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Many large scale problems in computational fluid dynamics such as uncertainty quantification, Bayesian inversion, data assimilation and PDE constrained optimization are considered very challenging computationally as they require a large…
Reverse Monte Carlo (RMC) is an algorithm that incorporates stochastic modification of the action as part of the process that updates the fields in a Monte Carlo simulation. Such update moves have the potential of lowering or eliminating…
Monte Carlo maximum likelihood (MCML) provides an elegant approach to find maximum likelihood estimators (MLEs) for latent variable models. However, MCML algorithms are computationally expensive when the latent variables are…
Monte Carlo methods play an important role in scientific computation, especially when problems have a vast phase space. In this lecture an introduction to the Monte Carlo method is given. Concepts such as Markov chains, detailed balance,…
Markov chain Monte Carlo (MCMC) algorithms are ubiquitous in Bayesian computations. However, they need to access the full data set in order to evaluate the posterior density at every step of the algorithm. This results in a great…
Preliminary low-thrust spacecraft mission design is a global search problem characterized by a complex solution landscape, multiple objectives, and numerous local minima. During this phase, mission parameters are often not yet fully…
Markov chain Monte Carlo is a class of algorithms for drawing Markovian samples from high-dimensional target densities to approximate the numerical integration associated with computing statistical expectation, especially in Bayesian…
A class of Monte Carlo algorithms which incorporate absorbing Markov chains is presented. In a particular limit, the lowest-order of these algorithms reduces to the $n$-fold way algorithm. These algorithms are applied to study the escape…
Sampling from known probability distributions is a ubiquitous task in computational science, underlying calculations in domains from linguistics to biology and physics. Generative machine-learning (ML) models have emerged as a promising…
General-purpose Markov Chain Monte Carlo sampling algorithms suffer from a dramatic reduction in efficiency as the system being studied is driven towards a critical point. Recently, a series of seminal studies suggested that normalizing…
We study the possibility of using multilevel algorithms for the computation of correlation functions of gradient flow observables. For each point in the correlation function an approximate flow is defined which depends only on links in a…
Bayesian inference for Markov processes has become increasingly relevant in recent years. Problems of this type often have intractable likelihoods and prior knowledge about model rate parameters is often poor. Markov Chain Monte Carlo…
Stochastic optimization in learning and inference often relies on Markov chain Monte Carlo (MCMC) to approximate gradients when exact computation is intractable. However, finite-time MCMC estimators are biased, and reducing this bias…
Most works on federated learning (FL) focus on the most common frequentist formulation of learning whereby the goal is minimizing the global empirical loss. Frequentist learning, however, is known to be problematic in the regime of limited…
Quasi-Monte Carlo (QMC) methods for estimating integrals are attractive since the resulting estimators typically converge at a faster rate than pseudo-random Monte Carlo. However, they can be difficult to set up on arbitrary posterior…
Markov Chain Monte Carlo (MCMC) methods are algorithms for sampling probability distributions, commonly applied to the Boltzmann distribution in physical and chemical models such as protein folding and the Ising model. These methods enable…
While Markov chain Monte Carlo methods (MCMC) provide a general framework to sample from a probability distribution defined up to normalization, they often suffer from slow convergence to the target distribution when the latter is highly…
This work introduces a novel multilevel Monte Carlo (MLMC) metamodeling approach for variance function estimation. Although devising an efficient experimental design for simulation metamodeling can be elusive, the MLMC-based approach…
Many machine learning problems involve Monte Carlo gradient estimators. As a prominent example, we focus on Monte Carlo variational inference (MCVI) in this paper. The performance of MCVI crucially depends on the variance of its stochastic…
We investigate the applicability of Quasi-Monte Carlo methods to Euclidean lattice systems for quantum mechanics in order to improve the asymptotic error behavior of observables for such theories. In most cases the error of an observable…