Related papers: Efficient simulation techniques for biochemical re…
A multilevel Monte Carlo (MLMC) method for quantifying model-form uncertainties associated with the Reynolds-Averaged Navier-Stokes (RANS) simulations is presented. Two, high-dimensional, stochastic extensions of the RANS equations are…
A reaction network is a chemical system involving multiple reactions and chemical species. Stochastic models of such networks treat the system as a continuous time Markov chain on the number of molecules of each species with reactions as…
We develop new multilevel Monte Carlo (MLMC) methods to estimate the expectation of the smallest eigenvalue of a stochastic convection-diffusion operator with random coefficients. The MLMC method is based on a sequence of finite element…
Switching state-space models (SSSM) are a very popular class of time series models that have found many applications in statistics, econometrics and advanced signal processing. Bayesian inference for these models typically relies on Markov…
Microscopic processes on surfaces such as adsorption, desorption, diffusion and reaction of interacting particles can be simulated using kinetic Monte Carlo (kMC) algorithms. Even though kMC methods are accurate, they are computationally…
The Multilevel Monte Carlo method is an efficient variance reduction technique. It uses a sequence of coarse approximations to reduce the computational cost in uncertainty quantification applications. The method is nowadays often considered…
Methods for generating sequences of surrogates approximating fine scale models of two-phase random heterogeneous media are presented that are designed to adaptively control the modeling error in key quantities of interest (QoIs). For…
Generative diffusion models have recently emerged as a powerful strategy to perform stochastic sampling in Bayesian inverse problems, delivering remarkably accurate solutions for a wide range of challenging applications. However, diffusion…
Computer simulations have become an important tool across the biomedical sciences and beyond. For many important problems several different models or hypotheses exist and choosing which one best describes reality or observed data is not…
Molecular simulations can provide microscopic insight into the physical and chemical driving forces of complex molecular processes. Despite continued advancement of simulation methodology, model errors may lead to inconsistencies between…
Importance sampling is a variance reduction technique for efficient estimation of rare-event probabilities by Monte Carlo. In standard importance sampling schemes, the system is simulated using an a priori fixed change of measure suggested…
The role of AI-generated synthetic data has recently been expanded to support realistic Monte Carlo simulations. However, guidance is limited on generating data with multilevel structures and designing simulations based on such data. This…
In this paper we address the problem of the prohibitively large computational cost of existing Markov chain Monte Carlo methods for large--scale applications with high dimensional parameter spaces, e.g. in uncertainty quantification in…
The system-level dynamics of multivalent biomolecular interactions can be simulated using a rule-based kinetic Monte Carlo method in which a rejection sampling strategy is used to generate reaction events. This method becomes inefficient…
The possibility to simulate the properties of many-body open quantum systems with a large number of degrees of freedom is the premise to the solution of several outstanding problems in quantum science and quantum information. The challenge…
Computational determination of the equilibrium state of heterogeneous phospholipid mem-branes is a significant challenge. We wish to explore the rich phase diagram of these multi-component systems. However, the diffusion and mixing times in…
Markov chain Monte Carlo methods are a powerful tool for sampling equilibrium configurations in complex systems. One problem these methods often face is slow convergence over large energy barriers. In this work, we propose a novel method…
Markov chain Monte Carlo methods are primarily used for sampling from a given probability distribution and estimating multi-dimensional integrals based on the information contained in the generated samples. Whenever it is possible, more…
The stochastic description of chemical reaction networks with the kinetic chemical master equation (CME) is important for studying biological cells, but it suffers from the curse of dimensionality: The amount of data to be stored grows…
Mixture models provide a flexible representation of heterogeneity in a finite number of latent classes. From the Bayesian point of view, Markov Chain Monte Carlo methods provide a way to draw inferences from these models. In particular,…