Related papers: Quantum Monte Carlo methods for Newsvendor problem…

The Variational Monte Carlo method has recently seen important advances through the use of neural network quantum states. While more and more sophisticated ans\"atze have been designed to tackle a wide variety of quantum many-body problems,…

In this article, we present a review of the recent developments on the topic of Multilevel Monte Carlo (MLMC) algorithm, in the paradigm of applications in financial engineering. We specifically focus on the recent studies conducted in two…

This paper introduces a novel and scalable framework for uncertainty estimation and separation with applications in data driven modeling in science and engineering tasks where reliable uncertainty quantification is critical. Leveraging an…

Variational Monte Carlo (VMC) is a powerful and fast-growing method for optimizing and evolving parameterized many-body wave functions, especially with modern neural-network quantum states. In practice, however, the stochastic estimators…

In the context of Monte Carlo (MC) simulation of particle transport Uncertainty Quantification (UQ) addresses the issue of predicting non statistical errors affecting the physical results, i.e. errors deriving mainly from uncertainties in…

Neural networks are a commonly used approach to replace physical models with computationally cheap surrogates. Parametric uncertainty quantification can be included in training, assuming that an accurate prior distribution of the model…

We develop a multilevel Monte Carlo (MLMC) framework for uncertainty quantification with Monte Carlo dropout. Treating dropout masks as a source of epistemic randomness, we define a fidelity hierarchy by the number of stochastic forward…

We analyze the accuracy and sample complexity of variational Monte Carlo approaches to simulate the dynamics of many-body quantum systems classically. By systematically studying the relevant stochastic estimators, we are able to: (i) prove…

Portfolio optimization is a fundamental problem in finance that aims to determine the optimal allocation of assets within a portfolio to maximize returns while minimizing risk. It can be formulated as a Quadratic Unconstrained Binary…

Inverse problems aim to determine model parameters of a mathematical problem from given observational data. Neural networks can provide an efficient tool to solve these problems. In the context of Bayesian inverse problems, Uncertainty…

For many complex simulation tasks spanning areas such as healthcare, engineering, and finance, Monte Carlo (MC) methods are invaluable due to their unbiased estimates and precise error quantification. Nevertheless, Monte Carlo simulations…

Accurate uncertainty quantification is a critical challenge in machine learning. While neural networks are highly versatile and capable of learning complex patterns, they often lack interpretability due to their ``black box'' nature. On the…

This paper considers the problem of optimizing the average tracking error for an elliptic partial differential equation with an uncertain lognormal diffusion coefficient. In particular, the application of the multilevel quasi-Monte Carlo…

Quantifying uncertainty is important for actionable predictions in real-world applications. A crucial part of predictive uncertainty quantification is the estimation of epistemic uncertainty, which is defined as an integral of the product…

Price signals from distribution networks (DNs) guide energy communities (ECs) in adjusting their energy usage, enabling effective coordination for reliable power system operation. However, this coordinated operation faces significant…

We present a generic study on the information-theoretic security of multi-setting device-independent quantum key distribution protocols, i.e., ones that involve more than two measurements (or inputs) for each party to perform, and yield…

This Perspective focuses on the several overlaps between quantum algorithms and Monte Carlo methods in the domains of physics and chemistry. We will analyze the challenges and possibilities of integrating established quantum Monte Carlo…

Variational Monte Carlo (VMC) methods are used to sample classically from distributions corresponding to quantum states which have an efficient classical description. VMC methods are based on performing a number of steps of a Markov chain…

Quantum computers theoretically promise computational advantage in many tasks, but it is much less clear how such advantage can be maintained when using existing and near-term hardware that has limitations in the number and quality of its…

Multifidelity Monte Carlo methods rely on a hierarchy of possibly less accurate but statistically correlated simplified or reduced models, in order to accelerate the estimation of statistics of high-fidelity models without compromising the…