Related papers: Multi-Polynomial Monte Carlo for Trace Estimation …
An algorithm is proposed to solve robust control problems constrained by partial differential equations with uncertain coefficients, based on the so-called MG/OPT framework. The levels in this MG/OPT hierarchy correspond to discretization…
In this paper, we propose a new kind of numerical scheme for high-dimensional backward stochastic differential equations based on modified multi-level Picard iteration. The proposed scheme is very similar to the original multi-level Picard…
Current differentiable renderers provide light transport gradients with respect to arbitrary scene parameters. However, the mere existence of these gradients does not guarantee useful update steps in an optimization. Instead, inverse…
We study fast Monte-Carlo methods for testing irreducibility and detecting arithmetic imprimitivity of polynomials over $\mathbb{Q}$. Building on the subset-sum criterion of Pemantle-Peres-Rivin, we develop a probabilistic irreducibility…
High-dimensional data are routinely collected in many areas. We are particularly interested in Bayesian classification models in which one or more variables are imbalanced. Current Markov chain Monte Carlo algorithms for posterior…
This paper introduces a new Monte Carlo algorithm to invert large matrices. It is based on simultaneous coupled draws from two random vectors whose covariance is the required inverse. It can be considered a generalization of a previously…
In this paper we present computational experiments with the Markov Chain Monte Carlo Matrix Inversion ($(\text{MC})^2\text{MI}$) on several accelerator architectures and investigate their impact on performance and scalability of the method.…
This paper proposes a new multilevel Monte Carlo (MLMC) method for the ergodic SDEs which do not satisfy the contractivity condition. By introducing the change of measure technique, we simulate the path with contractivity and add the…
Operator learning is a rapidly growing field that aims to approximate nonlinear operators related to partial differential equations (PDEs) using neural operators. These rely on discretization of input and output functions and are, usually,…
We introduce a new Markov-Chain Monte Carlo (MCMC) approach designed for efficient sampling of highly correlated and multimodal posteriors. Parallel tempering, though effective, is a costly technique for sampling such posteriors. Our…
We use a Monte Carlo method to assemble finite element matrices for polynomial Chaos approximations of elliptic equations with random coefficients. In this approach, all required expectations are approximated by a Monte Carlo method. The…
The Self-Learning Monte Carlo (SLMC) method is a Monte Carlo approach that has emerged in recent years by integrating concepts from machine learning with conventional Monte Carlo techniques. Designed to accelerate the numerical study of…
Monte Carlo studies involving real time dynamics are severely restricted by the sign problem that emerges from highly oscillatory phase of the path integral. In this letter, we present a new method to compute real time quantities on the…
Many fields require computing the trace of the inverse of a large, sparse matrix. The typical method used for such computations is the Hutchinson method which is a Monte Carlo (MC) averaging over matrix quadratures. To improve its…
The effect of different move sets on the folding kinetics of the Monte Carlo simulations is analysed based on the conformation-network and the temperature-dependent folding kinetics. A new scheme of implementing Metropolis algorithm is…
In this paper a novel modification of the multilevel Monte Carlo approach, allowing for further significant complexity reduction, is proposed. The idea of the modification is to use the method of control variates to reduce variance at level…
Uncertainty estimation in deep models is essential in many real-world applications and has benefited from developments over the last several years. Recent evidence suggests that existing solutions dependent on simple Gaussian formulations…
An efficient continuous-time path-integral Quantum Monte Carlo algorithm for the lattice polaron is presented. It is based on Feynman's integration of phonons and subsequent simulation of the resulting single-particle self-interacting…
We propose and investigate a new multi-level Monte Carlo scheme for numerical solutions of the kinetic Boltzmann equation for neutral species in edge plasmas. In particular, this method explicitly exploits a key structural property of…
Recently, Stochastic Gradient Markov Chain Monte Carlo (SG-MCMC) methods have been proposed for scaling up Monte Carlo computations to large data problems. Whilst these approaches have proven useful in many applications, vanilla SG-MCMC…