Related papers: Multi-Level Monte Carlo sampling with Parallel-in-…
Multilevel Monte Carlo is a key tool for approximating integrals involving expensive scientific models. The idea is to use approximations of the integrand to construct an estimator with improved accuracy over classical Monte Carlo. We…
Stochastic spectral methods have become a popular technique to quantify the uncertainties of nano-scale devices and circuits. They are much more efficient than Monte Carlo for certain design cases with a small number of random parameters.…
Financial derivative pricing is a significant challenge in finance, involving the valuation of instruments like options based on underlying assets. While some cases have simple solutions, many require complex classical computational methods…
Multilevel Monte Carlo can efficiently compute statistical estimates of discretized random variables, for a given error tolerance. Traditionally, only a certain statistic is computed from a particular implementation of multilevel Monte…
Recently, Velazquez and Curilef have proposed a methodology to extend Monte Carlo algorithms based on canonical ensemble, which is aimed to overcome slow sampling problems associated with temperature-driven discontinuous phase transitions.…
Monte Carlo and Quasi-Monte Carlo methods present a convenient approach for approximating the expected value of a random variable. Algorithms exist to adaptively sample the random variable until a user defined absolute error tolerance is…
The recently-introduced self-learning Monte Carlo method is a general-purpose numerical method that speeds up Monte Carlo simulations by training an effective model to propose uncorrelated configurations in the Markov chain. We implement…
We present a continuous-variable photonic quantum algorithm for the Monte Carlo evaluation of multi-dimensional integrals. Our algorithm encodes n-dimensional integration into n+3 modes and can provide a quadratic speedup in runtime…
The Multilevel Monte Carlo (MLMC) method has been applied successfully in a wide range of settings since its first introduction by Giles (2008). When using only two levels, the method can be viewed as a kind of control-variate approach to…
The basic problem in equilibrium statistical mechanics is to compute phase space average, in which Monte Carlo method plays a very important role. We begin with a review of nonlocal algorithms for Markov chain Monte Carlo simulation in…
We develop a parallel rejection algorithm to tackle the problem of low acceptance in Monte Carlo methods, and apply it to the simulation of the hopping conduction in Coulomb glasses using Graphics Processing Units, for which we also…
Ensemble Kalman methods solve problems in domains such as filtering and inverse problems with interacting particles that evolve over time. For computationally expensive problems, the cost of attaining a high accuracy quickly becomes…
Tau-leaping is a popular discretization method for generating approximate paths of continuous time, discrete space, Markov chains, notably for biochemical reaction systems. To compute expected values in this context, an appropriate…
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…
Generative diffusion models have recently emerged as a powerful strategy to perform stochastic sampling in Bayesian inverse problems, delivering remarkably accurate solutions for a wide range of challenging applications. However, diffusion…
In this paper, we present a probabilistic numerical algorithm combining dynamic programming, Monte Carlo simulations and local basis regressions to solve non-stationary optimal multiple switching problems in infinite horizon. We provide the…
Recent advances in machine learning have led to the development of new methods for enhancing Monte Carlo methods such as Markov chain Monte Carlo (MCMC) and importance sampling (IS). One such method is normalizing flows, which use a neural…
The paper presents a new perspective on the mixture of Dirichlet process model which allows the recovery of full and correct uncertainty quantification associated with the full model, even after having integrated out the random distribution…
We consider the problem of forecasting debt recovery from large portfolios of non-performing unsecured consumer loans under management. The state of the art in industry is to use stochastic processes to approximately model payment behaviour…
In the nano era in integrated circuit fabrication technologies, the performance variability due to statistical process and circuit parameter variations is becoming more and more significant. Considerable effort has been expended in the EDA…