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The entropy-based moment method is a well-known discretization for the velocity variable in kinetic equations which has many desirable theoretical properties but is difficult to implement with high-order numerical methods. The regularized…
A macroscopic mesoscopic, deterministic stochastic coupling strategy is proposed to accelerate the direct simulation Monte Carlo (DSMC) method for chemical reaction. First, a macroscopic synthetic equation is formulated by integrating…
The basic problem in equilibrium statistical mechanics is to compute phase space average, in which Monte Carlo method plays a very important role. We begin with a review of nonlocal algorithms for Markov chain Monte Carlo simulation in…
Quasi-Monte Carlo methods have proven to be effective extensions of traditional Monte Carlo methods in, amongst others, problems of quadrature and the sample path simulation of stochastic differential equations. By replacing the random…
We propose efficient numerical algorithms for approximating statistical solutions of scalar conservation laws. The proposed algorithms combine finite volume spatio-temporal approximations with Monte Carlo and multi-level Monte Carlo…
We consider Monte Carlo approximations to the maximum likelihood estimator in models with intractable norming constants. This paper deals with adaptive Monte Carlo algorithms, which adjust control parameters in the course of simulation. We…
This paper presents a tool for addressing a key component in many algorithms for planning robot trajectories under uncertainty: evaluation of the safety of a robot whose actions are governed by a closed-loop feedback policy near a nominal…
This paper addresses finite sample stability properties of sequential Monte Carlo methods for approximating sequences of probability distributions. The results presented herein are applicable in the scenario where the start and end…
We obtain an expansion of the implicit weak discretization error for the target of stochastic approximation algorithms introduced and studied in [Frikha2013]. This allows us to extend and develop the Richardson-Romberg extrapolation method…
Various kinetic Monte Carlo algorithms become inefficient when some of the population sizes in a system are large, which gives rise to a large number of reaction events per unit time. Here, we present a new acceleration algorithm based on…
We present a principled approach for estimating the matrix of microscopic rates among states of a Markov process, given only its stationary state population distribution and a single average global kinetic observable. We adapt Maximum…
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, a novel method to adaptively approximate the solution to stochastic differential equations, which is based on compressive sampling and sparse recovery, is introduced. The proposed method consider the problem of sparse…
The montecarlo method, which is quite commonly used to solve maximum entropy problems in statistical physics, can actually be used to solve inverse problems in a much wider context. The probability distribution which maximizes entropy can…
We review a recently devised Monte Carlo simulation method for the direct study of quasi-stationary properties of stochastic processes with an absorbing state. The method is used to determine the static correlation function and the…
We introduce a randomly extrapolated primal-dual coordinate descent method that adapts to sparsity of the data matrix and the favorable structures of the objective function. Our method updates only a subset of primal and dual variables with…
The approach to the ergodic limit in Monte Carlo simulations is studied using both analytic and numerical methods. With the help of a stochastic model, a metric is defined that enables the examination of a simulation in both the ergodic and…
We present an analysis of an adaptive time-stepping scheme for the Super-Droplet Method (SDM), a Monte Carlo algorithm for simulating particle coagulation. SDM represents cloud droplets as weighted superdroplets, enabling high-fidelity…
This work develops Monte Carlo Euler adaptive time stepping methods for the weak approximation problem of jump diffusion driven stochastic differential equations. The main result is the derivation of a new expansion for the omputational…
Parameter estimation for discretely observed Markov processes is a challenging problem. However, simulation of Markov processes is straightforward using the Gillespie algorithm. We exploit this ease of simulation to develop an effective…