Related papers: Global Sensitivity Analysis via Multi-Fidelity Pol…
Frequency response functions (FRFs) are important for assessing the behavior of stochastic linear dynamic systems. For large systems, their evaluations are time-consuming even for a single simulation. In such cases, uncertainty…
Uncertainty quantification seeks to provide a quantitative means to understand complex systems that are impacted by parametric uncertainty. The polynomial chaos method is a computational approach to solve stochastic partial differential…
In the context of air quality control, our objective is to quantify the impact of uncertain inputs such as meteorological conditions and traffic parameters on pollutant dispersion maps. It is worth noting that the majority of sensitivity…
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…
Sensitivity analysis (SA) is a procedure for studying how sensitive are the output results of large-scale mathematical models to some uncertainties of the input data. The models are described as a system of partial differential equations.…
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…
Polynomial chaos expansions (PCEs) have been used in many real-world engineering applications to quantify how the uncertainty of an output is propagated from inputs. PCEs for models with independent inputs have been extensively explored in…
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…
In the framework of the estimation of safety margins in nuclear accident analysis, a quantitative assessment of the uncertainties tainting the results of computer simulations is essential. Accurate uncertainty propagation (estimation of…
It is well-known that Sobol indices, which count among the most popular sensitivity indices, are based on the Sobol decomposition. Here we challenge this construction by redefining Sobol indices without the Sobol decomposition. In fact, we…
Polynomial chaos expansions (PCE) are widely used in the framework of uncertainty quantification. However, when dealing with high dimensional complex problems, challenging issues need to be faced. For instance, high-order polynomials may be…
Many mathematical models involve input parameters, which are not precisely known. Global sensitivity analysis aims to identify the parameters whose uncertainty has the largest impact on the variability of a quantity of interest (output of…
Stochastic models are necessary for the realistic description of an increasing number of applications. The ability to identify influential parameters and variables is critical to a thorough analysis and understanding of the underlying…
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…
We introduce PoCET: a free and open-scource Polynomial Chaos Expansion Toolbox for Matlab, featuring the automatic generation of polynomial chaos expansion (PCE) for linear and nonlinear dynamic systems with time-invariant stochastic…
In global sensitivity analysis, the well known Sobol' sensitivity indices aim to quantify how the variance in the output of a mathematical model can be apportioned to the different variances of its input random variables. These indices are…
Surrogate modelling techniques have opened up new possibilities to overcome the limitations of computationally intensive numerical models in various areas of engineering and science. However, while fundamental in many engineering…
Models with high-dimensional parameter spaces are common in many applications. Global sensitivity analyses can provide insights on how uncertain inputs and interactions influence the outputs. Many sensitivity analysis methods face…
Computational inverse problems for biomedical simulators suffer from limited data and relatively high parameter dimensionality. This often requires sensitivity analysis, where parameters of the model are ranked based on their influence on…
One-dimensional Poincare inequalities are used in Global Sensitivity Analysis (GSA) to provide derivative-based upper bounds and approximations of Sobol indices. We add new perspectives by investigating weighted Poincare inequalities. Our…