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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

The declining response rates in probability surveys along with the widespread availability of unstructured data has led to growing research into non-probability samples. Existing robust approaches are not well-developed for non-Gaussian…

Methodology · Statistics 2022-03-29 Ali Rafei , Michael R. Elliott , Carol A. C. Flannagan

In recent years, surrogate models have been successfully used in likelihood-free inference to decrease the number of simulator evaluations. The current state-of-the-art performance for this task has been achieved by Bayesian Optimization…

Machine Learning · Computer Science 2021-10-06 Alexander Aushev , Henri Pesonen , Markus Heinonen , Jukka Corander , Samuel Kaski

This work presents a technique for statistically modeling errors introduced by reduced-order models. The method employs Gaussian-process regression to construct a mapping from a small number of computationally inexpensive `error indicators'…

Numerical Analysis · Computer Science 2015-04-16 Martin Drohmann , Kevin Carlberg

Fast machine learning-based surrogate models are trained to emulate slow, high-fidelity engineering simulation models to accelerate engineering design tasks. This introduces uncertainty as the surrogate is only an approximation of the…

Machine Learning · Statistics 2020-10-08 Paul Westermann , Ralph Evins

Active learning of Gaussian process (GP) surrogates has been useful for optimizing experimental designs for physical/computer simulation experiments, and for steering data acquisition schemes in machine learning. In this paper, we develop a…

Machine Learning · Computer Science 2025-09-10 Chiwoo Park , Robert Waelder , Bonggwon Kang , Benji Maruyama , Soondo Hong , Robert Gramacy

Uncertainty Quantification (UQ) is essential for the reliable application of computational models in engineering and science. Among surrogate modeling techniques, Gaussian Process Regression (GPR) is particularly valuable for its…

Computation · Statistics 2025-12-15 Jinglai Li , Hongqiao Wang

Gaussian processes (GPs) serve as flexible surrogates for complex surfaces, but buckle under the cubic cost of matrix decompositions with big training data sizes. Geospatial and machine learning communities suggest pseudo-inputs, or…

Methodology · Statistics 2021-02-05 D. Austin Cole , Ryan Christianson , Robert B. Gramacy

We introduce a novel adaptive Gaussian Process Regression (GPR) methodology for efficient construction of surrogate models for Bayesian inverse problems with expensive forward model evaluations. An adaptive design strategy focuses on…

Numerical Analysis · Mathematics 2024-05-01 Paolo Villani , Jörg Unger , Martin Weiser

Several applications such as nuclear forensics, nuclear fuel cycle simulations and sensitivity analysis require methods to quickly compute spent fuel nuclide compositions for various irradiation histories. Traditionally, this has been done…

Computational Physics · Physics 2021-03-16 Antonio Figueroa , Malte Goettsche

Limiting the injection rate to restrict the pressure below a threshold at a critical location can be an important goal of simulations that model the subsurface pressure between injection and extraction wells. The pressure is approximated by…

Excessive loads near wounds produce pathological scarring and other complications. Presently, stress cannot easily be measured by surgeons in the operating room. Instead, surgeons rely on intuition and experience. Predictive computational…

Medical Physics · Physics 2020-10-07 Casey Stowers , Taeksang Lee , Ilias Bilionis , Arun Gosain , Adrian Buganza Tepole

Machine learning surrogates are increasingly employed to replace expensive computational models for physics-based reliability analysis. However, their use introduces epistemic uncertainty from model approximation errors, which couples with…

Machine Learning · Computer Science 2025-09-24 Amirreza Tootchi , Xiaoping Du

Multidisciplinary design optimization methods aim at adapting numerical optimization techniques to the design of engineering systems involving multiple disciplines. In this context, a large number of mixed continuous, integer and…

Markov chain Monte Carlo methods for exponential family models with intractable normalizing constant, such as the exchange algorithm, require simulations of the sufficient statistics at every iteration of the Markov chain, which often…

Computation · Statistics 2023-02-21 Quan Vu , Matthew T. Moores , Andrew Zammit-Mangion

There is a high interest in accelerating multiscale models using data-driven surrogate modeling techniques. Creating a large training dataset encompassing all relevant load scenarios is essential for a good surrogate, yet the computational…

Numerical Analysis · Mathematics 2025-04-24 J. Storm , W. Sun , I. B. C. M. Rocha , F. P. van der Meer

This paper presents a physics and data co-driven surrogate modeling method for efficient rare event simulation of civil and mechanical systems with high-dimensional input uncertainties. The method fuses interpretable low-fidelity physical…

Computation · Statistics 2024-05-10 Jianhua Xian , Ziqi Wang

Global sensitivity analysis of complex numerical simulators is often limited by the small number of model evaluations that can be afforded. In such settings, surrogate models built from a limited set of simulations can substantially reduce…

Machine Learning · Statistics 2026-01-21 Guerlain Lambert , Céline Helbert , Claire Lauvernet

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

Sensor-based sorting systems enable the physical separation of a material stream into two fractions. The sorting decision is based on the image data evaluation of the sensors used and is carried out using actuators. Various process…

Machine Learning · Computer Science 2025-10-24 Felix Kronenwett , Georg Maier , Thomas Längle