Related papers: Confidence intervals for sensitivity indices using…
Global sensitivity analysis of a numerical code, more specifically estimation of Sobol indices associated with input variables, generally requires a large number of model runs. When those demand too much computation time, it is necessary to…
The reduced basis method is a powerful model reduction technique designed to speed up the computation of multiple numerical solutions of parametrized partial differential equations. We consider a quantity of interest, which is a linear…
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…
The global sensitivity analysis of a complex numerical model often calls for the estimation of variance-based importance measures, named Sobol' indices. Metamodel-based techniques have been developed in order to replace the cpu…
Sobol' sensitivity indices allow to quantify the respective effects of random input variables and their combinations on the variance of mathematical model output. We focus on the problem of Sobol' indices estimation via a metamodeling…
The machine learning literature contains several constructions for prediction intervals that are intuitively reasonable but ultimately ad-hoc in that they do not come with provable performance guarantees. We present methods from the…
We present a novel and easy-to-use method for calibrating error-rate based confidence intervals to evidence-based support intervals. Support intervals are obtained from inverting Bayes factors based on a parameter estimate and its standard…
The offline time of the reduced basis method can be very long given a large training set of parameter samples. This usually happens when the system has more than two independent parameters. On the other hand, if the training set includes…
Variance-based sensitivity indices have established themselves as a reference among practitioners of sensitivity analysis of model output. It is not unusual to consider a variance-based sensitivity analysis as informative if it produces at…
Global sensitivity analysis of complex numerical models can be performed by calculating variance-based importance measures of the input variables, such as the Sobol indices. However, these techniques, requiring a large number of model…
Parametric model order reduction using reduced basis methods can be an effective tool for obtaining quickly solvable reduced order models of parametrized partial differential equation problems. With speedups that can reach several orders of…
In real case applications within the virtual prototyping process, it is not always possible to reduce the complexity of the physical models and to obtain numerical models which can be solved quickly. Usually, every single numerical…
Global sensitivity analysis is used to quantify the influence of uncertain input parameters on the response variability of a numerical model. The common quantitative methods are applicable to computer codes with scalar input variables. This…
Predictive models are often used for real-time decision making. However, typical machine learning techniques ignore feature evaluation cost, and focus solely on the accuracy of the machine learning models obtained utilizing all the features…
In the context of global sensitivity analysis, the Sobol' indices constitute a powerful tool for assessing the relative significance of the uncertain input parameters of a model. We herein introduce a novel approach for evaluating these…
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…
In the reduced basis method, the evaluation of the a posteriori estimator can become very sensitive to round-off errors. In this note, the origin of the loss of accuracy is revealed, and a solution to this problem is proposed and…
Data-driven risk analysis involves the inference of probability distributions from measured or simulated data. In the case of a highly reliable system, such as the electricity grid, the amount of relevant data is often exceedingly limited,…
We consider the computation of averaged coefficients for the homogenization of elliptic partial differential equations. In this problem, like in many multiscale problems, a large number of similar computations parametrized by the…
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…