相关论文: Data-driven sparse polynomial chaos expansion for …

A probabilistic performance-oriented controller design approach based on polynomial chaos expansion and optimization is proposed for flight dynamic systems. Unlike robust control techniques where uncertainties are conservatively handled,…

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 paper proposes a novel computationally efficient dynamic bi-orthogonality based approach for calibration of a computer simulator with high dimensional parametric and model structure uncertainty. The proposed method is based on a…

This paper introduces a novel method for approximating the dynamics of a large autonomous system projected onto a fixed subspace. The core contribution is a novel recursive algorithm to construct an effective time-dependent generator that…

This article is devoted to providing a review of mathematical formulations in which Polynomial Chaos Theory (PCT) has been incorporated into stochastic model predictive control (SMPC). In the past decade, PCT has been shown to provide a…

The authors present a Polynomial Chaos (PC)-based Bayesian inference method for quantifying the uncertainties of the K-Profile Parametrization (KPP) within the MIT General Circulation Model (MITgcm) of the tropical pacific. The inference of…

In this contribution, we discuss the construction of Polynomial Chaos surrogates for Monte Carlo radiation transport applications via non-intrusive spectral projection. This contribution focuses on improvements with respect to the approach…

As non-institutive polynomial chaos expansion (PCE) techniques have gained growing popularity among researchers, we here provide a comprehensive review of major sampling strategies for the least squares based PCE. Traditional sampling…

We analyze a practical algorithm for sparse PCA on incomplete and noisy data under a general non-random sampling scheme. The algorithm is based on a semidefinite relaxation of the $\ell_1$-regularized PCA problem. We provide theoretical…

We consider the numerical approximation of different ordinary differential equations (ODEs) and partial differential equations (PDEs) with periodic boundary conditions involving a one-dimensional random parameter, comparing the intrusive…

Data-driven control based on the fundamental lemma by Willems et al. is frequently considered for deterministic LTI systems subject to measurement noise. However, besides measurement noise, stochastic disturbances might also directly affect…

We apply the Tensor Train (TT) approximation to construct the Polynomial Chaos Expansion (PCE) of a random field, and solve the stochastic elliptic diffusion PDE with the stochastic Galerkin discretization. We compare two strategies of the…

The discovery of Partial Differential Equations (PDEs) is an essential task for applied science and engineering. However, data-driven discovery of PDEs is generally challenging, primarily stemming from the sensitivity of the discovered…

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…

Multivariate global polynomial approximations - such as polynomial chaos or stochastic collocation methods - are now in widespread use for sensitivity analysis and uncertainty quantification. The pseudospectral variety of these methods uses…

Polynomial chaos is a powerful technique for propagating uncertainty through ordinary and partial differential equations. Random variables are expanded in terms of orthogonal polynomials and differential equations are derived for the…

In an ever-increasing interest for Machine Learning (ML) and a favorable data development context, we here propose an original methodology for data-based prediction of two-dimensional physical fields. Polynomial Chaos Expansion (PCE),…

Data-driven discovery of partial differential equations (PDEs) has attracted increasing attention in recent years. Although significant progress has been made, certain unresolved issues remain. For example, for PDEs with high-order…

Microgrids (MGs) are regarded as effective solutions to provide ramping support to the main grid during heavy-load periods. Nevertheless, the uncertain renewable energy sources (RES) and electric vehicles (EVs) integrated into an MG may…

Inducing-point-based sparse variational Gaussian processes have become the standard workhorse for scaling up GP models. Recent advances show that these methods can be improved by introducing a diagonal scaling matrix to the conditional…