Related papers: Global sensitivity analysis in the context of impr…
We present an exact approach to analyze and quantify the sensitivity of higher moments of probabilistic loops with symbolic parameters, polynomial arithmetic and potentially uncountable state spaces. Our approach integrates methods from…
This work focuses on the simulation of $CO_2$ storage in deep underground formations under uncertainty and seeks to understand the impact of uncertainties in reservoir properties on $CO_2$ leakage. To simulate the process, a non-isothermal…
Neighborhood selection is a widely used method used for estimating the support set of sparse precision matrices, which helps determine the conditional dependence structure in undirected graphical models. However, reporting only point…
We propose to estimate a metamodel and the sensitivity indices of a complex model m in the Gaussian regression framework. Our approach combines methods for sensitivity analysis of complex models and statistical tools for sparse…
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…
Many problems in engineering and sciences require the solution of large scale optimization constrained by partial differential equations (PDEs). Though PDE-constrained optimization is itself challenging, most applications pose additional…
We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such…
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…
Machine learning (ML) surrogate models are increasingly used in engineering analysis and design to replace computationally expensive simulation models, significantly reducing computational cost and accelerating decision-making processes.…
This paper develops a systematic parametric method for analyzing stochastic systems under volatility uncertainty within the $G$-expectation framework. Leveraging the dual representation of the $G$-expectation as a supremum over a family of…
Gaussian processes (GPs) are frequently used in machine learning and statistics to construct powerful models. However, when employing GPs in practice, important considerations must be made, regarding the high computational burden,…
For models evaluated at a random set of independent variables, the variance-based Shapley effects range between Sobol' indices, and the corresponding total indices admit derivative-based upper-bounds. Such relationships fail when the inputs…
The Shapley effects are global sensitivity indices: they quantify the impact of each input variable on the output variable in a model. In this work, we suggest new estimators of these sensitivity indices. When the input distribution is…
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…
Global polynomial optimization is an important tool across applied mathematics, with many applications in operations research, engineering, and physical sciences. In various settings, the polynomials depend on external parameters that may…
This chapter makes a review, in a complete methodological framework, of various global sensitivity analysis methods of model output. Numerous statistical and probabilistic tools (regression, smoothing, tests, statistical learning, Monte…
Polynomial chaos expansion (PCE) is a versatile tool widely used in uncertainty quantification and machine learning, but its successful application depends strongly on the accuracy and reliability of the resulting PCE-based response…
Accurate prediction of remaining useful life under creep conditions is essential for the structural reliability of high-temperature components in critical engineering systems. Traditional approaches based on deterministic parametric models…
Stochastic expansion-based methods of uncertainty quantification, such as polynomial chaos and separated representations, require basis functions orthogonal with respect to the density of random inputs. Many modern engineering problems…
The PAWN index is gaining traction among the modelling community as a sensitivity measure. However, the robustness to its design parameters has not yet been scrutinized: the size ($N$) and sampling ($\varepsilon$) of the model output, the…