Related papers: Stochastic Optimization using Polynomial Chaos Exp…
Robustness analysis is very important in biology and neuroscience, to unravel behavioural patterns of systems that are conserved despite large parametric uncertainties. To make studies of probabilistic robustness more efficient and scalable…
We consider the effect of multiple stochastic parameters on the time-average quantities of chaotic systems. We employ the recently proposed \cite{Kantarakias_Papadakis_2023} sensitivity-enhanced generalized polynomial chaos expansion,…
We provide a novel computer-assisted technique for systematically analyzing first-order methods for optimization. In contrast with previous works, the approach is particularly suited for handling sublinear convergence rates and stochastic…
We present an optimization-based method to plan the motion of an autonomous robot under the uncertainties associated with dynamic obstacles, such as humans. Our method bounds the marginal risk of collisions at each point in time by…
Independent sampling of orthogonal polynomial bases via Monte Carlo is of interest for uncertainty quantification of models, using Polynomial Chaos (PC) expansions. It is known that bounding the spectral radius of a random matrix consisting…
For decades, uncertainty quantification techniques based on the spectral approach have been demonstrated to be computationally more efficient than the Monte Carlo method for a wide variety of problems, particularly when the dimensionality…
This paper proposes an adaptive sparse polynomial chaos expansion(PCE)-based method to quantify the impacts of uncertainties on critical clearing time (CCT) that is an important index in transient stability analysis. The proposed method can…
Presence of a high-dimensional stochastic parameter space with discontinuities poses major computational challenges in analyzing and quantifying the effects of the uncertainties in a physical system. In this paper, we propose a stochastic…
Growing uncertainty from renewable energy integration and distributed energy resources motivate the need for advanced tools to quantify the effect of uncertainty and assess the risks it poses to secure system operation. Polynomial chaos…
Differential equations with random parameters have gained significant prominence in recent years due to their importance in mathematical modelling and data assimilation. In many cases, random ordinary differential equations (RODEs) are…
This work introduces a method to equip data-driven polynomial chaos expansion surrogate models with intervals that quantify the predictive uncertainty of the surrogate. To that end, jackknife-based conformal prediction is integrated into…
This paper studies the utility of techniques within uncertainty quantification, namely spectral projection and polynomial chaos expansion, in reducing sampling needs for characterizing acoustic metamaterial dispersion band responses given…
Global polynomial optimization is an important tool across applied mathematics, with many applications in operations research, engineering, and physical sciences. In various settings, the polynomials depend on external parameters that may…
Numerical simulation of stochastic differential equations over long time intervals poses significant computational challenges. In this paper, we propose a novel recursive polynomial chaos evolution method that achieves model reduction…
A numerically efficient inverse method for parametric model uncertainty identification using maximum likelihood estimation is presented. The goal is to identify a probability model for a fixed number of model parameters based on a set of…
We analyze convergence rates of stochastic optimization procedures for non-smooth convex optimization problems. By combining randomized smoothing techniques with accelerated gradient methods, we obtain convergence rates of stochastic…
In complex and unknown processes, global models are initially generated over the entire experimental space but often fail to provide accurate predictions in local areas. A common approach is to use local models, which requires partitioning…
Polynomial chaos expansion (PCE) is a versatile tool widely used in uncertainty quantification and machine learning, but its successful application depends strongly on the accuracy and reliability of the resulting PCE-based response…
Optimal Bayesian design techniques provide an estimate for the best parameters of an experiment in order to maximize the value of measurements prior to the actual collection of data. In other words, these techniques explore the space of…
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…