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Surrogate modeling of costly mathematical models representing physical systems is challenging since it is typically not possible to create a large experimental design. Thus, it is beneficial to constrain the approximation to adhere to the…

Machine Learning · Computer Science 2023-09-06 Lukáš Novák , Himanshu Sharma , Michael D. Shields

In many mechanistic medical, biological, physical and engineered spatiotemporal dynamic models the numerical solution of partial differential equations (PDEs) can make simulations impractically slow. Biological models require the…

Soft Condensed Matter · Physics 2021-02-11 J. Quetzalcóatl Toledo-Marín , Geoffrey Fox , James P. Sluka , James A. Glazier

Deep surrogate models for parametric partial differential equations (PDEs) can deliver high-fidelity approximations but remain prohibitively data-hungry: training often requires thousands of fine-grid simulations, each incurring substantial…

Machine Learning · Computer Science 2026-03-03 Yang Meng , Ruoxi Jiang , Zhuokai Zhao , Chong Liu , Rebecca Willett , Yuxin Chen

Structural reliability methods aim at computing the probability of failure of systems with respect to some prescribed performance functions. In modern engineering such functions usually resort to running an expensive-to-evaluate…

Methodology · Statistics 2011-05-10 V. Dubourg , F. Deheeger , B. Sudret

Reliability analysis is a sub-field of uncertainty quantification that assesses the probability of a system performing as intended under various uncertainties. Traditionally, this analysis relies on deterministic models, where experiments…

Computation · Statistics 2026-05-19 Anderson V. Pires , Maliki Moustapha , Stefano Marelli , Bruno Sudret

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

Running a reliability analysis on engineering problems involving complex numerical models can be computationally very expensive, requiring advanced simulation methods to reduce the overall numerical cost. Gaussian process based active…

Machine Learning · Statistics 2020-12-01 Morgane Menz , Sylvain Dubreuil , Jérôme Morio , Christian Gogu , Nathalie Bartoli , Marie Chiron

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

In the context of uncertainty quantification, computational models are required to be repeatedly evaluated. This task is intractable for costly numerical models. Such a problem turns out to be even more severe for stochastic simulators, the…

Computation · Statistics 2022-11-29 X. Zhu , B. Sudret

Estimating the probability of rare failure events is an essential step in the reliability assessment of engineering systems. Computing this failure probability for complex non-linear systems is challenging, and has recently spurred the…

Machine Learning · Computer Science 2022-02-10 P. -R. Wagner , S. Marelli , I. Papaioannou , D. Straub , B. Sudret

Data-driven surrogate models are widely used for applications such as design optimization and uncertainty quantification, where repeated evaluations of an expensive simulator are required. For most partial differential equation (PDE)…

Computational Physics · Physics 2019-10-18 Wei Xing , Robert M. Kirby , Shandian Zhe

A problem of considerable importance within the field of uncertainty quantification (UQ) is the development of efficient methods for the construction of accurate surrogate models. Such efforts are particularly important to applications…

Computational Physics · Physics 2019-03-01 Rohit Tripathy , Ilias Bilionis

Partial Least Squares (PLS) is a widely used method for data integration, designed to extract latent components shared across paired high-dimensional datasets. Despite decades of practical success, a precise theoretical understanding of its…

Machine Learning · Statistics 2025-12-18 Victor Léger , Florent Chatelain

High-dimensional, heterogeneous data with complex feature interactions pose significant challenges for traditional predictive modeling approaches. While Projection to Latent Structures (PLS) remains a popular technique, it struggles to…

Machine Learning · Computer Science 2025-10-21 Farwa Abbas , Hussain Ahmad , Claudia Szabo

To tackle the curse of dimensionality and multicollinearity problems of polynomial chaos expansion for analyzing global sensitivity and reliability of models with high stochastic dimensions, this paper proposes a novel non-intrusive…

Numerical Analysis · Mathematics 2024-12-20 Ling-Ze Bu , Wei Zhao , Wei Wang

Accurate surrogate construction for PDE-driven high-dimensional rare-event simulation is challenging when performance evaluations are expensive. Since a globally accurate surrogate may require many high-fidelity evaluations, adaptive…

Numerical Analysis · Mathematics 2026-05-18 Zhiwei Gao , George Karniadakis

This paper considers the creation of parametric surrogate models for applications in science and engineering where the goal is to predict high-dimensional spatiotemporal output quantities of interest, such as pressure, temperature and…

Computational Physics · Physics 2022-03-24 Chi Hoang , Kenny Chowdhary , Kookjin Lee , Jaideep Ray

We present a scalable framework for learning deterministic and probabilistic neural surrogates for high-resolution 3D physics simulations. We introduce a hybrid CNN-Transformer backbone architecture targeted for 3D physics simulations,…

Machine Learning · Computer Science 2025-10-09 Benjamin Holzschuh , Georg Kohl , Florian Redinger , Nils Thuerey

Polynomial chaos expansions (PCEs) have been used in many real-world engineering applications to quantify how the uncertainty of an output is propagated from inputs. PCEs for models with independent inputs have been extensively explored in…

Systems and Control · Electrical Eng. & Systems 2021-06-02 Zhanlin Liu , Youngjun Choe

Failure probability evaluation for complex physical and engineering systems governed by partial differential equations (PDEs) are computationally intensive, especially when high-dimensional random parameters are involved. Since standard…

Numerical Analysis · Mathematics 2019-08-06 Ke Li , Kejun Tang , Jinglai Li , Tianfan Wu , Qifeng Liao