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The effect of uncertainties and noise on a quantity of interest (model output) is often better described by its probability density function (PDF) than by its moments. Although density estimation is a common task, the adequacy of…

Numerical Analysis · Mathematics 2019-06-21 Adi Ditkowski , Gadi Fibich , Amir Sagiv

[Abridged] We propose a solution to the problem of quickly and accurately predicting gravitational waveforms within any given physical model. The method is relevant for both real-time applications and in more traditional scenarios where the…

General Relativity and Quantum Cosmology · Physics 2014-07-23 Scott E. Field , Chad R. Galley , Jan S. Hesthaven , Jason Kaye , Manuel Tiglio

The need to rapidly solve PDEs in engineering design workflows has spurred the rise of neural surrogate models. In particular, neural operator models provide a discretization-invariant surrogate by retaining the infinite-dimensional,…

Machine Learning · Computer Science 2026-02-12 Yash Patel , Ambuj Tewari

Optimization problems with nonlinear cost functions and combinatorial constraints appear in many real-world applications but remain challenging to solve efficiently compared to their linear counterparts. To bridge this gap, we propose…

Machine Learning · Computer Science 2023-07-20 Aaron Ferber , Taoan Huang , Daochen Zha , Martin Schubert , Benoit Steiner , Bistra Dilkina , Yuandong Tian

Gaussian process surrogates are a popular alternative to directly using computationally expensive simulation models. When the simulation output consists of many responses, dimension-reduction techniques are often employed to construct these…

Methodology · Statistics 2023-05-04 Moses Y-H. Chan , Matthew Plumlee , Stefan M. Wild

Complex black-box predictive models may have high accuracy, but opacity causes problems like lack of trust, lack of stability, sensitivity to concept drift. On the other hand, interpretable models require more work related to feature…

Machine Learning · Computer Science 2019-03-01 Alicja Gosiewska , Aleksandra Gacek , Piotr Lubon , Przemyslaw Biecek

The widespread adoption of machine learning surrogate models has significantly improved the scale and complexity of systems and processes that can be explored accurately and efficiently using atomistic modeling. However, the inherently…

Chemical Physics · Physics 2025-03-13 Federico Grasselli , Sanggyu Chong , Venkat Kapil , Silvia Bonfanti , Kevin Rossi

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

Machine learning can significantly improve performance for decision-making under uncertainty across a wide range of domains. However, ensuring robustness guarantees requires well-calibrated uncertainty estimates, which can be difficult to…

Machine Learning · Computer Science 2026-02-03 Christopher Yeh , Nicolas Christianson , Alan Wu , Adam Wierman , Yisong Yue

Surrogate models are often used as computationally efficient approximations to complex simulation models, enabling tasks such as solving inverse problems, sensitivity analysis, and probabilistic forward predictions, which would otherwise be…

Machine Learning · Statistics 2026-05-13 Philipp Reiser , Paul-Christian Bürkner , Anneli Guthke

Forecasting surgical instrument trajectories and predicting the next surgical action recently started to attract attention from the research community. Both these tasks are crucial for automation and assistance in endoscopy surgery. Given…

Computer Vision and Pattern Recognition · Computer Science 2025-03-13 Sara Sangalli , Gary Sarwin , Ertunc Erdil , Alessandro Carretta , Victor Staartjes , Carlo Serra , Ender Konukoglu

In engineering, uncertainty propagation aims to characterise system outputs under uncertain inputs. For interval uncertainty, the goal is to determine output bounds given interval-valued inputs, which is critical for robust design…

Machine Learning · Computer Science 2026-03-24 Ghifari Adam Faza , Jolan Wauters , Fabio Cuzzolin , Hans Hallez , David Moens

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

Structured prediction involves learning to predict complex structures rather than simple scalar values. The main challenge arises from the non-Euclidean nature of the output space, which generally requires relaxing the problem formulation.…

Machine Learning · Statistics 2024-11-19 Junjie Yang , Matthieu Labeau , Florence d'Alché-Buc

Surrogate modeling is a powerful methodology in chemical process engineering, frequently employed to accelerate optimization tasks where traditional flowsheet simulators are computationally prohibitive. However, the state-of-the-art is…

Computational Engineering, Finance, and Science · Computer Science 2025-09-30 Martin Bubel , Tobias Seidel , Michael Bortz

Gaussian processes (GPs) are a Bayesian machine learning approach widely used to construct surrogate models for the uncertainty quantification of computer simulation codes in industrial applications. It provides both a mean predictor and an…

Leveraging neural networks as surrogate models for turbulence simulation is a topic of growing interest. At the same time, embodying the inherent uncertainty of simulations in the predictions of surrogate models remains very challenging.…

Fluid Dynamics · Physics 2024-10-10 Qiang Liu , Nils Thuerey

Conformal prediction is a framework for uncertainty quantification that constructs prediction sets for previously unseen data, guaranteeing coverage of the true label with a specified probability. However, the efficiency of these prediction…

Machine Learning · Computer Science 2026-01-06 Erfan Hajihashemi , Yanning Shen

Computational models provide crucial insights into complex biological processes such as cancer evolution, but their mechanistic nature often makes them nonlinear and parameter-rich, complicating calibration. We systematically evaluate…

Analysis of PDEs · Mathematics 2025-09-24 Christina Schenk , Jacobo Ayensa Jiménez , Ignacio Romero

This paper introduces Fast Calibrated Explanations, a method designed for generating rapid, uncertainty-aware explanations for machine learning models. By incorporating perturbation techniques from ConformaSight - a global explanation…

Machine Learning · Computer Science 2024-10-29 Tuwe Löfström , Fatima Rabia Yapicioglu , Alessandra Stramiglio , Helena Löfström , Fabio Vitali
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