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Related papers: Hierarchical adaptive polynomial chaos expansions

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In this work, we consider optimal control problems constrained by elliptic partial differential equations (PDEs) with lognormal random coefficients, which are represented by a countably infinite-dimensional random parameter with i.i.d.…

Numerical Analysis · Mathematics 2019-03-14 Peng Chen , Omar Ghattas

Physics-informed polynomial chaos expansions (PC$^2$) provide an efficient physically constrained surrogate modeling framework by embedding governing equations and other physical constraints into the standard data-driven polynomial chaos…

Machine Learning · Statistics 2025-12-12 Qitian Lu , Himanshu Sharma , Michael D. Shields , Lukáš Novák

This work introduces a method to equip data-driven polynomial chaos expansion surrogate models with intervals that quantify the predictive uncertainty of the surrogate. To that end, jackknife-based conformal prediction is integrated into…

Methodology · Statistics 2025-12-18 Dimitrios Loukrezis , Dimitris G. Giovanis

Solving sparse linear systems from discretized PDEs is challenging. Direct solvers have in many cases quadratic complexity (depending on geometry), while iterative solvers require problem dependent preconditioners to be robust and…

Numerical Analysis · Mathematics 2017-03-14 Kai Yang , Hadi Pouransari , Eric Darve

Materials exhibiting a substitutional disorder such as multicomponent alloys and mixed metal oxides/oxyfluorides are of great importance in many scientific and technological sectors. Disordered materials constitute an overwhelmingly large…

We introduce PoCET: a free and open-scource Polynomial Chaos Expansion Toolbox for Matlab, featuring the automatic generation of polynomial chaos expansion (PCE) for linear and nonlinear dynamic systems with time-invariant stochastic…

Systems and Control · Electrical Eng. & Systems 2020-07-13 Felix Petzke , Ali Mesbah , Stefan Streif

Compressive sensing has become a powerful addition to uncertainty quantification in recent years. This paper identifies new bases for random variables through linear mappings such that the representation of the quantity of interest is more…

Statistics Theory · Mathematics 2016-03-08 Xiu Yang , Huan Lei , Nathan A. Baker , Guang Lin

High-dimensional linear contextual bandit problems remain a significant challenge due to the curse of dimensionality. Existing methods typically consider either the model parameters to be sparse or the eigenvalues of context covariance…

Statistics Theory · Mathematics 2025-10-10 Rui Zhao , Zihan Chen , Zemin Zheng

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

In recent years, the use of sparse recovery techniques in the approximation of high-dimensional functions has garnered increasing interest. In this work we present a survey of recent progress in this emerging topic. Our main focus is on the…

Numerical Analysis · Mathematics 2017-06-12 Ben Adcock , Simone Brugiapaglia , Clayton G. Webster

Presence of a high-dimensional stochastic parameter space with discontinuities poses major computational challenges in analyzing and quantifying the effects of the uncertainties in a physical system. In this paper, we propose a stochastic…

Numerical Analysis · Mathematics 2018-08-01 Anindya Bhaduri , Yanyan He , Michael D. Shields , Lori Graham-Brady , Robert M. Kirby

Accurate modeling of radio wave propagation over irregular terrains is crucial for designing reliable wireless communication systems in such environments, yet uncertainties in the antenna configuration are not quantified within…

Signal Processing · Electrical Eng. & Systems 2026-03-04 Sicheng An , Luca Di Rienzo , Hao Qin , Xingqi Zhang , Lorenzo Codecasa

A quantitative first-principles description of complex substitutional materials like alloys is challenging due to the vast number of configurations and the high computational cost of solving the quantum-mechanical problem. Therefore,…

Materials Science · Physics 2025-06-24 Adrian Stroth , Claudia Draxl , Santiago Rigamonti

Many natural optimization problems derived from $\sf NP$ admit bilevel and multilevel extensions in which decisions are made sequentially by multiple players with conflicting objectives, as in interdiction, adversarial selection, and…

Computational Complexity · Computer Science 2026-02-16 Christoph Grüne , Berit Johannes , James B. Orlin , Lasse Wulf

We develop a novel algorithm, Predictive Hierarchical Clustering (PHC), for agglomerative hierarchical clustering of current procedural terminology (CPT) codes. Our predictive hierarchical clustering aims to cluster subgroups, not…

Methodology · Statistics 2017-08-03 Elizabeth C. Lorenzi , Stephanie L. Brown , Zhifei Sun , Katherine Heller

An integrated optimization method based on the constrained multi-objective evolutionary algorithm (MOEA) and non-intrusive polynomial chaos expansion (PCE) is proposed, which solves robust multi-objective optimization problems under…

Neural and Evolutionary Computing · Computer Science 2022-09-29 Yuji Takubo , Masahiro Kanazaki

We extend the concept of polynomial time approximation algorithms to apply to problems for hierarchically specified graphs, many of which are PSPACE-complete. Assuming P != PSPACE, the existence or nonexistence of such efficient…

Combinatorics · Mathematics 2016-09-06 Madhav V. Marathe , Harry B. Hunt , S. S. Ravi

In this letter, we compare three polynomial chaos expansion (PCE)-based methods for ANCOVA (ANalysis of COVAriance) indices based global sensitivity analysis for correlated random inputs in two power system applications. Surprisingly, the…

Signal Processing · Electrical Eng. & Systems 2023-07-17 Xiaoting Wang , Rong-Peng Liu , Xiaozhe Wang , François Bouffard

Coupled problems with various combinations of multiple physics, scales, and domains can be found in numerous areas of science and engineering. A key challenge in the formulation and implementation of corresponding coupled models is to…

Analysis of PDEs · Mathematics 2012-07-05 Maarten Arnst , Roger Ghanem , Eric Phipps , John Red-Horse

In this work, we extend the sparse iterative covariance-based estimator (SPICE), by generalizing the formulation to allow for different norm constraints on the signal and noise parameters in the covariance model. For a given norm, the…

Methodology · Statistics 2017-04-21 Johan Swärd , Stefan Ingi Adalbjörnsson , Andreas Jakobsson
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