Related papers: A New Fast Monte Carlo Code for Solving Radiative …
We present a Monte Carlo algorithm that allows the simultaneous determination of a few extremal eigenpairs of a very large matrix without the need to compute the inner product of two vectors or store all the components of any one vector.…
A first-order, Monte Carlo ensemble method has been recently introduced for solving parabolic equations with random coefficients in [26], which is a natural synthesis of the ensemble-based, Monte Carlo sampling algorithm and the…
To achieve efficient and accurate long-time integration, we propose a fast, accurate, and stable high-order numerical method for solving fractional-in-space reaction-diffusion equations. The proposed method is explicit in nature and…
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…
The Monte Carlo method is a thriving and mathematically beautiful numerical technique used extensively, nowadays, to deal with many demanding problems in diverse fields. Here, we present an iterative Monte Carlo algorithm to work out very…
Consider testing multiple hypotheses using tests that can only be evaluated by simulation, such as permutation tests or bootstrap tests. This article introduces MMCTest, a sequential algorithm which gives, with arbitrarily high probability,…
We introduce a powerful Monte Carlo (MC) algorithm for the atomistic simulation of bulk models of oligo- and poly-thiophenes by redesigning MC moves originally developed for considerably simpler polymer structures and architectures, such as…
This paper introduces the MCT Self-Refine (MCTSr) algorithm, an innovative integration of Large Language Models (LLMs) with Monte Carlo Tree Search (MCTS), designed to enhance performance in complex mathematical reasoning tasks. Addressing…
An extensive study of population control techniques (PCTs) for time-dependent and eigenvalue Monte Carlo (MC) neutron transport calculations is presented. We define PCT as a technique that takes a censused population and returns a…
This work presents an optimal sampling-based method to solve the real-time motion planning problem in static and dynamic environments, exploiting the Rapid-exploring Random Trees (RRT) algorithm and the Model Predictive Path Integral (MPPI)…
Robots have become increasingly prevalent in dynamic and crowded environments such as airports and shopping malls. In these scenarios, the critical challenges for robot navigation are reliability and timely arrival at predetermined…
Reinforcement learning (RL) enables an agent interacting with an unknown MDP $M$ to optimise its behaviour by observing transitions sampled from $M$. A natural entity that emerges in the agent's reasoning is $\widehat{M}$, the maximum…
Monte Carlo (MC) neutron transport provides detailed estimates of radiological quantities within fission reactors. This involves tracking individual neutrons through a computational geometry. CPU-based MC codes use multiple polymorphic…
Optimal transport (OT) is a powerful tool for measuring the distance between two defined probability distributions. In this paper, we develop a new manifold named the coupling matrix manifold (CMM), where each point on CMM can be regarded…
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…
We discuss precision Monte Carlo (MC) calculations for solving the QCD evolution equations up to the next-to-leading-order (NLO) level. They employ forward Markovian Monte Carlo algorithms, which provide rigorous solutions of the above…
Context. The interpretation of polarised radiation emerging from a planetary atmosphere must rely on solutions to the vector Radiative Transport Equation (vRTE). Monte Carlo integration of the vRTE is a valuable approach for its flexible…
We develop a new relativistic radiation hydrodynamics code based on the Monte-Carlo algorithm. In this code, we implement a new scheme to achieve the second-order accuracy in time in the limit of a large packet number for solving the…
We present Doubly Robust Monte Carlo Tree Search (DR-MCTS), a novel algorithm that integrates Doubly Robust (DR) off-policy estimation into Monte Carlo Tree Search (MCTS) to enhance sample efficiency and decision quality in complex…
Subsurface remediation often involves reconstruction of contaminant release history from sparse observations of solute concentration. Markov Chain Monte Carlo (MCMC), the most accurate and general method for this task, is rarely used in…