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Monte Carlo simulation is often used for the reliability assessment of power systems, but it converges slowly when the system is complex. Multilevel Monte Carlo (MLMC) can be applied to speed up computation without compromises on model…
Methods for generating sequences of surrogates approximating fine scale models of two-phase random heterogeneous media are presented that are designed to adaptively control the modeling error in key quantities of interest (QoIs). For…
In multi-objective design tasks, the computational cost increases rapidly when high-fidelity simulations are used to evaluate objective functions. Surrogate models help mitigate this cost by approximating the simulation output, simplifying…
Many problems require to approximate an expected value by some kind of Monte Carlo (MC) sampling, e.g. molecular dynamics (MD) or simulation of stochastic reaction models (also termed kinetic Monte Carlo (kMC)). Often, we are furthermore…
We explore a hybrid technique to quantify the variability in the numerical solutions to a free boundary problem associated with magnetic equilibrium in axisymmetric fusion reactors amidst parameter uncertainties. The method aims at reducing…
We propose a multi-fidelity neural network surrogate sampling method for the uncertainty quantification of physical/biological systems described by ordinary or partial differential equations. We first generate a set of low/high-fidelity…
Emulating high-accuracy computationally expensive models is crucial for tasks requiring numerous model evaluations, such as uncertainty quantification and optimization. When lower-fidelity models are available, they can be used to improve…
A multi-fidelity surrogate model for highly nonlinear multiscale problems is proposed. It is based on the introduction of two different surrogate models and an adaptive on-the-fly switching. The two concurrent surrogates are built…
High-fidelity models are essential for accurately capturing nonlinear system dynamics. However, simulation of these models is often computationally too expensive and, due to their complexity, they are not directly suitable for analysis,…
Several methods have been proposed in the literature to solve reliability-based optimization problems, where failure probabilities are design constraints. However, few methods address the problem of life-cycle cost or risk optimization,…
The linear micro-instabilities driving turbulent transport in magnetized fusion plasmas (as well as the respective nonlinear saturation mechanisms) are known to be sensitive with respect to various physical parameters characterizing the…
The transition of the power grid requires new technologies and methodologies, which can only be developed and tested in simulations. Especially larger simulation setups with many levels of detail can become quite slow. Therefore, the number…
Metropolis Monte Carlo simulation is a powerful tool for studying the equilibrium properties of matter. In complex condensed-phase systems, however, it is difficult to design Monte Carlo moves with high acceptance probabilities that also…
Hybrid methods for simulating rarefied gas flows reduce computational cost by coupling a particle-based model, typically the direct simulation Monte Carlo (DSMC) method, to a continuum-based solver, i.e. a computational fluid dynamics (CFD)…
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,…
We present a hybrid sampling-surrogate approach for reducing the computational expense of uncertainty quantification in nonlinear dynamical systems. Our motivation is to enable rapid uncertainty quantification in complex mechanical systems…
Monte Carlo (MC) sampling is a popular method for estimating the statistics (e.g. expectation and variance) of a random variable. Its slow convergence has led to the emergence of advanced techniques to reduce the variance of the MC…
The equilibrium configuration of a plasma in an axially symmetric reactor is described mathematically by a free boundary problem associated with the celebrated Grad--Shafranov equation. The presence of uncertainty in the model parameters…
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…
Multifidelity Monte Carlo methods often rely on a preprocessing phase consisting of standard Monte Carlo sampling to estimate correlation coefficients between models of different fidelity to determine the weights and number of samples for…