Related papers: Adaptive Multilevel Monte Carlo Methods for Stocha…
We consider the numerical solution of scalar, nonlinear degenerate convection-diffusion problems with random diffusion coefficient and with random flux functions. Building on recent results on the existence, uniqueness and continuous…
We develop a novel Markov chain Monte Carlo (MCMC) method that exploits a hierarchy of models of increasing complexity to efficiently generate samples from an unnormalized target distribution. Broadly, the method rewrites the Multilevel…
Adaptive and interacting Markov chain Monte Carlo algorithms (MCMC) have been recently introduced in the literature. These novel simulation algorithms are designed to increase the simulation efficiency to sample complex distributions.…
This paper develops and analyzes an efficient numerical method for solving elliptic partial differential equations, where the diffusion coefficients are random perturbations of deterministic diffusion coefficients. The method is based upon…
In this work we propose a hierarchy of Monte Carlo methods for sampling equilibrium properties of stochastic lattice systems with competing short and long range interactions. Each Monte Carlo step is composed by two or more sub - steps…
Inspired by the latest developments in multilevel Monte Carlo (MLMC) methods and randomised sketching for linear algebra problems we propose a MLMC estimator for real-time processing of matrix structured random data. Our algorithm is…
Practical structural engineering problems are often characterized by significant uncertainties. Historically, one of the prevalent methods to account for this uncertainty has been the standard Monte Carlo (MC) method. Recently, improved…
A method for the multifidelity Monte Carlo (MFMC) estimation of statistical quantities is proposed which is applicable to computational budgets of any size. Based on a sequence of optimization problems each with a globally minimizing…
Self-learning Monte Carlo (SLMC) methods are recently proposed to accelerate Markov chain Monte Carlo (MCMC) methods using a machine learning model. With latent generative models, SLMC methods realize efficient Monte Carlo updates with less…
The convergence analysis for least-squares finite element methods led to various adaptive mesh-refinement strategies: Collective marking algorithms driven by the built-in a posteriori error estimator or an alternative explicit…
In this paper we present a rigorous cost and error analysis of a multilevel estimator based on randomly shifted Quasi-Monte Carlo (QMC) lattice rules for lognormal diffusion problems. These problems are motivated by uncertainty…
A first-order, Monte Carlo ensemble method has been recently introduced for solving parabolic equations with random coefficients in [26], which is a natural synthesis of the ensemble-based, Monte Carlo sampling algorithm and the…
We consider adaptive increasingly rare Markov chain Monte Carlo (MCMC) algorithms, which are adaptive MCMC methods, where the adaptation concerning the "past'' happens less and less frequently over time. Under a contraction assumption with…
We present a twofold contribution to the numerical simulation of Lindblad equations. First, an adaptive numerical approach to approximate Lindblad equations using low-rank dynamics is described: a deterministic low-rank approximation of the…
We investigate the problem of computing a nested expectation of the form $\mathbb{P}[\mathbb{E}[X|Y] \!\geq\!0]\!=\!\mathbb{E}[\textrm{H}(\mathbb{E}[X|Y])]$ where $\textrm{H}$ is the Heaviside function. This nested expectation appears, for…
In this article we consider computing expectations w.r.t.~probability laws associated to a certain class of stochastic systems. In order to achieve such a task, one must not only resort to numerical approximation of the expectation, but…
We introduce a gradient-based learning method to automatically adapt Markov chain Monte Carlo (MCMC) proposal distributions to intractable targets. We define a maximum entropy regularised objective function, referred to as generalised speed…
In many applications of practical interest, solutions of partial differential equation models arise as critical points of an underlying (energy) functional. If such solutions are saddle points, rather than being maxima or minima, then the…
We consider the problem of adaptive stratified sampling for Monte Carlo integration of a differentiable function given a finite number of evaluations to the function. We construct a sampling scheme that samples more often in regions where…
We consider a class of finite time horizon nonlinear stochastic optimal control problem, where the control acts additively on the dynamics and the control cost is quadratic. This framework is flexible and has found applications in many…