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This article was motivated by the desire to improve Markov chain Monte Carlo methods for spatial survival models in which the locations of individuals in space are known. For a dataset comprising information on n individuals, standard…

To achieve high performance of a machine learning (ML) task, a deep learning-based model must implicitly capture the entire distribution from data. Thus, it requires a huge amount of training samples, and data are expected to fully present…

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…

In this article, we study the application of Multi-Level Monte Carlo (MLMC) approaches to numerical random homogenization. Our objective is to compute the expectation of some functionals of the homogenized coefficients, or of the…

Data heterogeneity plays a pivotal role in determining the performance of machine learning (ML) systems. Traditional algorithms, which are typically designed to optimize average performance, often overlook the intrinsic diversity within…

Purpose: We address the challenge of inaccurate parameter estimation in diffusion MRI when the signal-to-noise ratio (SNR) is very low, as in the spinal cord. The accuracy of conventional maximum-likelihood estimation (MLE) depends highly…

The Monte Carlo simulation (MCS) is a statistical methodology used in a large number of applications. It uses repeated random sampling to solve problems with a probability interpretation to obtain high-quality numerical results. The MCS is…

We present a multilevel Monte Carlo (MLMC) method for the uncertainty quantification of variably saturated porous media flow that are modeled using the Richards' equation. We propose a stochastic extension for the empirical models that are…

We consider the computational efficiency of Monte Carlo (MC) and Multilevel Monte Carlo (MLMC) methods applied to partial differential equations with random coefficients. These arise, for example, in groundwater flow modelling, where a…

In this article we develop a new sequential Monte Carlo (SMC) method for multilevel (ML) Monte Carlo estimation. In particular, the method can be used to estimate expectations with respect to a target probability distribution over an…

This work introduces two Monte Carlo (MC)-based sampling methods, known as line sampling and subset simulation, to improve the performance of standard MC analyses in the context of asteroid impact risk assessment. Both techniques sample the…

We present a novel machine learning (ML) method to accelerate conservative-to-primitive inversion, focusing on hybrid piecewise polytropic and tabulated equations of state. Traditional root-finding techniques are computationally expensive,…

Global climate models (GCMs), typically run at ~100-km resolution, capture large-scale environmental conditions but cannot resolve convection and cloud processes at kilometer scales. Convection-permitting models offer higher-resolution…

Predicting the probability of default (PD) of prospective loans is a critical objective for financial institutions. In recent years, machine learning (ML) algorithms have achieved remarkable success across a wide variety of prediction…

The algorithm for Monte Carlo simulation of parton-level events based on an Artificial Neural Network (ANN) proposed in arXiv:1810.11509 is used to perform a simulation of $H\to 4\ell$ decay. Improvements in the training algorithm have been…

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…

Hamiltonian Monte Carlo (HMC) is a powerful and accurate method to sample from the posterior distribution in Bayesian inference. However, HMC techniques are computationally demanding for Bayesian neural networks due to the high…

We present an adaptive multilevel Monte Carlo (AMLMC) algorithm for approximating deterministic, real-valued, bounded linear functionals that depend on the solution of a linear elliptic PDE with a lognormal diffusivity coefficient and…

Despite successful use in a wide variety of disciplines for data analysis and prediction, machine learning (ML) methods suffer from a lack of understanding of the reliability of predictions due to the lack of transparency and black-box…

The stochastic simulation algorithm (SSA) and the corresponding Monte Carlo (MC) method are among the most common approaches for studying stochastic processes. They rely on knowledge of interevent probability density functions (PDFs) and on…