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We introduce a data-driven dynamic factor framework for modeling the joint evolution of high-dimensional covariates and responses without parametric assumptions. Standard factor models applied to covariates alone often lose explanatory…

Machine Learning · Statistics 2026-01-16 Graeme Baker , Agostino Capponi , J. Antonio Sidaoui

We analyze an ensemble-based approach for uncertainty quantification (UQ) in atomistic neural networks. This method generates an epistemic uncertainty signal without requiring changes to the underlying multi-headed regression neural network…

Chemical Physics · Physics 2025-11-21 Idan Fonea , Amir Peles , Sivan Niv , Goren Gordon , Amir Natan

Manifold learning aims to discover and represent low-dimensional structures underlying high-dimensional data while preserving critical topological and geometric properties. Existing methods often fail to capture local details with global…

Machine Learning · Computer Science 2025-05-08 Ren Wang , Pengcheng Zhou

Nonlinear manifold learning algorithms, such as diffusion maps, have been fruitfully applied in recent years to the analysis of large and complex data sets. However, such algorithms still encounter challenges when faced with real data. One…

Mathematical Physics · Physics 2015-05-25 Carmeline J. Dsilva , Ronen Talmon , Ronald R. Coifman , Ioannis G. Kevrekidis

The present work addresses the issue of accurate stochastic approximations in high-dimensional parametric space using tools from uncertainty quantification (UQ). The basis adaptation method and its accelerated algorithm in polynomial chaos…

Numerical Analysis · Mathematics 2022-12-22 Xiaoshu Zeng , Roger Ghanem

Most uncertainty quantification (UQ) approaches provide a single scalar value as a measure of model reliability. However, different uncertainty measures could provide complementary information on the prediction confidence. Even measures…

This paper proposes and analyzes a novel clustering algorithm that combines graph-based diffusion geometry with techniques based on density and mode estimation. The proposed method is suitable for data generated from mixtures of…

Machine Learning · Statistics 2019-01-01 Mauro Maggioni , James M. Murphy

In recent years, large language models (LLMs) have become increasingly prevalent, offering remarkable text generation capabilities. However, a pressing challenge is their tendency to make confidently wrong predictions, highlighting the…

Computation and Language · Computer Science 2024-03-06 Xiang Gao , Jiaxin Zhang , Lalla Mouatadid , Kamalika Das

This paper studies the utility of techniques within uncertainty quantification, namely spectral projection and polynomial chaos expansion, in reducing sampling needs for characterizing acoustic metamaterial dispersion band responses given…

This paper deals with the applications of stochastic spectral methods for structural topology optimization in the presence of uncertainties. A non-intrusive polynomial chaos expansion is integrated into a topology optimization algorithm to…

Computational Engineering, Finance, and Science · Computer Science 2021-08-04 Nilton Cuellar , Anderson Pereira , Ivan F. M. Menezes , Americo Cunha

Uncertainty Quantification (UQ) research has primarily focused on closed-book factual question answering (QA), while contextual QA remains unexplored, despite its importance in real-world applications. In this work, we focus on UQ for the…

The recently introduced graph-accelerated non-intrusive polynomial chaos (NIPC) method has shown effectiveness in solving a broad range of uncertainty quantification (UQ) problems with multidisciplinary systems. It uses integration-based…

Computational Engineering, Finance, and Science · Computer Science 2024-05-10 Bingran Wang , Nicholas C. Orndorff , Mark Sperry , John T. Hwang

This article proposes an active learning method for high dimensional data, based on intrinsic data geometries learned through diffusion processes on graphs. Diffusion distances are used to parametrize low-dimensional structures on the…

Machine Learning · Computer Science 2019-05-31 Mauro Maggioni , James M. Murphy

In inverse problems, distribution-free uncertainty quantification (UQ) aims to obtain error bars with coverage guarantees that are independent of any prior assumptions about the data distribution. In the context of mass mapping,…

Cosmology and Nongalactic Astrophysics · Physics 2025-02-26 Hubert Leterme , Jalal Fadili , Jean-Luc Starck

Generative models for quantum data pose significant challenges but hold immense potential in fields such as chemoinformatics and quantum physics. Quantum denoising diffusion probabilistic models (QuDDPMs) enable efficient learning of…

Quantum Physics · Physics 2026-03-03 Quoc Hoan Tran , Koki Chinzei , Yasuhiro Endo , Hirotaka Oshima

The prohibitive cost of performing Uncertainty Quantification (UQ) tasks with a very large number of input parameters can be addressed, if the response exhibits some special structure that can be discovered and exploited. Several physical…

Computational Physics · Physics 2016-02-16 Ilias Bilionis , Rohit Tripathy , Marcial Gonzalez

Uncertainty quantification (UQ) is important for reliability assessment and enhancement of machine learning models. In deep learning, uncertainties arise not only from data, but also from the training procedure that often injects…

Machine Learning · Statistics 2023-11-13 Ziyi Huang , Henry Lam , Haofeng Zhang

Parameter identification is crucial in virtual engineering processes, yet determining appropriate system excitations for identifying specific parameters remains challenging. In practice, extensive experimental programs often fail to…

Optimization and Control · Mathematics 2026-05-07 Kevin Schmidt , Nicola Henkelmann , Christoph Mark , Johannes von Keler

Deep neural networks (DNNs) have achieved tremendous success in computer vision, natural language processing, and scientific and engineering domains. However, DNNs can make unexpected, incorrect, yet overconfident predictions, leading to…

Machine Learning · Computer Science 2025-12-16 Wenchong He , Zhe Jiang , Tingsong Xiao , Zelin Xu , Yukun Li

Deep unrolling is an emerging deep learning-based image reconstruction methodology that bridges the gap between model-based and purely deep learning-based image reconstruction methods. Although deep unrolling methods achieve…

Image and Video Processing · Electrical Eng. & Systems 2022-12-21 Canberk Ekmekci , Mujdat Cetin