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We construct numerical integrators for Hamiltonian problems that may advantageously replace the standard Verlet time-stepper within Hybrid Monte Carlo and related simulations. Past attempts have often aimed at boosting the order of accuracy…
A higher-order change-of-measure multilevel Monte Carlo (MLMC) method is developed for computing weak approximations of the invariant measures of SDE with drift coefficients that do not satisfy the contractivity condition. This is achieved…
In many real-world engineering systems, the performance or reliability of the system is characterised by a scalar parameter. The distribution of this performance parameter is important in many uncertainty quantification problems, ranging…
Accurately and efficiently estimating system performance under uncertainty is paramount in power system planning and operation. Monte Carlo simulation is often used for this purpose, but convergence may be slow, especially when detailed…
The computational complexity of naive, sampling-based uncertainty quantification for 3D partial differential equations is extremely high. Multilevel approaches, such as multilevel Monte Carlo (MLMC), can reduce the complexity significantly,…
Model uncertainty sets are required in many robust optimization problems, such as robust control and prediction with uncertainty, but there is no definite methodology to generate uncertainty sets for nonlinear dynamical systems. In this…
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…
Partial differential equation is a powerful tool to characterize various physics systems. In practice, measurement errors are often present and probability models are employed to account for such uncertainties. In this paper, we present a…
When evolving in time the solution of a hyperbolic partial differential equation, it is often desirable to use high order strong stability preserving (SSP) time discretizations. These time discretizations preserve the monotonicity…
A real-time path integral Monte Carlo approach is developed to study the dynamics in a many-body quantum system until reaching a nonequilibrium stationary state. The approach is based on augmenting an exact reduced equation for the…
We propose a Multilevel Monte-Carlo (MLMC) method for computing entropy measure valued solutions of hyperbolic conservation laws. Sharp bounds for the narrow convergence of MLMC for the entropy measure valued solutions are proposed. An…
Uncertainty quantification (UQ) techniques are frequently used to ascertain output variability in systems with parametric uncertainty. Traditional algorithms for UQ are either system-agnostic and slow (such as Monte Carlo) or fast with…
This paper proposes a novel uncertainty quantification framework for computationally demanding systems characterized by a large vector of non-Gaussian uncertainties. It combines state-of-the-art techniques in advanced Monte Carlo sampling…
We consider a class of density-driven flow problems. We are particularly interested in the problem of the salinization of coastal aquifers. We consider the Henry saltwater intrusion problem with uncertain porosity, permeability, and…
Explicit stabilized methods are highly efficient time integrators for large and stiff systems of ordinary differential equations especially when applied to semi-discrete parabolic problems. However, when local spatial mesh refinement is…
Practical structural engineering problems often exhibit a significant degree of uncertainty in the material properties being used, the dimensions of the modeled structures, etc. In this paper, we consider a cantilever beam and a beam…
Multilevel sampling methods, such as multilevel and multifidelity Monte Carlo, multilevel stochastic collocation, or delayed acceptance Markov chain Monte Carlo, have become standard uncertainty quantification (UQ) tools for a wide class of…
We investigate the applicability of the well-known multilevel Monte Carlo (MLMC) method to the class of density-driven flow problems, in particular the problem of salinisation of coastal aquifers. As a test case, we solve the uncertain…
We review recent results on dimension-robust higher order convergence rates of Quasi-Monte Carlo Petrov-Galerkin approximations for response functionals of infinite-dimensional, parametric operator equations which arise in computational…
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…