相关论文: Error analysis of coarse-grained kinetic Monte Car…

Gaussian process (GP) models form a core part of probabilistic machine learning. Considerable research effort has been made into attacking three issues with GP models: how to compute efficiently when the number of data is large; how to…

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…

We design and implement a novel algorithm for computing a multilevel Monte Carlo (MLMC) estimator of the cumulative distribution function of a quantity of interest in problems with random input parameters or initial conditions. Our approach…

Monte Carlo (MC) simulations of lattice models are a widely used way to compute thermodynamic properties of substitutional alloys. A limitation to their more widespread use is the difficulty of driving a MC simulation in order to obtain the…

Reverse Monte Carlo (RMC) is an algorithm that incorporates stochastic modification of the action as part of the process that updates the fields in a Monte Carlo simulation. Such update moves have the potential of lowering or eliminating…

We study a random sampling technique to approximate integrals $\int_{[0,1]^s}f(\mathbf{x})\,\mathrm{d}\mathbf{x}$ by averaging the function at some sampling points. We focus on cases where the integrand is smooth, which is a problem which…

Hamiltonian Monte Carlo (HMC) sampling methods provide a mechanism for defining distant proposals with high acceptance probabilities in a Metropolis-Hastings framework, enabling more efficient exploration of the state space than standard…

Adaptive Monte Carlo methods are very efficient techniques designed to tune simulation estimators on-line. In this work, we present an alternative to stochastic approximation to tune the optimal change of measure in the context of…

Conventional Monte Carlo simulations are stochastic in the sense that the acceptance of a trial move is decided by comparing a computed acceptance probability with a random number, uniformly distributed between 0 and 1. Here we consider the…

Multiscale molecular modeling is widely applied in scientific research of molecular properties over large time and length scales. Two specific challenges are commonly present in multiscale modeling, provided that information between the…

We investigate the applicability of Quasi-Monte Carlo methods to Euclidean lattice systems for quantum mechanics in order to improve the asymptotic error behavior of observables for such theories. In most cases the error of an observable…

This work presents an efficient approach for accelerating multilevel Markov Chain Monte Carlo (MCMC) sampling for large-scale problems using low-fidelity machine learning models. While conventional techniques for large-scale Bayesian…

Molecular dynamics simulations provide theoretical insight into the microscopic behavior of materials in condensed phase and, as a predictive tool, enable computational design of new compounds. However, because of the large temporal and…

Minimum-weight perfect matching (MWPM) has been been the primary classical algorithm for error correction in the surface code, since it is of low runtime complexity and achieves relatively low logical error rates [Phys. Rev. Lett. 108,…

We define a natural coarse-graining procedure which can be applied to any closed equilibrium quantum system described by a density matrix ensemble and we show how the coarse-graining leads to the Gaussian and canonical ensembles. After this…

Fitting stochastic kinetic models represented by Markov jump processes within the Bayesian paradigm is complicated by the intractability of the observed data likelihood. There has therefore been considerable attention given to the design of…

We present a computer-assisted approach to coarse-graining the evolutionary dynamics of a system of nonidentical oscillators coupled through a (fixed) network structure. The existence of a spectral gap for the coupling network graph…

The recently-introduced self-learning Monte Carlo method is a general-purpose numerical method that speeds up Monte Carlo simulations by training an effective model to propose uncorrelated configurations in the Markov chain. We implement…

We investigate the application of randomized quasi-Monte Carlo (RQMC) methods in random feature approximations for kernel-based learning. Compared to the classical Monte Carlo (MC) approach \citep{rahimi2007random}, RQMC improves the…

Motivated by penalized likelihood maximization in complex models, we study optimization problems where neither the function to optimize nor its gradient have an explicit expression, but its gradient can be approximated by a Monte Carlo…