Related papers: Monte Carlo Eigenvalue Methods in Quantum Mechanic…

We consider quantile estimation using Markov chain Monte Carlo and establish conditions under which the sampling distribution of the Monte Carlo error is approximately Normal. Further, we investigate techniques to estimate the associated…

Population Monte Carlo (PMC) sampling methods are powerful tools for approximating distributions of static unknowns given a set of observations. These methods are iterative in nature: at each step they generate samples from a proposal…

The self-learning Metropolis-Hastings algorithm is a powerful Monte Carlo method that, with the help of machine learning, adaptively generates an easy-to-sample probability distribution for approximating a given hard-to-sample distribution.…

Monte Carlo and Quasi-Monte Carlo methods present a convenient approach for approximating the expected value of a random variable. Algorithms exist to adaptively sample the random variable until a user defined absolute error tolerance is…

We develop two Regression Monte Carlo algorithms (value and performance iteration) to solve general problems of optimal stochastic control of discrete-time Markov processes. We formulate our method within an innovative framework that allow…

We present an efficient method to find minimum energy structures using energy estimates from accurate quantum Monte Carlo calculations. This method involves a stochastic process formed from the stochastic energy estimates from Monte Carlo…

Safety evaluation of self-driving technologies has been extensively studied. One recent approach uses Monte Carlo based evaluation to estimate the occurrence probabilities of safety-critical events as safety measures. These Monte Carlo…

Active subspaces can effectively reduce the dimension of high-dimensional parameter studies enabling otherwise infeasible experiments with expensive simulations. The key components of active subspace methods are the eigenvectors of a…

Due to the advances in the manufacturing of quantum hardware in the recent years, significant research efforts have been directed towards employing quantum methods to solving problems in various areas of interest. Thus a plethora of novel…

Various physical models can be expressed in terms of matrices. A valuable tool for analysing matrix models is numerical simulations, often the Metropolis algorithm with various improvements. The downside of this approach is that the…

Closed-form stochastic filtering equations can be derived in a general setting where probability distributions are replaced by some specific outer measures. In this article, we study how the principles of the sequential Monte Carlo method…

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…

This article is a brief introduction to quantum algorithms for the eigenvalue problem in quantum many-body systems. Rather than a broad survey of topics, we focus on providing a conceptual understanding of several quantum algorithms that…

We propose and analyze a method for computing failure probabilities of systems modeled as numerical deterministic models (e.g., PDEs) with uncertain input data. A failure occurs when a functional of the solution to the model is below (or…

This article analyzes and develops a method to solve fractional ordinary differential equations using the Monte Carlo Method. A numerical simulation is performed for some differential equations, comparing the results with what exists in the…

Monte Carlo (MC) simulations of many systems, in particular those with conflicting constraints, can be considerably speeded up by using multicanonical or related methods. Some of these approaches sample with a-priori unknown weight factors.…

Control variates are a well-established tool to reduce the variance of Monte Carlo estimators. However, for large-scale problems including high-dimensional and large-sample settings, their advantages can be outweighed by a substantial…

In this paper, I investigate more closely the recently proposed Free Energy Monte Carlo algorithm that is devised in particular for calculations where conventional Monte Carlo simulations struggle with ergodicity problems. The simplest…

A number of optimal decision problems with uncertainty can be formulated into a stochastic optimal control framework. The Least-Squares Monte Carlo (LSMC) algorithm is a popular numerical method to approach solutions of such stochastic…

We investigate the use of different variational principles in quantum Monte Carlo, namely energy and variance minimization, prompted by the interest in the robust and accurate estimate of electronic excited states. For two prototypical,…