Physically interpretable machine learning algorithm on multidimensional non-linear fields

DOI10.1016/j.jcp.2020.110074OpenAlexW3030373417MaRDI QIDQ2128352

Cédric Goeury, Rem-Sophia Mouradi, Pablo Tassi, Olivier Thual, Fabrice Zaoui

Publication date: 21 April 2022

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2005.13912

zbMATH Keywords

polynomial chaos expansion (PCE)proper orthogonal decomposition (POD)geosciencesmachine learning (ML)data-driven model (DDM)dimensionality reduction (DM)

Mathematics Subject Classification ID

Computer science (68-XX) Information and communication theory, circuits (94-XX)

Related Items (1)

Proper orthogonal decomposition and physical field reconstruction with artificial neural networks (ANN) for supercritical flow problems

Uses Software

• Scikit
• ElemStatLearn

Cites Work

• Unnamed Item
• About the convergence of POD and EPOD modes computed from CFD simulation
• Time-dependent generalized polynomial chaos
• Adaptive sparse polynomial chaos expansion based on least angle regression
• Bootstrap methods for standard errors, confidence intervals, and other measures of statistical accuracy
• A stochastic projection method for fluid flow. II: Random process
• Modeling uncertainty in flow simulations via generalized polynomial chaos.
• Non-intrusive reduced order modeling of unsteady flows using artificial neural networks with application to a combustion problem
• Data-driven polynomial chaos expansion for machine learning regression
• Regression-based sparse polynomial chaos for uncertainty quantification of subsurface flow models
• PHYSICAL INTERPRETATION OF THE PROPER ORTHOGONAL MODES USING THE SINGULAR VALUE DECOMPOSITION
• Dynamic mode decomposition of numerical and experimental data
• Machine Learning for Fluid Mechanics
• Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures
• Turbulence and the dynamics of coherent structures. I. Coherent structures
• Physical Systems with Random Uncertainties: Chaos Representations with Arbitrary Probability Measure
• The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
• 10.1162/153244303322753616
• A Registration Method for Model Order Reduction: Data Compression and Geometry Reduction
• Definitions, methods, and applications in interpretable machine learning
• On Consistency and Sparsity for Principal Components Analysis in High Dimensions
• Error Analysis of the Dynamically Orthogonal Approximation of Time Dependent Random PDEs
• Understanding Machine Learning
• The Homogeneous Chaos
• A stochastic projection method for fluid flow. I: Basic formulation

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