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Efficient surrogate modelling is a key requirement for uncertainty quantification in data-driven scenarios. In this work, a novel approach of using Sparse Random Features for surrogate modelling in combination with self-supervised…

Machine Learning · Computer Science 2023-01-02 Maternus Herold , Anna Veselovska , Jonas Jehle , Felix Krahmer

Background: Scatterometry is a fast, indirect and non-destructive optical method for quality control in the production of lithography masks. To solve the inverse problem in compliance with the upcoming need for improved accuracy, a…

Data Analysis, Statistics and Probability · Physics 2020-05-12 Nando Farchmin , Martin Hammerschmidt , Philipp-Immanuel Schneider , Matthias Wurm , Bernd Bodermann , Markus Bär , Sebastian Heidenreich

Polynomial expansions are important in the analysis of neural network nonlinearities. They have been applied thereto addressing well-known difficulties in verification, explainability, and security. Existing approaches span classical Taylor…

Machine Learning · Computer Science 2021-11-25 Mauro J. Sanchirico , Xun Jiao , C. Nataraj

A novel approach for non-intrusive uncertainty propagation is proposed. Our approach overcomes the limitation of many traditional methods, such as generalised polynomial chaos methods, which may lack sufficient accuracy when the quantity of…

Numerical Analysis · Mathematics 2018-03-20 Yous van Halder , Benjamin Sanderse , Barry Koren

Crash simulations play an essential role in improving vehicle safety, design optimization, and injury risk estimation. Unfortunately, numerical solutions of such problems using state-of-the-art high-fidelity models require significant…

Machine Learning · Computer Science 2024-02-16 Jonas Kneifl , Jörg Fehr , Steven L. Brunton , J. Nathan Kutz

Assessing the safety and environmental impacts of subsurface resource exploitation and management is critical and requires robust geomechanical modeling. However, uncertainties stemming from model assumptions, intrinsic variability of…

Numerical Analysis · Mathematics 2025-02-19 Caterina Millevoi , Claudia Zoccarato , Massimiliano Ferronato

In this paper we present applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. According to variational approach in the general case we have the solution as a…

Accelerator Physics · Physics 2009-10-31 Antonina N. Fedorova , Michael G. Zeitlin , Zohreh Parsa

Multivariate global polynomial approximations - such as polynomial chaos or stochastic collocation methods - are now in widespread use for sensitivity analysis and uncertainty quantification. The pseudospectral variety of these methods uses…

Numerical Analysis · Mathematics 2013-04-09 Paul G. Constantine , Michael S. Eldred , Eric T. Phipps

Accurate modeling of radio wave propagation over irregular terrains is crucial for designing reliable wireless communication systems in such environments, yet uncertainties in the antenna configuration are not quantified within…

Signal Processing · Electrical Eng. & Systems 2026-03-04 Sicheng An , Luca Di Rienzo , Hao Qin , Xingqi Zhang , Lorenzo Codecasa

This paper proposes a new algorithm for compensating external disturbances for class of multi-channel linear systems. The solution to this problem is based on the use of the internal model principle and the extended error adaptation…

Systems and Control · Electrical Eng. & Systems 2023-10-12 V. H. Bui , A. A. Margun

This work proposes an adaptive framework to solve a robust structural shape optimization problem governed by linear elasticity models that account for uncertainties in the loading and material inputs. A posteriori error estimators are…

Optimization and Control · Mathematics 2026-02-06 Oğuz Han Altıntaş , Hamdullah Yücel

Recent studies have shown that chaotic maps are well-suited for applications requiring unpredictable behaviour, making them a valuable tool for enhancing unpredictability and complexity. A method is developed using 3D parametric equations…

Chaotic Dynamics · Physics 2024-10-25 Harisankar R , Abhishek Kaushik , Sishu Shankar Muni

We present a new adaptive method for electronic structure calculations based on novel fast algorithms for reduction of multivariate mixtures. In our calculations, spatial orbitals are maintained as Gaussian mixtures whose terms are selected…

Numerical Analysis · Mathematics 2019-06-19 Gregory Beylkin , Lucas Monzon , Xinshuo Yang

Extreme response assessment is important in the design and operation of engineering structures, and is a crucial part of structural risk and reliability analyses. Structures should be designed in a way that enables them to withstand the…

Computation · Statistics 2025-03-04 Sebastian Winter , Christian Agrell , Juan Camilo Guevara Gómez , Erik Vanem

Adaptive designs are increasingly used in clinical trials and online experiments to improve participant outcomes by dynamically updating treatment allocation as data accumulate. In practice, experimenters often consider multiple candidate…

Methodology · Statistics 2026-04-08 Wenxin Zhang , Aaron Hudson , Maya Petersen , Mark van der Laan

This paper extends the subjects dicussed in the Data Analysis and Dynamical Systems courses by looking at the subject of modelling data. This task is nontrivial as the underlying process could be non-linear. In the paper some common…

Statistics Theory · Mathematics 2011-08-02 Vincent Mellor

Orthogonal polynomial approximations form the foundation to a set of well-established methods for uncertainty quantification known as polynomial chaos. These approximations deliver models for emulating physical systems in a variety of…

Computational Engineering, Finance, and Science · Computer Science 2022-03-23 Chun Yui Wong , Pranay Seshadri , Andrew B. Duncan , Ashley Scillitoe , Geoffrey Parks

In modern engineering, physical processes are modelled and analysed using advanced computer simulations, such as finite element models. Furthermore, concepts of reliability analysis and robust design are becoming popular, hence, making…

Methodology · Statistics 2017-03-20 Roland Schöbi , Bruno Sudret

Highly accurate datasets from numerical or physical experiments are often expensive and time-consuming to acquire, posing a significant challenge for applications that require precise evaluations, potentially across multiple scenarios and…

Machine Learning · Computer Science 2026-02-06 Paolo Conti , Mengwu Guo , Attilio Frangi , Andrea Manzoni

Compressive sampling has been widely used for sparse polynomial chaos (PC) approximation of stochastic functions. The recovery accuracy of compressive sampling highly depends on the incoherence properties of the measurement matrix. In this…

Computation · Statistics 2018-10-17 Negin Alemazkoor , Hadi Meidani