Related papers: A Massively Parallel Implementation of Multilevel …
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…
Stochastic PDEs of Fluctuating Hydrodynamics are a powerful tool for the description of fluctuations in many-particle systems. In this paper, we develop and analyze a Multilevel Monte Carlo (MLMC) scheme for the Dean--Kawasaki equation, a…
We present a multilevel stochastic gradient descent method for the optimal control of systems governed by partial differential equations under uncertain input data. The gradient descent method used to find the optimal control leverages a…
Probabilistic models are conceptually powerful tools for finding structure in data, but their practical effectiveness is often limited by our ability to perform inference in them. Exact inference is frequently intractable, so approximate…
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 kinetic Monte Carlo (kMC) method is used in many scientific fields in applications involving rare-event transitions. Due to its discrete stochastic nature, efforts to parallelize kMC approaches often produce unbalanced time evolutions…
Low-density parity-check (LDPC) codes are among the most prominent error-correction schemes. They find application to fortify various modern storage, communication, and computing systems. Protograph-based (PB) LDPC codes offer many degrees…
We introduce three related but distinct improvements to multilevel Monte Carlo (MLMC) methods for the solution of systems of stochastic differential equations (SDEs). Firstly, we show that when the payoff function is twice continuously…
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…
Markov chain Monte Carlo (MCMC) methods are foundational algorithms for Bayesian inference and probabilistic modeling. However, most MCMC algorithms are inherently sequential and their time complexity scales linearly with the sequence…
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…
Applications that require substantial computational resources today cannot avoid the use of heavily parallel machines. Embracing the opportunities of parallel computing and especially the possibilities provided by a new generation of…
In this paper, we investigate the use of multilevel Monte Carlo (MLMC) methods for estimating the expectation of discretized random fields. Specifically, we consider a setting in which the input and output vectors of numerical simulators…
In this article we consider recursive approximations of the smoothing distribution associated to partially observed stochastic differential equations (SDEs), which are observed discretely in time. Such models appear in a wide variety of…
This work introduces a new method designed for Bayesian deep learning called scalable Bayesian Monte Carlo (SBMC). The method is comprised of a model and an algorithm. The model interpolates between a point estimator and the posterior. The…
Scientific computing has long relied on double precision (64-bit floating point) arithmetic to guarantee accuracy in simulations of real-world phenomena. However, the growing availability of hardware accelerators such as Graphics Processing…
To effectively control large-scale distributed systems online, model predictive control (MPC) has to swiftly solve the underlying high-dimensional optimization. There are multiple techniques applied to accelerate the solving process in the…
We consider the problem of estimating expectations with respect to a target distribution with an unknown normalizing constant, and where even the unnormalized target needs to be approximated at finite resolution. This setting is ubiquitous…
Current trends in parallel processors call for the design of efficient massively parallel algorithms for scientific computing. Parallel algorithms for Monte Carlo simulations of thermodynamic ensembles of particles have received little…
We introduce and analyze a parallel sequential Monte Carlo methodology for the numerical solution of optimization problems that involve the minimization of a cost function that consists of the sum of many individual components. The proposed…