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A version of the time-parallel algorithm parareal is analyzed and applied to stochastic models in chemical kinetics. A fast predictor at the macroscopic scale (evaluated in serial) is available in the form of the usual reaction rate…
Automatic machine learning of empirical models from experimental data has recently become possible as a result of increased availability of computational power and dedicated algorithms. Despite the successes of non-parametric inference and…
This article addresses reaction networks in which spatial and stochastic effects are of crucial importance. For such systems, particle-based models allow us to describe all microscopic details with high accuracy. However, they suffer from…
When simulating multiscale stochastic differential equations (SDEs) in high-dimensions, separation of timescales, stochastic noise and high-dimensionality can make simulations prohibitively expensive. The computational cost is dictated by…
A major challenge in flow through porous media is to better understand the link between microstructure and macroscale flow and transport. For idealised microstructures, the mathematical framework of homogenisation theory can be used for…
In this chapter we review stochastic modelling methods in climate science. First we provide a conceptual framework for stochastic modelling of deterministic dynamical systems based on the Mori-Zwanzig formalism. The Mori-Zwanzig equations…
Common techniques for the spatial discretisation of PDEs on a macroscale grid include finite difference, finite elements and finite volume methods. Such methods typically impose assumed microscale structures on the subgrid fields, so…
The Equation-Free approach to efficient multiscale numerical computation marries trusted micro-scale simulations to a framework for numerical macro-scale reduction -- the patch dynamics scheme. A recent novel patch scheme empowered the…
Master equations are typically adopted to describe the dynamics of open quantum systems. Such equations are either in integro-differential or in time-local form, with the latter class more frequently adopted due to the simpler numerical…
The emergence of organized multiscale patterns resulting from convection is ubiquitous, observed throughout different cloud types. The reproduction of such patterns by general circulation models remains a challenge due to the complex nature…
Recently, hybrid models have emerged that combine microscopic and mesoscopic regimes in a single stochastic reaction-diffusion simulation. Microscopic simulations track every individual molecule and are generally more accurate. Mesoscopic…
Mesoscopic density functional theory for inhomogeneous mixtures of sperical particles is developed in terms of mesoscopic volume fractions by a systematic coarse-graining procedure starting form microscopic theory. Approximate expressions…
Constructing discrete models of stochastic partial differential equations is very delicate. Stochastic centre manifold theory provides novel support for coarse grained, macroscale, spatial discretisations of nonlinear stochastic partial…
In our recent work [8], we have studied the homogenization of the Poisson equation in a class of non periodically perforated domains. In this paper, we examine the case of the Stokes system. We consider a porous medium in which the…
We consider stochastic thermodynamics as a theory of statistical inference for experimentally observed fluctuating time-series. To that end, we introduce a general framework for quantifying the knowledge about the dynamical state of the…
This paper presents a rigorous mathematical analysis, alongside simulation studies, of a spatially extended stochastic electrophysiology model, the Hodgkin-Huxley model of the squid giant axon being a classical example. Although most…
The simulation of complex stochastic network dynamics arising, for instance, from models of coupled biomolecular processes remains computationally challenging. Often, the necessity to scan a models' dynamics over a large parameter space…
Equations governing physico-chemical processes are usually known at microscopic spatial scales, yet one suspects that there exist equations, e.g. in the form of Partial Differential Equations (PDEs), that can explain the system evolution at…
We address the nonadiabatic quantum dynamics of macrosystems with several coupled electronic states, taking into account the possibility of multi-state conical intersections. The general situation of an arbitrary number of states and…
Stochastic variational inference makes it possible to approximate posterior distributions induced by large datasets quickly using stochastic optimization. The algorithm relies on the use of fully factorized variational distributions.…