相关论文: A Variational Approach to Enhanced Sampling and Fr…

Most applications of Bayesian Inference for parameter estimation and model selection in astrophysics involve the use of Monte Carlo techniques such as Markov Chain Monte Carlo (MCMC) and nested sampling. However, these techniques are time…

In the context of Monte Carlo sampling for lattice models, the complexity of the energy landscape often leads to Markov chains being trapped in local optima, thereby increasing the correlation between samples and reducing sampling…

Variational Monte Carlo methods have recently been applied to the calculation of excited states; however, it is still an open question what objective function is most effective. A promising approach is to optimize excited states using a…

Optimization in the Bures-Wasserstein space has been gaining popularity in the machine learning community since it draws connections between variational inference and Wasserstein gradient flows. The variational inference objective function…

We present a method for determining the free energy dependence on a selected number of collective variables using an adaptive bias. The formalism provides a unified description which has metadynamics and canonical sampling as limiting…

We advance a variational method to prove qualitative properties such as symmetries, monotonicity, upper and lower bounds, sign properties, and comparison principles for a large class of doubly-nonlinear evolutionary problems including…

Quantum Monte Carlo is an efficient technique for finding the ground-state energy and related properties of small molecules. A major challenge remains in accurate determination of a molecule's geometry, i.e. the optimal location of its…

The "equation-free'' approach has been proposed in recent years as a general framework for developing multiscale methods to efficiently capture the macroscale behavior of a system using only the microscale models. In this paper, we take a…

Quality by design in pharmaceutical manufacturing hinges on computational methods and tools that are capable of accurate quantitative prediction of the design space. This paper investigates Bayesian approaches to design space…

In statistics and machine learning, approximation of an intractable integration is often achieved by using the unbiased Monte Carlo estimator, but the variances of the estimation are generally high in many applications. Control variates…

An algorithm is proposed to optimize quantum Monte Carlo (QMC) wave functions based on New ton's method and analytical computation of the first and second derivatives of the variati onal energy. This direct application of the variational…

Recent advances in stochastic gradient variational inference have made it possible to perform variational Bayesian inference with posterior approximations containing auxiliary random variables. This enables us to explore a new synthesis of…

Monte Carlo simulations are an essential tool in particle physics data analysis. Events are typically generated alongside weights that redistribute the cross section of the simulated process across the phase space. These weights can be…

n a recent paper we proposed the expansion of the space of variations in energy calculations by considering the approximate wave function $\psi$ to be a functional of functions $\chi: \psi = \psi[\chi]$ rather than a function. For the…

While recent work towards the development of tight-binding and ab-initio algorithms has focused on molecular dynamics, Monte Carlo methods can often lead to better results with relatively little effort. We present here a multi-step Monte…

Bayesian design of experiments and sample size calculations usually rely on complex Monte Carlo simulations in practice. Obtaining bounds on Bayesian notions of the false-positive rate and power therefore often lack closed-form or…

Rejection Sampling is a fundamental Monte-Carlo method. It is used to sample from distributions admitting a probability density function which can be evaluated exactly at any given point, albeit at a high computational cost. However,…

Matrices are said to behave as free non-commuting random variables if the action which governs their dynamics constrains only their eigenvalues, i.e. depends on traces of powers of individual matrices. The authors use recently developed…

In Monte Carlo calculations of expectation values in lattice quantum field theories, the stochastic variance of the sampling procedure that is used defines the precision of the calculation for a fixed number of samples. If the variance of…

The numerical solution of problems in nonlinear magnetostatics is typically based on a variational formulation in terms of magnetic potentials, the discretization by finite elements, and iterative solvers like the Newton method. The vector…