Related papers: Deep Polynomial Chaos Expansion
The challenges for non-intrusive methods for Polynomial Chaos modeling lie in the computational efficiency and accuracy under a limited number of model simulations. These challenges can be addressed by enforcing sparsity in the series…
We propose a Dynamical generalized Polynomial Chaos (DgPC) method to solve time-dependent stochastic partial differential equations (SPDEs) with white noise forcing. The long-time simulation of SPDE solutions by Polynomial Chaos (PC)…
Constructing surrogate models for uncertainty quantification (UQ) on complex partial differential equations (PDEs) having inherently high-dimensional $\mathcal{O}(10^{\ge 2})$ stochastic inputs (e.g., forcing terms, boundary conditions,…
Compressive sampling has been widely used for sparse polynomial chaos (PC) approximation of stochastic functions. The recovery accuracy of compressive sampling highly depends on the incoherence properties of the measurement matrix. In this…
In this work we introduce a manifold learning-based surrogate modeling framework for uncertainty quantification in high-dimensional stochastic systems. Our first goal is to perform data mining on the available simulation data to identify a…
In this paper we propose an algorithm for recovering sparse orthogonal polynomials using stochastic collocation. Our approach is motivated by the desire to use generalized polynomial chaos expansions (PCE) to quantify uncertainty in models…
This paper addresses the Bayesian calibration of dynamic models with parametric and structural uncertainties, in particular where the uncertain parameters are unknown/poorly known spatio-temporally varying subsystem models. Independent…
This work suggests an interpolation-based stochastic collocation method for the non-intrusive and adaptive construction of sparse polynomial chaos expansions (PCEs). Unlike pseudo-spectral projection and regression-based stochastic…
We present an algorithm for computing sparse, least squares-based polynomial chaos expansions, incorporating both adaptive polynomial bases and sequential experimental designs. The algorithm is employed to approximate stochastic…
Gradient-enhanced Uncertainty Quantification (UQ) has received recent attention, in which the derivatives of a Quantity of Interest (QoI) with respect to the uncertain parameters are utilized to improve the surrogate approximation.…
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…
Increasing frequency and intensity of extreme weather events motivates the assessment of power system resilience. The random nature of power system failures during these events mandates probabilistic resilience assessment, but…
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…
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,…
Methods based on polynomial chaos expansion allow to approximate the behavior of systems with uncertain parameters by deterministic dynamics. These methods are used in a wide range of applications, spanning from simulation of uncertain…
Accurate modeling of radio wave propagation over irregular terrains is crucial for designing reliable wireless communication systems in such environments, yet uncertainties in the antenna configuration are not quantified within…
Sequential generative models conditioned on uncertain rewards are central to AI-driven scientific discovery, yet the epistemic uncertainty they inherit from imperfect reward estimates remains unquantified. We propagate this uncertainty…
This paper presents an approach for estimating Shapley effects for use as global sensitivity metrics to quantify the relative importance of uncertain model parameters. Polynomial Chaos expansion, a well established approach for developing…
Orthogonal polynomial approximations form the foundation to a set of well-established methods for uncertainty quantification known as polynomial chaos. These approximations deliver models for emulating physical systems in a variety of…
As uncertainty and sensitivity analysis of complex models grows ever more important, the difficulty of their timely realizations highlights a need for more efficient numerical operations. Non-intrusive Polynomial Chaos methods are highly…