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This study demonstrates the capabilities of several methods for analyzing the sensitivity of neural networks to perturbations of the input data and interpreting their underlying mechanisms. The investigated approaches include the Sobol…

Numerical Analysis · Mathematics 2025-04-22 Jiaxuan Miao , Sergey Matveev

Forecast verification plays a crucial role in the development cycle of operational numerical weather prediction models. At the same time, verification remains a challenge as the traditionally used non-spatial forecast quality metrics…

Atmospheric and Oceanic Physics · Physics 2026-05-25 Gregor Skok , Katarina Kosovelj

The variance-based method of global sensitivity indices based on Sobol sensitivity indices became very popular among practitioners due to its easiness of interpretation. For complex practical problems computation of Sobol indices generally…

Numerical Analysis · Mathematics 2016-06-03 Sergei Kucherenko , Shufang Song

In recent years two sets of planar (2D) shape attributes, provided with an intuitive physical meaning, were proposed to the remote sensing community by, respectively, Nagao & Matsuyama and Shackelford & Davis in their seminal works on the…

Computer Vision and Pattern Recognition · Computer Science 2017-02-03 Andrea Baraldi , João V. B. Soares

Driven by the critical challenges in biomanufacturing, including high complexity and high uncertainty, we propose a comprehensive and computationally efficient sensitivity analysis framework for general nonlinear policy-augmented knowledge…

Machine Learning · Statistics 2024-12-03 Junkai Zhao , Wei Xie , Jun Luo

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…

Bridge scour is a complex phenomenon combining hydrological, geotechnical and structural processes. Bridge scour is the leading cause of bridge collapse, which can bring catastrophic consequences including the loss of life. Estimating scour…

Applications · Statistics 2026-01-13 Gianna Gavriel , Maria Pregnolato , Francesca Pianosi , Theo Tryfonas , Paul Vardanega

The power-flow sensitivity coefficients (PFSCs) are widely used in the power system for expressing linearized dependencies between the controlled (i.e., the nodal voltages, lines currents) and control variables (e.g., active and reactive…

Systems and Control · Electrical Eng. & Systems 2023-12-18 Rahul Gupta

Superhydrophobic surfaces (SHS) have demonstrated significant potential in reducing turbulent drag by introducing slip conditions through micro-structured geometries. While previous studies have examined individual SHS configurations such…

Many multivariate functions in engineering models vary primarily along a few directions in the space of input parameters. When these directions correspond to coordinate directions, one may apply global sensitivity measures to determine the…

Numerical Analysis · Mathematics 2014-07-28 Paul G. Constantine , Eric Dow , Qiqi Wang

Machine learning methods, such as diffusion models, are widely explored as a promising way to accelerate high-fidelity fluid dynamics computation via a super-resolution process from faster-to-compute low-fidelity input. However, existing…

Computational Engineering, Finance, and Science · Computer Science 2025-12-24 Ruoyan Li , Zijie Huang , Haixin Wang , Guancheng Wan , Yizhou Sun , Wei Wang

Shallow flow models are used for a large number of applications including weather forecasting, open channel hydraulics and simulation-based natural hazard assessment. In these applications the shallowness of the process motivates…

Computational Physics · Physics 2021-08-09 Julia Kowalski , Manuel Torrilhon

Quantifying uncertainty in predictive simulations for real-world problems is of paramount importance - and far from trivial, mainly due to the large number of stochastic parameters and significant computational requirements. Adaptive sparse…

Computational Physics · Physics 2019-11-25 Ionut-Gabriel Farcas , Tobias Görler , Hans-Joachim Bungartz , Frank Jenko , Tobias Neckel

In this paper we extend the parametric sensitivity analysis (SA) methodology proposed in Ref. [Y. Pantazis and M. A. Katsoulakis, J. Chem. Phys. 138, 054115 (2013)] to continuous time and continuous space Markov processes represented by…

Information Theory · Computer Science 2014-12-22 Anastasios Tsourtis , Yannis Pantazis , Markos A. Katsoulakis , Vagelis Harmandaris

The stochastic variational approach for geophysical fluid dynamics was introduced by Holm (Proc Roy Soc A, 2015) as a framework for deriving stochastic parameterisations for unresolved scales. This paper applies the variational stochastic…

Fluid Dynamics · Physics 2022-09-16 Colin Cotter , Dan Crisan , Darryl D. Holm , Wei Pan , Igor Shevchenko

Various complex water management decisions are made in snow-dominant watersheds with the knowledge of Snow-Water Equivalent (SWE) -- a key measure widely used to estimate the water content of a snowpack. However, forecasting SWE is…

Variance-based global sensitivity analysis (GSA) can provide a wealth of information when applied to complex models. A well-known Achilles' heel of this approach is its computational cost which often renders it unfeasible in practice. An…

Numerical Analysis · Mathematics 2026-01-08 John Darges , Alen Alexanderian , Pierre Gremaud

Unobserved confounding is common in many applications, making causal inference from observational data challenging. As a remedy, causal sensitivity analysis is an important tool to draw causal conclusions under unobserved confounding with…

Machine Learning · Computer Science 2024-04-10 Dennis Frauen , Fergus Imrie , Alicia Curth , Valentyn Melnychuk , Stefan Feuerriegel , Mihaela van der Schaar

In nuclear engineering studies, uncertainty and sensitivity analyses of simulation computer codes can be faced to the complexity of the input and/or the output variables. If these variables represent a transient or a spatial phenomenon, the…

Applications · Statistics 2023-12-05 Anne-Laure Popelin , Bertrand Iooss

Randomized controlled trials (RCT's) allow researchers to estimate causal effects in an experimental sample with minimal identifying assumptions. However, to generalize or transport a causal effect from an RCT to a target population,…

Methodology · Statistics 2022-02-08 Melody Huang