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This paper addresses the complexity reduction of stochastic homogenisation of a class of random materials for a stationary diffusion equation. A cost-efficient approximation of the correctors is built using a method designed to exploit…
X-ray dose constantly gains interest in the interventional suite. With dose being generally difficult to monitor reliably, fast computational methods are desirable. A major drawback of the gold standard based on Monte Carlo (MC) methods is…
This paper concerns numerical assessment of Monte Carlo error in particle filters. We show that by keeping track of certain key features of the genealogical structure arising from resampling operations, it is possible to estimate variances…
This topical review describes the methodology of continuum variational and diffusion quantum Monte Carlo calculations. These stochastic methods are based on many-body wave functions and are capable of achieving very high accuracy. The…
Monte Carlo (MC) integration is an important calculational technique in the physical sciences. Practical considerations require that the calculations are performed as accurately as possible for a given set of computational resources. To…
These lectures given to graduate students in high energy physics, provide an introduction to Monte Carlo methods. After an overview of classical numerical quadrature rules, Monte Carlo integration together with variance-reducing techniques…
The Monte Carlo Hamiltonian method developed recently allows to investigate ground state and low-lying excited states of a quantum system, using Monte Carlo algorithm with importance sampling. However, conventional MC algorithm has some…
In this article, we present a review of the recent developments on the topic of Multilevel Monte Carlo (MLMC) algorithm, in the paradigm of applications in financial engineering. We specifically focus on the recent studies conducted in two…
Multilevel Monte Carlo (MLMC) is a recently proposed variation of Monte Carlo (MC) simulation that achieves variance reduction by simulating the governing equations on a series of spatial (or temporal) grids with increasing resolution.…
Within the HMC algorithm, we discuss how, by using the shadow Hamiltonian and the Poisson brackets, one can achieve a simple factorization in the dependence of the Hamiltonian violations upon either the algorithmic parameters or the…
Constructing more expressive ansatz has been a primary focus for quantum Monte Carlo, aimed at more accurate \textit{ab initio} calculations. However, with more powerful ansatz, e.g. various recent developed models based on neural-network…
Probability measures supported on submanifolds can be sampled by adding an extra momentum variable to the state of the system, and discretizing the associated Hamiltonian dynamics with some stochastic perturbation in the extra variable. In…
Classical algorithms in numerical analysis for numerical integration (quadrature/cubature) follow the principle of approximate and integrate: the integrand is approximated by a simple function (e.g. a polynomial), which is then integrated…
We show several results on convergence of the Monte Carlo method applied to consistent approximations of the isentropic Euler system of gas dynamics with uncertain initial data. Our method is based on combination of several new concepts. We…
We investigate the properties of a sequential Monte Carlo method where the particle weight that appears in the algorithm is estimated by a positive, unbiased estimator. We present broadly-applicable convergence results, including a central…
We study several aspects of the recently introduced fixed-phase spin-orbit diffusion Monte Carlo (FPSODMC) method, in particular, its relation to the fixed-node method and its potential use as a general approach for electronic structure…
We present a simple and efficient method to optimize within energy minimization the determinantal component of the many-body wave functions commonly used in quantum Monte Carlo calculations. The approach obtains the optimal wave function as…
We propose a variance reduction framework for variational inference using the Multilevel Monte Carlo (MLMC) method. Our framework is built on reparameterized gradient estimators and "recycles" parameters obtained from past update history in…
Multi-fidelity Monte Carlo (MFMC) is a variance reduction method that leverages a multi-fidelity ensemble of models of varying cost and accuracy levels. Constructing an MFMC estimator with optimal variance requires knowledge of the…
For many complex simulation tasks spanning areas such as healthcare, engineering, and finance, Monte Carlo (MC) methods are invaluable due to their unbiased estimates and precise error quantification. Nevertheless, Monte Carlo simulations…