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This work proposes a statistically enhanced framework to address the instability and limited predictive capability of conventional Galerkin-Proper Orthogonal Decomposition (Galerkin-POD) models. The method reformulates the correction of the…

Fluid Dynamics · Physics 2026-04-15 Bijie Yang , Chengyuan Liu , Lu Tian , Yuping Qian , Mingyang Yang

Posterior distributions on parameters computed from experimental data using Bayesian techniques are only as accurate as the models used to construct them. In many applications these models are incomplete, which both reduces the prospects of…

General Relativity and Quantum Cosmology · Physics 2015-06-23 Christopher J. Moore , Jonathan R. Gair

We present an approach to the simulation of quantum systems driven by classical stochastic processes that is based on the polynomial chaos expansion, a well-known technique in the field of uncertainty quantification. The polynomial chaos…

Quantum Physics · Physics 2013-12-17 Kevin C. Young , Matthew D. Grace

Local volatility is an important quantity in option pricing, portfolio hedging, and risk management. It is not directly observable from the market; hence calibrations of local volatility models are necessary using observable market data.…

Applications · Statistics 2022-05-18 Kai Yin , Anirban Mondal

In this paper is proposed a novel incremental iterative Gauss-Newton-Markov-Kalman filter method for state estimation of dynamic models given noisy measurements. The mathematical formulation of the proposed filter is based on the…

Optimization and Control · Mathematics 2019-09-17 Bojana Rosic

In this paper, we study the generalized polynomial chaos (gPC) based stochastic Galerkin method for the linear semiconductor Boltzmann equation under diffusive scaling and with random inputs from an anisotropic collision kernel and the…

Analysis of PDEs · Mathematics 2018-02-19 Liu Liu

Optimization problems with uncertain black-box constraints, modeled by warped Gaussian processes, have recently been considered in the Bayesian optimization setting. This work introduces a new class of constraints in which the same…

Optimization and Control · Mathematics 2020-06-16 Johannes Wiebe , Inês Cecílio , Jonathan Dunlop , Ruth Misener

Uncertainty quantification is essential when dealing with ill-conditioned inverse problems due to the inherent nonuniqueness of the solution. Bayesian approaches allow us to determine how likely an estimation of the unknown parameters is…

Machine Learning · Statistics 2020-01-16 Ali Siahkoohi , Gabrio Rizzuti , Felix J. Herrmann

In this paper, we study porous media flows in heterogeneous stochastic media. We propose an efficient forward simulation technique that is tailored for variational Bayesian inversion. As a starting point, the proposed forward simulation…

Applications · Statistics 2018-02-12 Keren Yang , Nilabja Guha , Yalchin Efendiev , Bani K. Mallick

The Kalman filter is an established tool for the analysis of dynamic systems with normally distributed noise, and it has been successfully applied in numerous application areas. It provides sequentially calculated estimates of the system…

Systems and Control · Computer Science 2016-10-26 S. Eichstädt , N. Makarava , C. Elster

Reliable spatial uncertainty evaluation of object detection models is of special interest and has been subject of recent work. In this work, we review the existing definitions for uncertainty calibration of probabilistic regression tasks.…

Machine Learning · Computer Science 2022-08-22 Fabian Küppers , Jonas Schneider , Anselm Haselhoff

Bayesian hierarchical models can provide efficient algorithms for finding sparse solutions to ill-posed inverse problems. The models typically comprise a conditionally Gaussian prior model for the unknown which is augmented by a generalized…

Numerical Analysis · Mathematics 2025-01-09 Jonathan Lindbloom , Jan Glaubitz , Anne Gelb

Calibration or parameter identification is used with computational mechanics models related to observed data of the modeled process to find model parameters such that good similarity between model prediction and observation is achieved. We…

Computational Engineering, Finance, and Science · Computer Science 2022-12-26 Harald Willmann , Jonas Nitzler , Sebastian Brandstaeter , Wolfgang A. Wall

Gaussian process regression is widely applied in computational science and engineering for surrogate modeling owning to its kernel-based and probabilistic nature. In this work, we propose a Bayesian approach that integrates the variability…

Machine Learning · Computer Science 2025-01-03 Dongwei Ye , Weihao Yan , Christoph Brune , Mengwu Guo

A probabilistic performance-oriented controller design approach based on polynomial chaos expansion and optimization is proposed for flight dynamic systems. Unlike robust control techniques where uncertainties are conservatively handled,…

Systems and Control · Electrical Eng. & Systems 2021-04-20 Dalong Shi , Xiang Fang , Florian Holzapfel

Parameter calibration is essential for reducing uncertainty and improving predictive fidelity in physics-based models, yet it is often limited by the high computational cost of model evaluations. Bayesian calibration methods provide a…

Methodology · Statistics 2026-01-21 Maike F. Holthuijzen , Atlanta Chakraborty , Elizabeth Krath , Tommie Catanach

The large-scale integration of renewable energy sources introduces significant operational uncertainty into power systems. Although Polynomial Chaos Expansion (PCE) provides an efficient tool for uncertainty quantification (UQ) in power…

Systems and Control · Electrical Eng. & Systems 2026-03-24 Le Fang , Wangkun Xu , Fei Teng

Gaussian graphical models, where it is assumed that the variables of interest jointly follow a multivariate normal distribution with a sparse precision matrix, have been used to study intrinsic dependence among variables, but the normality…

Methodology · Statistics 2020-05-20 Jami J. Mulgrave , Subhashis Ghosal

The study of uncertainty propagation is of fundamental importance in plasma physics simulations. To this end, in the present work we propose a novel stochastic Galerkin (sG) particle {method} for collisional kinetic models of plasmas under…

Numerical Analysis · Mathematics 2023-03-22 Andrea Medaglia , Lorenzo Pareschi , Mattia Zanella

We introduce a Bayesian approach to predictive density calibration and combination that accounts for parameter uncertainty and model set incompleteness through the use of random calibration functionals and random combination weights.…

Applications · Statistics 2016-10-26 Federico Bassetti , Roberto Casarin , Francesco Ravazzolo