Related papers: Efficient Representation of Uncertainty for Stocha…
We present a sampling-free approach for computing the epistemic uncertainty of a neural network. Epistemic uncertainty is an important quantity for the deployment of deep neural networks in safety-critical applications, since it represents…
The correlations of multiple renewable power plants (RPPs) should be fully considered in the power system with very high penetration renewable power integration. This paper models the uncertainties, spatial correlation of multiple RPPs…
Coupled problems with various combinations of multiple physics, scales, and domains can be found in numerous areas of science and engineering. A key challenge in the formulation and implementation of corresponding coupled models is to…
This article considers stochastic algorithms for efficiently solving a class of large scale non-linear least squares (NLS) problems which frequently arise in applications. We propose eight variants of a practical randomized algorithm where…
We investigate the Monte Carlo approach to propagation of experimental uncertainties within the context of the established "MSTW 2008" global analysis of parton distribution functions (PDFs) of the proton at next-to-leading order in the…
In the context of Monte Carlo sampling for lattice models, the complexity of the energy landscape often leads to Markov chains being trapped in local optima, thereby increasing the correlation between samples and reducing sampling…
Conservation laws in the form of elliptic and parabolic partial differential equations (PDEs) are fundamental to the modeling of many problems such as heat transfer and flow in porous media. Many of such PDEs are stochastic due to the…
Robust inference for stochastic dynamical systems is often hampered by sparse sampling and the absence of closed-form likelihoods. We introduce a Monte Carlo path-inference framework that leverages full-path statistics and bridge processes…
In applications of imprecise probability, analysts must compute lower (or upper) expectations, defined as the infimum of an expectation over a set of parameter values. Monte Carlo methods consistently approximate expectations at fixed…
Uncertainty quantification seeks to provide a quantitative means to understand complex systems that are impacted by parametric uncertainty. The polynomial chaos method is a computational approach to solve stochastic partial differential…
This paper introduces a new computational framework to account for uncertainties in day-ahead electricity market clearing process in the presence of demand response providers. A central challenge when dealing with many demand response…
The Diffusion Monte Carlo method with constant number of walkers, also called Stochastic Reconfiguration as well as Sequential Monte Carlo, is a widely used Monte Carlo methodology for computing the ground-state energy and wave function of…
Continuous-time random disturbances (also called stochastic excitations) due to increasing renewable generation have an increasing impact on power system dynamics; However, except from the Monte Carlo simulation, most existing methods for…
Through the Bayesian lens of data assimilation, uncertainty on model parameters is traditionally quantified through the posterior covariance matrix. However, in modern settings involving high-dimensional and computationally expensive…
Many random processes can be simulated as the output of a deterministic model accepting random inputs. Such a model usually describes a complex mathematical or physical stochastic system and the randomness is introduced in the input…
Computing systems interacting with real-world processes must safely and reliably process uncertain data. The Monte Carlo method is a popular approach for computing with such uncertain values. This article introduces a framework for…
We introduce a Monte Carlo algorithm to efficiently compute transport properties of chaotic dynamical systems. Our method exploits the importance sampling technique that favors trajectories in the tail of the distribution of displacements,…
Sample-based Bayesian inference provides a route to uncertainty quantification in the geosciences, and inverse problems in general, though is very computationally demanding in the naive form that requires simulating an accurate computer…
In this paper we introduce and discuss numerical schemes for the approximation of kinetic equations for flocking behavior with phase transitions that incorporate uncertain quantities. This class of schemes here considered make use of a…
Distortion risk measures play a critical role in quantifying risks associated with uncertain outcomes. Accurately estimating these risk measures in the context of computationally expensive simulation models that lack analytical tractability…