Speaker
Description
Biological reaction–diffusion systems are inherently multiscale, with particle copy numbers varying substantially across the spatial domain. In regions of low concentration, discrete stochastic methods capture noise-driven fluctuations that may critically influence dynamics. In regions of high concentration, continuum PDE models provide an efficient description. Simulating such systems entirely with stochastic methods becomes prohibitively costly for large systems, motivating hybrid approaches.
Existing hybrid frameworks partition the domain into stochastic and deterministic regions separated by a fixed spatial interface. This performs well when the interface is geometrically simple and known in advance, but fails when it is irregular, moving, or a priori unknown — as arises in Turing pattern formation.
We present the Spatial Regime Conversion Method (SRCM), a hybrid framework that removes the need for an explicit interface entirely. Mass converts dynamically between discrete and continuous representations according to local concentration, automatically confining stochastic computation to regions where it is required. The method adapts as concentration profiles evolve, faithfully capturing stochastic-driven noise where it is dynamically significant while remaining efficient to run.
We demonstrate the accuracy and efficiency of the SRCM on benchmark problems and apply it to pattern-forming systems in which stochastic-driven noise influences qualitative behaviour.
Bibliography
@article{cameron2025srcm,
author = {Cameron, Charles G. and Smith, Cameron A. and Yates, Christian A.},
title = {The Spatial Regime Conversion Method},
journal = {Mathematics},
year = {2025},
volume = {13},
number = {21},
pages = {3406},
doi = {10.3390/math13213406},
url = {https://doi.org/10.3390/math13213406}
}
