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A deterministic-stochastic coupling scheme is developed for simulating rarefied gas flows, where the key process is the alternative solving of the macroscopic synthetic equations [Su et al., J. Comput. Phys., 407 (2020) 109245] and the…
Models defined by stochastic differential equations (SDEs) allow for the representation of random variability in dynamical systems. The relevance of this class of models is growing in many applied research areas and is already a standard…
Stochastic simulation can make the molecular processes of cellular control more vivid than the traditional differential-equation approach by generating typical system histories instead of just statistical measures such as the mean and…
The use of stochastic models, in effect piecewise deterministic Markov processes (PDMP), has become increasingly popular especially for the modeling of chemical reactions and cell biophysics. Yet, exact simulation methods, for the…
The optimal selection of experimental conditions is essential to maximizing the value of data for inference and prediction, particularly in situations where experiments are time-consuming and expensive to conduct. We propose a general…
Stochasticity is a key characteristic of intracellular processes such as gene regulation and chemical signalling. Therefore, characterising stochastic effects in biochemical systems is essential to understand the complex dynamics of living…
This article presents a new numerical scheme for the discretization of dissipative particle dynamics with conserved energy. The key idea is to reduce elementary pairwise stochastic dynamics (either fluctuation/dissipation or thermal…
Discrete simulation methods are efficient tools to investigate the complex behaviors of complex fluids made of either dry granular materials or dilute suspensions. By contrast, materials made of soft and/or concentrated units (emulsions,…
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…
Stochastic reaction networks, which are usually modeled as continuous-time Markov chains on $\mathbb Z^d_{\ge 0}$, and simulated via a version of the "Gillespie algorithm," have proven to be a useful tool for the understanding of processes,…
Biochemical reactions involving three or more reactants, called higher-molecular reactions, play an important role in theoretical systems and synthetic biology. In particular, such reactions underpin a variety of important bio-dynamical…
In this paper, we investigate a class of multiscale McKean-Vlasov stochastic systems, where the entire system depends on the distributions of both fast and slow components. First of all, by applying the Poisson equation method, we prove…
Continuous-time Markov chains are used to model stochastic systems where transitions can occur at irregular times, e.g., birth-death processes, chemical reaction networks, population dynamics, and gene regulatory networks. We develop a…
We discuss two methods of an exact stochastic representation of the non-Markovian quantum dynamics of open systems. The first method employs a pair of stochastic product vectors in the total system's state space, while the second method…
Spatio-temporal point process models play a central role in the analysis of spatially distributed systems in several disciplines. Yet, scalable inference remains computa- tionally challenging both due to the high resolution modelling…
We consider a general class of high order weak approximation schemes for stochastic differential equations driven by L\'evy processes with infinite activity. These schemes combine a compound Poisson approximation for the jump part of the…
The aim of our study is to describe the dynamics of ant battles, with reference to laboratory experiments, by means of a chemical stochastic model. We focus on ants behavior as an interesting topic in order to predict the ecological…
A method for sequential inference of the fixed parameters of a dynamic latent Gaussian models is proposed and evaluated that is based on the iterated Laplace approximation. The method provides a useful trade-off between computational…
This paper deals with the construction of a metamodel (i.e. a simplified mathematical model) for a stochastic computer code (also called stochastic numerical model or stochastic simulator), where stochastic means that the code maps the…
We consider the problem of calibrating an imperfect computer model using experimental data. To compensate the misspecification of the computer model and make more accurate predictions, a discrepancy function is often included and modeled…