Related papers: Mean Field Limits of Particle-Based Stochastic Rea…
The reaction-diffusion master equation (RDME) is commonly used to model processes where both the spatial and stochastic nature of chemical reactions need to be considered. We show that the RDME in many cases is inconsistent with a…
We consider a generic class of stochastic particle-based models whose state at an instant in time is described by a set of continuous degrees of freedom (e.g. positions), and the length of this set changes stochastically in time due to…
This paper introduces a system of stochastic differential equations (SDE) of mean-field type that models pedestrian motion. The system lets the pedestrians spend time at, and move along, walls, by means of sticky boundaries and boundary…
Biochemical reactions typically occur at low copy numbers, but at once in crowded and diverse environments. Space and stochasticity therefore play an essential role in biochemical networks. Spatial-stochastic simulations have become a…
Mathematical models describing the spatial spreading and invasion of populations of biological cells are often developed in a continuum modelling framework using reaction-diffusion equations. While continuum models based on linear diffusion…
Stochastic epidemic models on networks are inherently high-dimensional and the resulting exact models are intractable numerically even for modest network sizes. Mean-field models provide an alternative but can only capture average…
Dissipative particle dynamics (DPD) is now a well-established method for simulating soft matter systems. However, its applicability was recently questioned because some investigations showed an upper coarse-graining limit that would prevent…
In this paper, we introduce and study one-dimensional models for the behavior of pedestrians in a narrow street or corridor. We begin at the microscopic level by formulating a stochastic cellular automata model with explicit rules for…
Stochastic simulation methods can be applied successfully to model exact spatio-temporally resolved reaction-diffusion systems. However, in many cases, these methods can quickly become extremely computationally intensive with increasing…
The dynamics of short-lived mRNA results in bursts of protein production in gene regulatory networks. We investigate the propagation of bursting noise between different levels of mathematical modelling, and demonstrate that conventional…
We consider the numerical solution of coupled volume-surface reaction-diffusion systems having a detailed balance equilibrium. Based on the conservation of mass, an appropriate quadratic entropy functional is identified and an…
Mass-conserving reaction-diffusion (MCRD) systems are widely used to model phase separation and pattern formation in cell polarity, biomolecular condensates, and ecological systems. Numerical simulations and formal asymptotic analysis…
We derive a stochastic partial differential equation that describes the fluctuating behaviour of reaction-diffusion systems of N particles, undergoing Markovian, unary reactions. This generalises the work of Dean [J. Phys. A: Math. and…
We recover the so-called field-road diffusion model as the hydrodynamic limit of an interacting particle system. The former consists of two parabolic PDEs posed on two sets of different dimensions (a "field" and a "road" in a population…
We study the large deviation behavior of a system of diffusing particles with a mean field interaction, described through a collection of stochastic differential equations, in which each particle is driven by a vanishing independent…
Integration against a probability distribution given its unnormalized density is a central task in Bayesian inference and other fields. We introduce new methods for approximating such expectations with a small set of weighted samples --…
This paper investigates the well-posedness and small-noise asymptotics of a class of stochastic partial differential equations defined on a bounded domain of $\mathbb{R}^d$, where the diffusion coefficient depends nonlinearly and…
Diffusion models have become a central tool in deep generative modeling, but standard formulations rely on a single network and a single diffusion schedule to transform a simple prior, typically a standard normal distribution, into the…
It is known that when the diffuse interface thickness $\epsilon$ vanishes, the sharp interface limit of the stochastic reaction-diffusion equation is formally a stochastic geometric flow. To capture and simulate such geometric flow, it is…
The mean field limits of systems of interacting diffusions (also called stochastic interacting particle systems (SIPS)) have been intensively studied since McKean \cite{mckean1966class}. The interacting diffusions pave a way to…