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An adpative integration technique for time advancement of particle motion in the context of coupled computational fluid dynamics (CFD) - discrete element method (DEM) simulations is presented in this work. CFD-DEM models provide an accurate…
This work reviews deterministic and diffusion approximations of the stochastic chemical reaction networks and explains their applications. We discuss the added value the diffusion approximation provides for systems with different phenomena,…
Simulation is an efficient tool in the design and control of power electronic systems. However, quick and accurate simulation of them is still challenging, especially when the system contains a large number of switches and state variables.…
With the aim of establishing a framework to efficiently perform the practical application of quantum chemistry simulation on near-term quantum devices, we envision a hybrid quantum--classical framework for leveraging problem decomposition…
Piecewise Diffusion Markov Processes (PDifMPs) are valuable for modelling systems where continuous dynamics are interrupted by sudden shifts and/or changes in drift and diffusion. The first-passage time (FPT) in such models plays a central…
Fluid models are a popular formalism in the quantitative modeling of biochemical systems and analytical performance models. The main idea is to approximate a large-scale Markov chain by a compact set of ordinary differential equations…
We develop a new continuous-time stochastic gradient descent method for optimizing over the stationary distribution of stochastic differential equation (SDE) models. The algorithm continuously updates the SDE model's parameters using an…
We present a numerical approximation technique for the analysis of continuous-time Markov chains that describe networks of biochemical reactions and play an important role in the stochastic modeling of biological systems. Our approach is…
Particle flow (PFL) is an effective method for overcoming particle degeneracy, the main limitation of particle filtering. In PFL, particles are migrated towards regions of high likelihood based on the solution of a partial differential…
Ordinary and partial differential equations (ODEs/PDEs) play a paramount role in analyzing and simulating complex dynamic processes across all corners of science and engineering. In recent years machine learning tools are aspiring to…
Stochastic models are often used to help understand the behavior of intracellular biochemical processes. The most common such models are continuous time Markov chains (CTMCs). Parametric sensitivities, which are derivatives of expectations…
Simulating rare events, such as the transformation of a reactant into a product in a chemical reaction typically requires enhanced sampling techniques that rely on heuristically chosen collective variables (CVs). We propose using…
Diffusion models provide expressive priors for forecasting trajectories of dynamical systems, but are typically unreliable in the sparse data regime. Physics-informed machine learning (PIML) improves reliability in such settings; however,…
Chemistry has a key role in the evolution of the interstellar medium (ISM), so it is highly desirable to follow its evolution in numerical simulations. However, it may easily dominate the computational cost when applied to large systems. In…
Monte Carlo simulations of systems of particles such as hard spheres or soft spheres with singular kernels can display around a phase transition prohibitively long convergence times when using traditional Hasting-Metropolis reversible…
Recently there have been exciting developments in Monte Carlo methods, with the development of new MCMC and sequential Monte Carlo (SMC) algorithms which are based on continuous-time, rather than discrete-time, Markov processes. This has…
We present an algorithm for finding the probabilities of rare events in nonequilibrium processes. The algorithm consists of evolving the system with a modified dynamics for which the required event occurs more frequently. By keeping track…
Estimating rate coefficients from complex chemical reactions is essential for advancing detailed chemistry. However, the stiffness inherent in real-world atmospheric chemistry systems poses severe challenges, leading to training instability…
This article provides an introductory tutorial on structural results in partially observed Markov decision processes (POMDPs). Typically, computing the optimal policy of a POMDP is computationally intractable. We use lattice program- ming…
Mathematically modelling diffusive and advective transport of particles in heterogeneous layered media is important to many applications in computational, biological and medical physics. While deterministic continuum models of such…