion processes in complex spatial domains such as those modelling biochemical reactions, population evolution and epidemic spreading.
Original languageEnglish
Article number109248
Number of pages10
JournalMathematical biosciences
Volume375
Early online date8 Jul 2024
DOIs
Publication statusPublished - Sept 2024

Keywords / Materials (for Non-textual outputs)

  • Reaction–diffusion
  • Master equation
  • Neural networks

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