A Tailored Convolutional Neural Network for Nonlinear Manifold Learning of Computational Physics Data Using Unstructured Spatial Discretizations

DOI10.1137/20M1344263OpenAlexW3091802587MaRDI QIDQ5005016

Kevin Potter, John Tencer

Publication date: 4 August 2021

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2006.06154

zbMATH Keywords

autoencodermanifold learningmodel order reductionconvolutional neural networkgraph convolution

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07) PDEs in connection with fluid mechanics (35Q35) Neural networks for/in biological studies, artificial life and related topics (92B20) PDEs in connection with mechanics of deformable solids (35Q74) PDEs in connection with classical thermodynamics and heat transfer (35Q79) PDEs in connection with computer science (35Q68)

Related Items (1)

A numerical comparison of simplified Galerkin and machine learning reduced order models for vaginal deformations

Uses Software

• ImageNet
• PDE-Net
• AlexNet
• Graclus

Cites Work

• Unnamed Item
• The GNAT method for nonlinear model reduction: effective implementation and application to computational fluid dynamics and turbulent flows
• A priori hyperreduction method: an adaptive approach
• Balanced truncation model reduction for systems with inhomogeneous initial conditions
• A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs
• A data-driven approximation of the koopman operator: extending dynamic mode decomposition
• A versatile sharp interface immersed boundary method for incompressible flows with complex boundaries
• Time-series learning of latent-space dynamics for reduced-order model closure
• Non-intrusive reduced order modeling of unsteady flows using artificial neural networks with application to a combustion problem
• Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data
• Recovering missing CFD data for high-order discretizations using deep neural networks and dynamics learning
• PDE-Net 2.0: learning PDEs from data with a numeric-symbolic hybrid deep network
• Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders
• Dimensional hyper-reduction of nonlinear finite element models via empirical cubature
• Diffusion maps
• Diffusion maps, spectral clustering and reaction coordinates of dynamical systems
• The method of proper orthogonal decomposition for dynamical characterization and order reduction of mechanical systems: an overview
• On dynamic mode decomposition: theory and applications
• High-order compact finite-difference methods on general overset grids
• Frequency-Limited Balanced Truncation with Low-Rank Approximations
• A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems
• Efficient non-linear model reduction via a least-squares Petrov-Galerkin projection and compressive tensor approximations
• The immersed boundary method
• Spectral analysis of nonlinear flows
• A Survey of Model Reduction by Balanced Truncation and Some New Results
• Laplacian Eigenmaps for Dimensionality Reduction and Data Representation
• Data-Driven, Physics-Based Feature Extraction from Fluid Flow Fields using Convolutional Neural Networks
• Nonlinear mode decomposition with convolutional neural networks for fluid dynamics
• Linearly Recurrent Autoencoder Networks for Learning Dynamics

This page was built for publication: A Tailored Convolutional Neural Network for Nonlinear Manifold Learning of Computational Physics Data Using Unstructured Spatial Discretizations