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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…

Forward modeling approaches in cosmology have made it possible to reconstruct the initial conditions at the beginning of the Universe from the observed survey data. However the high dimensionality of the parameter space still poses a…

Quantum Monte Carlo (QMC) methods are the gold standard for studying equilibrium properties of quantum many-body systems -- their phase transitions, ground and thermal state properties. However, in many interesting situations QMC methods…

The Hamiltonian Monte Carlo (HMC) sampling algorithm exploits Hamiltonian dynamics to construct efficient Markov Chain Monte Carlo (MCMC), which has become increasingly popular in machine learning and statistics. Since HMC uses the gradient…

We propose a hybrid Monte Carlo (HMC) technique applicable to high-dimensional multivariate normal distributions that effectively samples along chaotic trajectories. The method is predicated on the freedom of choice of the HMC momentum…

Computational tools for characterizing electromagnetic scattering from objects with uncertain shapes are needed in various applications ranging from remote sensing at microwave frequencies to Raman spectroscopy at optical frequencies.…

Bayesian max-margin models have shown superiority in various practical applications, such as text categorization, collaborative prediction, social network link prediction and crowdsourcing, and they conjoin the flexibility of Bayesian…

The disordered microphases that develop in the high-temperature phase of systems with competing short-range attractive and long-range repulsive (SALR) interactions result in a rich array of distinct morphologies, such as cluster, void…

Sequential Monte Carlo (SMC), or particle filtering, is a popular class of methods for sampling from an intractable target distribution using a sequence of simpler intermediate distributions. Like other importance sampling-based methods,…

The Multilevel Monte Carlo method is an efficient variance reduction technique. It uses a sequence of coarse approximations to reduce the computational cost in uncertainty quantification applications. The method is nowadays often considered…

Variational auto-encoders (VAE) are popular deep latent variable models which are trained by maximizing an Evidence Lower Bound (ELBO). To obtain tighter ELBO and hence better variational approximations, it has been proposed to use…

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…

This paper concerns the use of sequential Monte Carlo methods (SMC) for smoothing in general state space models. A well-known problem when applying the standard SMC technique in the smoothing mode is that the resampling mechanism introduces…

Several disciplines, such as econometrics, neuroscience, and computational psychology, study the dynamic interactions between variables over time. A Bayesian nonparametric model known as the Wishart process has been shown to be effective in…

Quantitative photoacoustic tomography aims at estimating optical parameters from photoacoustic images that are formed utilizing the photoacoustic effect caused by the absorption of an externally introduced light pulse. This optical…

Sequential Monte Carlo (SMC) methods offer a principled approach to Bayesian uncertainty quantification but are traditionally limited by the need for full-batch gradient evaluations. We introduce a scalable variant by incorporating…

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…

Solving the quantum many-body ground state problem remains a central challenge in computational physics. In this context, the Variational Monte Carlo (VMC) framework based on Projected Entangled Pair States (PEPS) has witnessed rapid…

We introduce a Monte Carlo Virtual Element estimator based on Virtual Element discretizations for stochastic elliptic partial differential equations with random diffusion coefficients. We prove estimates for the statistical approximation…

Deep-Learning-based Variational Monte Carlo (DL-VMC) has recently emerged as a highly accurate approach for finding approximate solutions to the many-electron Schr\"odinger equation. Despite its favorable scaling with the number of…