Related papers: Surrogate-based multilevel Monte Carlo methods for…
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 magnetic confinement fusion devices, the equilibrium configuration of a plasma is determined by the balance between the hydrostatic pressure in the fluid and the magnetic forces generated by an array of external coils and the plasma…
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…
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…
Multiscale simulations utilizing high-fidelity, microscopic Monte Carlo models to provide the nonlinear response for continuum models can easily become computationally intractable. Surrogate models for the high-fidelity Monte Carlo models…
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…
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…
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…
Uncertainty quantification (UQ) is an active area of research, and an essential technique used in all fields of science and engineering. The most common methods for UQ are Monte Carlo and surrogate-modelling. The former method is…
Stochastic unit commitment models typically handle uncertainties in forecast demand by considering a finite number of realizations from a stochastic process model for loads. Accurate evaluations of expectations or higher moments for the…
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…
Plasma kinetic equations exhibit pronounced sensitivity to microscopic perturbations in model parameters and data, making reliable and efficient uncertainty quantification (UQ) essential for predictive simulations. However, the cost of…
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,…
While generally considered computationally expensive, Uncertainty Quantification using Monte Carlo sampling remains beneficial for applications with uncertainties of high dimension. As an extension of the naive Monte Carlo method, the…
Due to the need for robust uncertainty quantification, Bayesian neural learning has gained attention in the era of deep learning and big data. Markov Chain Monte-Carlo (MCMC) methods typically implement Bayesian inference which faces…
We propose an efficient surrogate modeling technique for uncertainty quantification. The method is based on a well-known dimension-adaptive collocation scheme. We improve the scheme by enhancing sparse polynomial surrogates with conformal…
In this work we consider a class of uncertainty quantification problems where the system performance or reliability is characterized by a scalar parameter $y$. The performance parameter $y$ is random due to the presence of various sources…
Multilevel Monte Carlo (MLMC) is a flexible and effective variance reduction technique for accelerating reliability assessments of complex power system. Recently, data-driven surrogate models have been proposed as lower-level models in the…
A parallel cut-cell algorithm is described to solve the free-boundary problem of the Grad-Shafranov equation. The algorithm reformulates the free-boundary problem in an irregular bounded domain and its important aspects include a searching…
Subsurface flow problems usually involve some degree of uncertainty. Consequently, uncertainty quantification is commonly necessary for subsurface flow prediction. In this work, we propose a methodology for efficient uncertainty…