299 citations · 1k across the 57 of their papers we have counts for
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Extended pseudo-spectral physics-informed neural networks for phase-field models
Callum Marsh, Radek Erban, Andreas Munch
Phase-field models play a central role in the continuum description of phase separation, in which the bulk free-energy density and the interfacial thickness parameter determine pat…
On the role of fractional Brownian motion in models of chemotaxis and stochastic gradient ascent
Gustavo Cornejo-Olea, Lucas Buvinic, Jerome Darbon +3
Cell migration often exhibits long-range temporal correlations and anomalous diffusion, even in the absence of external guidance cues such as chemical gradients or topographical co…
Neural networks for learning macroscopic chemotactic sensitivity from microscopic models
Radek Erban
The macroscopic (population-level) dynamics of chemotactic cell movement -- arising from underlying microscopic (individual-based) models -- are often described by parabolic partia…
Multi-grid reaction-diffusion master equation: applications to morphogen gradient modelling
Radek Erban, Stefanie Winkelmann
The multi-grid reaction-diffusion master equation (mgRDME) provides a generalization of stochastic compartment-based reaction-diffusion modelling described by the standard reaction…
Noise-induced multistability in chemical systems: Discrete vs Continuum modeling
Andrew Duncan, Shuohao Liao, Tomas Vejchodsky +2
The noisy dynamics of chemical systems is commonly studied using either the chemical master equation (CME) or the chemical Fokker-Planck equation (CFPE). The latter is a continuum…
Analysis of the two-regime method on square meshes
Mark B. Flegg, S. Jonathan Chapman, Likun Zheng +1
The two-regime method (TRM) has been recently developed for optimizing stochastic reaction-diffusion simulations. It is a multiscale (hybrid) algorithm which uses stochastic reacti…
Variable-free exploration of stochastic models: a gene regulatory network example
Radek Erban, Thomas A. Frewen, Xiao Wang +4
Finding coarse-grained, low-dimensional descriptions is an important task in the analysis of complex, stochastic models of gene regulatory networks. This task involves (a) identify…
Spatially Distributed Stochastic Systems: equation-free and equation-assisted preconditioned computation
Liang Qiao, Radek Erban, C. T. Kelley +1
Spatially distributed problems are often approximately modelled in terms of partial differential equations (PDEs) for appropriate coarse-grained quantities (e.g. concentrations). T…