Related papers: Variance extrapolation method for neural-network v…
Expectation values of physical quantities may accurately be obtained by the evaluation of integrals within Many-Body Quantum mechanics, and these multi-dimensional integrals may be estimated using Monte Carlo methods. In a previous…
We propose the use of Monte Carlo histogram reweighting to extrapolate predictions of machine learning methods. In our approach, we treat the output from a convolutional neural network as an observable in a statistical system, enabling its…
We study the approximation of $\mathbb{E}f(X_T)$ by a Monte Carlo algorithm, where $X$ is the solution of a stochastic differential equation and $f$ is a given function. We introduce a new variance reduction method, which can be viewed as a…
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 introduce several improvements to the penalty-based variational quantum Monte Carlo (VMC) algorithm for computing electronic excited states of Entwistle $\textit{et al.}$ [M. T. Entwistle $\textit{et al.}$, Nat. Commun. $\textbf{14}$,…
Solving partial differential equations in high dimensions by deep neural network has brought significant attentions in recent years. In many scenarios, the loss function is defined as an integral over a high-dimensional domain. Monte-Carlo…
We present a formalism that allows for the direct manipulation and optimization of subspaces, circumventing the need to optimize individual states when using subspace methods. Using the determinant state mapping, we can naturally extend…
This article addresses online variational estimation in parametric state-space models. We propose a new procedure for efficiently computing the evidence lower bound and its gradient in a streaming-data setting, where observations arrive…
This topical review describes the methodology of continuum variational and diffusion quantum Monte Carlo calculations. These stochastic methods are based on many-body wave functions and are capable of achieving very high accuracy. The…
A statistical learning approach for parametric PDEs related to Uncertainty Quantification is derived. The method is based on the minimization of an empirical risk on a selected model class and it is shown to be applicable to a broad range…
The Monte Carlo dropout method has proved to be a scalable and easy-to-use approach for estimating the uncertainty of deep neural network predictions. This approach was recently applied to Fault Detection and Di-agnosis (FDD) applications…
Recent studies have demonstrated the efficiency of Variational Autoencoders (VAE) to compress high-dimensional implied volatility surfaces into a low dimensional representation. Although this method can be effectively used for pricing…
Monte Carlo is a simple and flexible tool that is widely used in computational finance. In this context, it is common for the quantity of interest to be the expected value of a random variable defined via a stochastic differential equation.…
In this work, we study the approximation of expected values of functional quantities on the solution of a stochastic differential equation (SDE), where we replace the Monte Carlo estimation with the evaluation of a deep neural network. Once…
Control variates are a well-established tool to reduce the variance of Monte Carlo estimators. However, for large-scale problems including high-dimensional and large-sample settings, their advantages can be outweighed by a substantial…
Variational quantum Monte Carlo (QMC) is an ab-initio method for solving the electronic Schr\"odinger equation that is exact in principle, but limited by the flexibility of the available ansatzes in practice. The recently introduced deep…
We present three different methods to estimate error bars on the predictions made using a neural network. All of them represent lower bounds for the extrapolation errors. For example, we did not include an analysis on robustness against…
We discuss the improvement in the accuracy of a Monte Carlo integration that can be obtained by optimization of the `a-priori weights' of the various channels. These channels may be either the strata in a stratified-sampling approach, or…
Monte Carlo (MC) dropout is one of the state-of-the-art approaches for uncertainty estimation in neural networks (NNs). It has been interpreted as approximately performing Bayesian inference. Based on previous work on the approximation of…
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…