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Operator learning (OL) has emerged as a powerful tool in scientific machine learning (SciML) for approximating mappings between infinite-dimensional functional spaces. One of its main applications is learning the solution operator of…

Machine Learning · Statistics 2025-08-29 Himanshu Sharma , Lukáš Novák , Michael D. Shields

In numerous applications, surrogate models are used as a replacement for accurate parameter-to-observable mappings when solving large-scale inverse problems governed by partial differential equations (PDEs). The surrogate model may be a…

Optimization and Control · Mathematics 2025-12-08 Ruanui Nicholson , Radoslav Vuchkov , Umberto Villa , Noemi Petra

The challenges for non-intrusive methods for Polynomial Chaos modeling lie in the computational efficiency and accuracy under a limited number of model simulations. These challenges can be addressed by enforcing sparsity in the series…

Machine Learning · Statistics 2020-06-24 Panagiotis Tsilifis , Iason Papaioannou , Daniel Straub , Fabio Nobile

We apply the Tensor Train (TT) approximation to construct the Polynomial Chaos Expansion (PCE) of a random field, and solve the stochastic elliptic diffusion PDE with the stochastic Galerkin discretization. We compare two strategies of the…

Numerical Analysis · Mathematics 2014-06-12 Sergey Dolgov , Boris N. Khoromskij , Alexander Litvinenko , Hermann G. Matthies

Human exposure induced by wireless communication systems increasingly draws the public attention. Here, an indoor down-link scenario is concerned and the exposure level is statistically analyzed. The electromagnetic field (EMF) emitted by a…

Applications · Statistics 2020-04-14 Zicheng Liu , Dominique Lesselier , Bruno Sudret , Joe Wiart

The Polynomial Chaos Expansion (PCE) technique recovers a finite second order random variable exploiting suitable linear combinations of orthogonal polynomials which are functions of a given stochas- tic quantity {\xi}, hence acting as a…

Computational Finance · Quantitative Finance 2016-10-31 Luca Di Persio , Michele Bonollo , Gregorio Pellegrini

Transmission expansion planning (TEP) plays a critical role in ensuring power system reliability and facilitating the integration of renewable energy resources. However, this process requires planners to constantly deal with significant…

Systems and Control · Electrical Eng. & Systems 2026-04-21 Victor Schmitt , Farzaneh Pourahmadi , Angela Flores-Quiroz , Pablo Apablaza , Pierluigi Mancarella

Learning data representations under uncertainty is an important task that emerges in numerous scientific computing and data analysis applications. However, uncertainty quantification techniques are computationally intensive and become…

Machine Learning · Computer Science 2025-08-06 Paz Fink Shustin , Shashanka Ubaru , Małgorzata J. Zimoń , Songtao Lu , Vasileios Kalantzis , Lior Horesh , Haim Avron

Many physics and engineering applications demand Partial Differential Equations (PDE) property evaluations that are traditionally computed with resource-intensive high-fidelity numerical solvers. Data-driven surrogate models provide an…

Machine Learning · Computer Science 2023-12-18 Raphaël Pestourie , Youssef Mroueh , Chris Rackauckas , Payel Das , Steven G. Johnson

This paper deals with some of the methodologies used to construct polynomial surrogate models based on generalized polynomial chaos (gPC) expansions for applications to uncertainty quantification (UQ) in aerodynamic computations. A core…

Fluid Dynamics · Physics 2018-03-14 Eric Savin , Andrea Resmini , Jacques Peter

In this contribution, we discuss the construction of Polynomial Chaos surrogates for Monte Carlo radiation transport applications via non-intrusive spectral projection. This contribution focuses on improvements with respect to the approach…

Numerical Analysis · Mathematics 2024-03-19 Gianluca Geraci , Kayla Clements , Aaron J Olson

Oilfield development related decisions are made using reservoir simulation-based optimization study in which different production scenarios and well controls are compared. Such simulations are computationally expensive and so surrogate…

Machine Learning · Computer Science 2022-03-01 Ajitabh Kumar

Software engineers often have to estimate the performance of a software system before having full knowledge of the system parameters, such as workload and operational profile. These uncertain parameters inevitably affect the accuracy of…

Software Engineering · Computer Science 2018-01-16 Aldeida Aleti , Catia Trubiani , André van Hoorn , Pooyan Jamshidi

We introduce a surrogate-based black-box optimization method, termed Polynomial-model-based optimization (PMBO). The algorithm alternates polynomial approximation with Bayesian optimization steps, using Gaussian processes to model the error…

Optimization and Control · Mathematics 2024-03-13 Janina Schreiber , Pau Batlle , Damar Wicaksono , Michael Hecht

Characterizing the interior structure of exoplanets is an inverse problem often solved using Bayesian inference, but this approach is hampered by the high computational cost of planetary structure models. To overcome this barrier, we…

Earth and Planetary Astrophysics · Physics 2025-12-22 Tijn De Wringer , Caroline Dorn , Emily O. Garvin , Stefano Marelli

Machine learning models play a vital role in time series forecasting. These models, however, often overlook an important element: point uncertainty estimates. Incorporating these estimates is crucial for effective risk management, informed…

Machine Learning · Computer Science 2024-09-11 Leonid Erlygin , Vladimir Zholobov , Valeriia Baklanova , Evgeny Sokolovskiy , Alexey Zaytsev

A surrogate model approximates the outputs of a solver of Partial Differential Equations (PDEs) with a low computational cost. In this article, we propose a method to build learning-based surrogates in the context of parameterized PDEs,…

Machine Learning · Computer Science 2024-06-28 Alejandro Ribés , Nawfal Benchekroun , Théo Delagnes

A surrogate model approximates a computationally expensive solver. Polynomial Chaos is a method to construct surrogate models by summing combinations of carefully chosen polynomials. The polynomials are chosen to respect the probability…

Numerical Analysis · Mathematics 2017-06-29 Thomas A. McCourt , Brodie Lawson , Fengde Zhou , Bevan Thompson , Stephen Tyson , Diane Donovan

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…

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