DESCRIPTION OF RANDOM LEVEL SETS BY POLYNOMIAL CHAOS EXPANSIONS

被引：0

作者：

Bambach, Markus ^{[1
]}

Gerster, Stephan ^{[2
]}

Herty, Michael ^{[3
]}

Sikstel, Aleksey ^{[4
]}

机构：

[1] Swiss Fed Inst Technol, Adv Mfg Lab, CH-8005 Zurich, Switzerland

[2] Johannes Gutenberg Univ Mainz, Inst Math, D-55122 Mainz, Germany

[3] RWTH Aachen Univ Technol, Inst Geometrie & Prakt Math, D-52056 Aachen, Germany

[4] Tech Univ Darmstadt, Dept Math, D-64289 Darmstadt, Germany

来源：

COMMUNICATIONS IN MATHEMATICAL SCIENCES | 2024年 / 22卷 / 01期

关键词：

Level sets; uncertainty quantification; Hamilton-Jacobi equations; hyperbolic conser-vation laws; stochastic Galerkin; finite-volume method; HAMILTON-JACOBI EQUATIONS; STOCHASTIC GALERKIN METHOD; CONSERVATION-LAWS; VISCOSITY SOLUTIONS; SYSTEMS; PROPAGATION; IMAGES;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present a novel approach to determine the evolution of level sets under uncertainties in their velocity fields. This leads to a stochastic description of level sets. To compute the quantiles of random level sets, we use the stochastic Galerkin method for a hyperbolic reformulation of the equations for the propagation of level sets. A novel intrusive Galerkin formulation is presented and proven to be hyperbolic. It induces a corresponding finite-volume scheme that is specifically tailored to uncertain velocities.

引用

页码：95 / 112

页数：18

共 50 条

[21] Physics-informed polynomial chaos expansions
Novak, Lukas
Sharma, Himanshu
Shields, Michael D.
JOURNAL OF COMPUTATIONAL PHYSICS, 2024, 506
[22] Conformally mapped polynomial chaos expansions for Maxwell's source problem with random input data
Georg, Niklas
Roemer, Ulrich
INTERNATIONAL JOURNAL OF NUMERICAL MODELLING-ELECTRONIC NETWORKS DEVICES AND FIELDS, 2020, 33 (06)
[23] Reliability analysis of structures using polynomial chaos expansions
Zhang M.
Wang E.
Liu Y.
Qi W.
Wang D.
Qinghua Daxue Xuebao/Journal of Tsinghua University, 2022, 62 (08): : 1314 - 1320
[24] STOCHASTIC POLYNOMIAL CHAOS EXPANSIONS TO EMULATE STOCHASTIC SIMULATORS
Zhu, X.
Sudret, B.
INTERNATIONAL JOURNAL FOR UNCERTAINTY QUANTIFICATION, 2023, 13 (02) : 31 - 52
[25] Surrogate modeling based on resampled polynomial chaos expansions
Liu, Zicheng
Lesselier, Dominique
Sudret, Bruno
Wiart, Joe
RELIABILITY ENGINEERING & SYSTEM SAFETY, 2020, 202 (202)
[26] Sparse Polynomial Chaos Expansions: Literature Survey and Benchmark
Luethen, Nora
Marelli, Stefano
Sudret, Bruno
SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION, 2021, 9 (02): : 593 - 649
[27] Sequential Design of Experiment for Sparse Polynomial Chaos Expansions
Fajraoui, Noura
Marelli, Stefano
Sudret, Bruno
SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION, 2017, 5 (01): : 1085 - 1109
[28] Global sensitivity analysis using polynomial chaos expansions
Sudret, Bruno
RELIABILITY ENGINEERING & SYSTEM SAFETY, 2008, 93 (07) : 964 - 979
[29] Some greedy algorithms for sparse polynomial chaos expansions
Baptista, Ricardo
Stolbunov, Valentin
Nair, Prasanth B.
JOURNAL OF COMPUTATIONAL PHYSICS, 2019, 387 : 303 - 325
[30] Polynomial chaos for simulating random volatilities
Pulch, Roland
van Emmerich, Cathrin
MATHEMATICS AND COMPUTERS IN SIMULATION, 2009, 80 (02) : 245 - 255

← 1 2 3 4 5 →