Related papers: An Efficient Non-Intrusive Uncertainty Propagation…

Employing Stochastic Nonlinear Model Predictive Control (SNMPC) for real-time applications is challenging due to the complex task of propagating uncertainties through nonlinear systems. This difficulty becomes more pronounced in…

In this paper, we develop an efficient numerical solver for unsteady diffusion-type partial differential equations with random coefficients. A major computational challenge in such problems lies in repeatedly handling large-scale linear…

Reflected diffusions in polyhedral domains are commonly used as approximate models for stochastic processing networks in heavy traffic. Stationary distributions of such models give useful information on the steady state performance of the…

A common way to simulate the transport and spread of pollutants in the atmosphere is via stochastic Lagrangian dispersion models. Mathematically, these models describe turbulent transport processes with stochastic differential equations…

We present a novel distributed Gauss-Newton method for the non-linear state estimation (SE) model based on a probabilistic inference method called belief propagation (BP). The main novelty of our work comes from applying BP sequentially…

Methods for quantifying the effects of uncertainties in hyperbolic problems can be divided into intrusive and non-intrusive techniques. Non-intrusive methods allow the usage of a given deterministic solver in a black-box manner, while being…

This work is concerned with the propagation of uncertainty across coupled domain problems with high-dimensional random inputs. A stochastic model reduction approach based on low-rank separated representations is proposed for the partitioned…

In this paper we propose a constrained guaranteed cost robust model predictive controller (GCMPC) for uncertain discrete time systems. This controller was developed based on a quadratic cost functional and guarantee robustness with respect…

This article discusses the uncertainty quantification (UQ) for time-independent linear and nonlinear partial differential equation (PDE)-based systems with random model parameters carried out using sampling-free intrusive stochastic…

Efficient treatment of systematic uncertainties that depend on a large number of nuisance parameters is a persistent difficulty in particle physics experiments. Where low-level effects are not amenable to simple parameterization or…

Uncertainty propagation in non-linear dynamical systems has become a key problem in various fields including control theory and machine learning. In this work we focus on discrete-time non-linear stochastic dynamical systems. We present a…

We present a novel uncertainty quantification approach for high-dimensional stochastic partial differential equations that reduces the computational cost of polynomial chaos methods by decomposing the computational domain into…

Methods such as non-intrusive polynomial chaos (NIPC), and stochastic collocation are frequently used for uncertainty propagation problems. Particularly for low-dimensional problems, these methods often use a tensor-product grid for…

Stochastic economic dispatch models address uncertainties in forecasts of renewable generation output by considering a finite number of realizations drawn from a stochastic process model, typically via Monte Carlo sampling. Accurate…

In this paper, we study the stochastic collocation (SC) methods for uncertainty quantification (UQ) in hyperbolic systems of nonlinear partial differential equations (PDEs). In these methods, the underlying PDEs are numerically solved at a…

This paper presents a novel approach for propagating uncertainties in dynamical systems building on high-order Taylor expansions of the flow and moment-generating functions (MGFs). Unlike prior methods that focus on Gaussian distributions,…

This work proposes a framework, embedded within the Performance Estimation framework (PEP), for obtaining worst-case performance guarantees on stochastic first-order methods. Given a first-order method, a function class, and a noise model…

We consider a fully discrete scheme for nonlinear stochastic partial differential equations with non-globally Lipschitz coefficients driven by multiplicative noise in a multi-dimensional setting. Our method uses a polynomial based spectral…

Nonlocal diffusion model provides an appropriate description of the diffusion process of solute in the complex medium, which cannot be described properly by classical theory of PDE. However, the operators in the nonlocal diffusion models…

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…