Related papers: A micro-macro acceleration method for the Monte Ca…
Kinetic equations model the position-velocity distribution of particles subject to transport and collision effects. Under a diffusive scaling, these combined effects converge to a diffusion equation for the position density in the limit of…
This paper shows a simple implementation of the Histogram Method for extrapolations in Monte Carlo simulations, using the moments of the operators that define the energy, instead of their histogram. This implementation is suitable for…
In most sampling algorithms, including Hamiltonian Monte Carlo, transition rates between states correspond to the probability of making a transition in a single time step, and are constrained to be less than or equal to 1. We derive a…
Many problems require to approximate an expected value by some kind of Monte Carlo (MC) sampling, e.g. molecular dynamics (MD) or simulation of stochastic reaction models (also termed kinetic Monte Carlo (kMC)). Often, we are furthermore…
Sampling from multimodal distributions is a challenging task in scientific computing. When a distribution has an exact symmetry between the modes, direct jumps among them can accelerate the samplings significantly. However, the…
In this paper, we present a novel iterative Monte Carlo method for approximating the stationary probability of a single state of a positive recurrent Markov chain. We utilize the characterization that the stationary probability of a state…
We introduce a theoretical approach to study the quantum-dissipative dynamics of electronic excitations in macromolecules, which enables to perform calculations in large systems and cover long time intervals. All the parameters of the…
The safety concern for unmanned systems, namely the concern for the potential casualty caused by system abnormalities, has been a bottleneck for their development, especially in populated areas. Evidently, the collision between the unmanned…
We present a computer-assisted approach to approximating coarse optimal switching policies for systems described by microscopic/stochastic evolution rules. The coarse timestepper constitutes a bridge between the underlying kinetic Monte…
Recently a new class of Monte Carlo methods, called Time Relaxed Monte Carlo (TRMC), designed for the simulation of the Boltzmann equation close to fluid regimes have been introduced. A generalized Wild sum expansion of the solution is at…
In statistical data assimilation (SDA) and supervised machine learning (ML), we wish to transfer information from observations to a model of the processes underlying those observations. For SDA, the model consists of a set of differential…
We propose a generic Markov Chain Monte Carlo (MCMC) algorithm to speed up computations for datasets with many observations. A key feature of our approach is the use of the highly efficient difference estimator from the survey sampling…
We propose algorithms for solving high-dimensional Partial Differential Equations (PDEs) that combine a probabilistic interpretation of PDEs, through Feynman-Kac representation, with sparse interpolation. Monte-Carlo methods and…
We propose a hierarchy of multi-level kinetic Monte Carlo methods for sampling high-dimensional, stochastic lattice particle dynamics with complex interactions. The method is based on the efficient coupling of different spatial resolution…
Recent work has suggested using Monte Carlo methods based on piecewise deterministic Markov processes (PDMPs) to sample from target distributions of interest. PDMPs are non-reversible continuous-time processes endowed with momentum, and…
Monte Carlo methods play important part in modern statistical physics. The application of these methods suffer from two main difficulties.The first is caused by the relatively small number of particles that can participate in any numerical…
The kinetic Monte Carlo (kMC) method is used in many scientific fields in applications involving rare-event transitions. Due to its discrete stochastic nature, efforts to parallelize kMC approaches often produce unbalanced time evolutions…
Process monitoring and control requires detection of structural changes in a data stream in real time. This article introduces an efficient sequential Monte Carlo algorithm designed for learning unknown changepoints in continuous time. The…
A number of coupling strategies are presented for stochastically modeled biochemical processes with time-dependent parameters. In particular, the stacked coupling is introduced and is shown via a number of examples to provide an…
This work introduces two Monte Carlo (MC)-based sampling methods, known as line sampling and subset simulation, to improve the performance of standard MC analyses in the context of asteroid impact risk assessment. Both techniques sample the…