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Sequential Monte Carlo methods, also known as particle methods, are a popular set of techniques for approximating high-dimensional probability distributions and their normalizing constants. These methods have found numerous applications in…
Markov chain Monte Carlo is an inherently serial algorithm. Although likelihood calculations for individual steps can sometimes be parallelized, the serial evolution of the process is widely viewed as incompatible with parallelization,…
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…
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…
We present a modification to variational Monte Carlo's linear method optimization scheme that addresses a critical memory bottleneck while maintaining compatibility with both the traditional ground state variational principle and our…
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…
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…
We propose a novel $hp$-multilevel Monte Carlo method for the quantification of uncertainties in the compressible Navier-Stokes equations, using the Discontinuous Galerkin method as deterministic solver. The multilevel approach exploits…
This paper addresses optimization problems constrained by partial differential equations with uncertain coefficients. In particular, the robust control problem and the average control problem are considered for a tracking type cost…
We study statistical model checking of continuous-time stochastic hybrid systems. The challenge in applying statistical model checking to these systems is that one cannot simulate such systems exactly. We employ the multilevel Monte Carlo…
We consider a new formulation of the stochastic coupled cluster method in terms of the similarity transformed Hamiltonian. We show that improvement in the granularity with which the wavefunction is represented results in a reduction in the…
We propose a multilevel Monte Carlo method for a particle-based asymptotic-preserving scheme for kinetic equations. Kinetic equations model transport and collision of particles in a position-velocity phase-space. With a diffusive scaling,…
Kinetic equations model distributions of particles in position-velocity phase space. Often, one is interested in studying the long-time behavior of particles in high-collisional regimes in which an approximate (advection)-diffusion model…
Monte Carlo methods play important part in modern statistical physics. The application of these methods suffer from two main difficulties.The first is caused by the relatively small number of particles that can participate in any numerical…
While multilevel Monte Carlo (MLMC) methods for the numerical approximation of partial differential equations with random coefficients enjoy great popularity, combinations with spatial adaptivity seem to be rare. We present an adaptive MLMC…
We discuss the application of multilevel Monte Carlo methods to elliptic partial differential equations with random coefficients. Such problems arise, for example, in uncertainty quantification in subsurface flow modeling. We give a brief…
In this paper we address the problem of the prohibitively large computational cost of existing Markov chain Monte Carlo methods for large--scale applications with high dimensional parameter spaces, e.g. in uncertainty quantification in…
This paper considers the problem of optimizing the average tracking error for an elliptic partial differential equation with an uncertain lognormal diffusion coefficient. In particular, the application of the multilevel quasi-Monte Carlo…
This position paper summarizes a recently developed research program focused on inference in the context of data centric science and engineering applications, and forecasts its trajectory forward over the next decade. Often one endeavours…
We introduce a new high-performance design for parallelism within the Quantum Monte Carlo code QMCPACK. We demonstrate that the new design is better able to exploit the hierarchical parallelism of heterogeneous architectures compared to the…