Related papers: Global sensitivity analysis using derivative-based…
Traditionally, the sensitivity analysis of a Bayesian network studies the impact of individually modifying the entries of its conditional probability tables in a one-at-a-time (OAT) fashion. However, this approach fails to give a…
We propose a new statistical estimation framework for a large family of global sensitivity analysis indices. Our approach is based on rank statistics and uses an empirical correlation coefficient recently introduced by Chatterjee [9]. We…
In this paper we present a basis selection method that can be used with $\ell_1$-minimization to adaptively determine the large coefficients of polynomial chaos expansions (PCE). The adaptive construction produces anisotropic basis sets…
In surrogate modeling, polynomial chaos expansion (PCE) is popularly utilized to represent the random model responses, which are computationally expensive and usually obtained by deterministic numerical modeling approaches including finite…
Variance-based Sobol' sensitivity is one of the most well-known measures in global sensitivity analysis (GSA). However, uncertainties with certain distributions, such as highly skewed distributions or those with a heavy tail, cannot be…
We show how to apply Sobol's method of global sensitivity analysis to measure the influence exerted by a set of nodes' evidence on a quantity of interest expressed by a Bayesian network. Our method exploits the network structure so as to…
The surrogate model-based uncertainty quantification method has drawn much attention in many engineering fields. Polynomial chaos expansion (PCE) and deep learning (DL) are powerful methods for building a surrogate model. However, PCE needs…
Complex computer codes are widely used in science and engineering to model physical phenomena. Furthermore, it is common that they have a large number of input parameters. Global sensitivity analysis aims to identify those which have the…
Polynomial chaos expansions (PCE) allow us to propagate uncertainties in the coefficients of differential equations to the statistics of their solutions. Their main advantage is that they replace stochastic equations by systems of…
Sensitivity analysis plays an important role in the development of computer models/simulators through identifying the contribution of each (uncertain) input factor to the model output variability. This report investigates different aspects…
Development of new multiscale mathematical models often entails considerable complexity and multiple undetermined parameters, typically arising from closure relations. To enable reliable simulations, one must quantify how uncertain physical…
We propose and assess a new global (derivative-free) optimization algorithm, inspired by the LIPO algorithm, which uses variance-based sensitivity analysis (Sobol indices) to reduce the number of calls to the objective function. This method…
Polynomial chaos based methods enable the efficient computation of output variability in the presence of input uncertainty in complex models. Consequently, they have been used extensively for propagating uncertainty through a wide variety…
Generalized Polynomial Chaos (gPC) expansions are well established for forward uncertainty propagation in many application areas. Although the associated computational effort may be reduced in comparison to Monte Carlo techniques, for…
Given-data methods for variance-based sensitivity analysis have significantly advanced the feasibility of Sobol' index computation for computationally expensive models and models with many inputs. However, the limitations of existing…
The Trotter-Suzuki decomposition is one of the main approaches for realization of quantum simulations on digital quantum computers. Variance-based global sensitivity analysis (the Sobol method) is a wide used method which allows to…
This paper introduces an efficient sparse recovery approach for Polynomial Chaos (PC) expansions, which promotes the sparsity by breaking the dimensionality of the problem. The proposed algorithm incrementally explores sub-dimensional…
Global sensitivity analysis (GSA) aims at quantifying the contribution of input variables over the variability of model outputs. In the frame of functional outputs, a common goal is to compute sensitivity maps (SM), i.e sensitivity indices…
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…
The Sobol' indices are a recognized tool in global sensitivity analysis. When the uncertain variables in a model are statistically independent, the Sobol' indices may be easily interpreted and utilized. However, their interpretation and…