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Monte Carlo simulations are widely used to simulate complex molecular systems, but standard approaches suffer from metastability. Lately, the use of non-local proposal updates in a collective-variable (CV) space has been proposed in several…
The accuracy and efficiency of ab-initio quantum Monte Carlo (QMC) algorithms benefits greatly from compact variational trial wave functions that accurately reproduce ground state properties of a system. We investigate the possibility of…
We introduce a variant of the multi-grid Monte Carlo (MGMC) method, based on the embedding of an $XY$ model into the target model, and we study its mathematical properties for a variety of nonlinear $\sigma$-models. We then apply the method…
Traditionally, the field of computational Bayesian statistics has been divided into two main subfields: variational methods and Markov chain Monte Carlo (MCMC). In recent years, however, several methods have been proposed based on combining…
We propose a new framework of variance-reduced Hamiltonian Monte Carlo (HMC) methods for sampling from an $L$-smooth and $m$-strongly log-concave distribution, based on a unified formulation of biased and unbiased variance reduction…
Hamiltonian Monte Carlo (HMC) is an efficient method of simulating smooth distributions and has motivated the widely used No-U-turn Sampler (NUTS) and software Stan. We build on NUTS and the technique of "unbiased sampling" to design HMC…
Hamiltonian Monte Carlo (HMC) algorithms which combine numerical approximation of Hamiltonian dynamics on finite intervals with stochastic refreshment and Metropolis correction are popular sampling schemes, but it is known that they may…
In several implementations of Sequential Monte Carlo (SMC) methods it is natural, and important in terms of algorithmic efficiency, to exploit the information of the history of the samples to optimally tune their subsequent propagations. In…
In this work, we examine sampling problems with non-smooth potentials. We propose a novel Markov chain Monte Carlo algorithm for sampling from non-smooth potentials. We provide a non-asymptotical analysis of our algorithm and establish a…
One of the open challenges in quantum computing is to find meaningful and practical methods to leverage quantum computation to accelerate classical machine learning workflows. A ubiquitous problem in machine learning workflows is sampling…
We made a comparative analysis of numerical methods for multidimensional optimization. The main parameter is a number of computations of the test function to reach necessary accuracy, as it is computationally "slow". For complex functions,…
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…
Bayesian inverse problems highly rely on efficient and effective inference methods for uncertainty quantification (UQ). Infinite-dimensional MCMC algorithms, directly defined on function spaces, are robust under refinement of physical…
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…
This work introduces a novel multilevel Monte Carlo (MLMC) metamodeling approach for variance function estimation. Although devising an efficient experimental design for simulation metamodeling can be elusive, the MLMC-based approach…
Many real-world multi-agent systems exhibit nonlinear dynamics and complex inter-agent interactions. As these systems increase in scale, the main challenges arise from achieving scalability and handling nonconvexity. To address these…
Existing rigorous convergence guarantees for the Hamiltonian Monte Carlo (HMC) algorithm use Gaussian auxiliary momentum variables, which are crucially symmetrically distributed. We present a novel convergence analysis for HMC utilizing new…
We develop a novel advanced Particle Markov chain Monte Carlo algorithm that is capable of sampling from the posterior distribution of non-linear state space models for both the unobserved latent states and the unknown model parameters. We…
This chapter is devoted to the computation of equilibrium (thermodynamic) properties of quantum systems. In particular, we will be interested in the situation where the interaction between particles is so strong that it cannot be treated as…
Colloids have a striking relevance in a wide spectrum of industrial formulations, spanning from personal care products to protective paints. Their behaviour can be easily influenced by extremely weak forces, which disturb their…