Skip to main content
OSTI.GOVU.S. Department of Energy Office of Scientific and Technical Information
U.S. Department of Energy
Office of Scientific and Technical Information
 

Nonlinear proper orthogonal decomposition for convection-dominated flows

Journal Article · · Physics of Fluids
DOI:https://doi.org/10.1063/5.0074310· OSTI ID:1978997
 [1];  [1];  [2];  [3]
  1. Oklahoma State University, Stillwater, OK (United States)
  2. Norwegian University of Science and Technology, Trondheim (Norway); SINTEF Digital, Trondheim (Norway)
  3. Virginia Polytechnic Institute and State University (Virginia Tech), Blacksburg, VA (United States)
+ Show Author Affiliations
Autoencoder techniques find increasingly common use in reduced order modeling as a means to create a latent space. This reduced order representation offers a modular data-driven modeling approach for nonlinear dynamical systems when integrated with a time series predictive model. In this Letter, we put forth a nonlinear proper orthogonal decomposition (POD) framework, which is an end-to-end Galerkin-free model combining autoencoders with long short-term memory networks for dynamics. By eliminating the projection error due to the truncation of Galerkin models, a key enabler of the proposed nonintrusive approach is the kinematic construction of a nonlinear mapping between the full-rank expansion of the POD coefficients and the latent space where the dynamics evolve. We test our framework for model reduction of a convection-dominated system, which is generally challenging for reduced order models. Our approach not only improves the accuracy, but also significantly reduces the computational cost of training and testing.
Research Organization:
Oklahoma State University, Stillwater, OK (United States)
Sponsoring Organization:
National Science Foundation (NSF); USDOE; USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
Grant/Contract Number:
SC0019290
Other Award/Contract Number:
DMS-2012255
DMS-2012253
OSTI ID:
1978997
Alternate ID(s):
OSTI ID: 1833438
Journal Information:
Physics of Fluids, Journal Name: Physics of Fluids Journal Issue: 12 Vol. 33; ISSN 1070-6631
Publisher:
American Institute of Physics (AIP)Copyright Statement
Country of Publication:
United States
Language:
English

References (42)

Nonlinear principal component analysis using autoassociative neural networks journal February 1991
Principal interval decomposition framework for POD reduced-order modeling of convective Boussinesq flows: PRINCIPAL INTERVAL DECOMPOSITION MODEL REDUCTION FRAMEWORK journal February 2015
An autoencoder‐based reduced‐order model for eigenvalue problems with application to neutron diffusion
  • Phillips, Toby R. F.; Heaney, Claire E.; Smith, Paul N.
  • International Journal for Numerical Methods in Engineering, Vol. 122, Issue 15 https://doi.org/10.1002/nme.6681
journal May 2021
A priori analysis on deep learning of subgrid-scale parameterizations for Kraichnan turbulence journal January 2020
Convolutional neural networks for fluid flow analysis: toward effective metamodeling and low dimensionalization journal August 2021
Prediction of aerodynamic flow fields using convolutional neural networks journal June 2019
Decay of the Kolmogorov N -width for wave problems journal October 2019
Multi-level convolutional autoencoder networks for parametric prediction of spatio-temporal dynamics journal December 2020
Application of reduced-order models based on PCA & Kriging for the development of digital twins of reacting flow applications journal February 2019
Temporal Fusion Transformers for interpretable multi-horizon time series forecasting journal October 2021
Recovering missing CFD data for high-order discretizations using deep neural networks and dynamics learning journal October 2019
Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders journal November 2019
PhyGeoNet: Physics-informed geometry-adaptive convolutional neural networks for solving parameterized steady-state PDEs on irregular domain journal March 2021
Nonlinear principal component analysis of noisy data journal May 2007
A long short-term memory embedding for hybrid uplifted reduced order models journal August 2020
Latent-space time evolution of non-intrusive reduced-order models using Gaussian process emulation journal February 2021
pyNIROM—A suite of python modules for non-intrusive reduced order modeling of time-dependent problems journal November 2021
Nonlinear mode decomposition with convolutional neural networks for fluid dynamics journal November 2019
Sparse identification of nonlinear dynamics with low-dimensionalized flow representations journal September 2021
A deep learning enabler for nonintrusive reduced order modeling of fluid flows journal August 2019
Exploration and prediction of fluid dynamical systems using auto-encoder technology journal June 2020
Convolutional neural network based hierarchical autoencoder for nonlinear mode decomposition of fluid field data journal September 2020
Reduced-order modeling of advection-dominated systems with recurrent neural networks and convolutional autoencoders journal March 2021
Reduced order model using convolutional auto-encoder with self-attention journal July 2021
Model fusion with physics-guided machine learning: Projection-based reduced-order modeling journal June 2021
On closures for reduced order models—A spectrum of first-principle to machine-learned avenues journal September 2021
Data-driven discovery of coordinates and governing equations journal October 2019
Quantum system compression: A Hamiltonian guided walk through Hilbert space journal January 2021
Nonintrusive reduced order modeling framework for quasigeostrophic turbulence journal November 2019
Deep learning to discover and predict dynamics on an inertial manifold journal June 2020
Learning a reduced basis of dynamical systems using an autoencoder journal September 2021
Digital Twin: Values, Challenges and Enablers From a Modeling Perspective journal January 2020
Latent Space Physics: Towards Learning the Temporal Evolution of Fluid Flow journal May 2019
Linearly Recurrent Autoencoder Networks for Learning Dynamics journal January 2019
Physics-Informed Probabilistic Learning of Linear Embeddings of Nonlinear Dynamics with Guaranteed Stability journal January 2020
A New Look at Proper Orthogonal Decomposition journal January 2003
Nonlinear Principal Component Analysis by Neural Networks: Theory and Application to the Lorenz System journal February 2000
Non-intrusive reduced-order modeling for fluid problems: A brief review journal December 2019
Multifidelity computing for coupling full and reduced order models journal February 2021
Breaking the Kolmogorov Barrier in Model Reduction of Fluid Flows journal February 2020
Lagrangian Reduced Order Modeling Using Finite Time Lyapunov Exponents journal October 2020
Nonlinear principal component analysis by neural networks journal January 2001

Similar Records

Reduced-order modeling of advection-dominated systems with recurrent neural networks and convolutional autoencoders
Journal Article · Thu Mar 04 19:00:00 EST 2021 · Physics of Fluids · OSTI ID:1840551

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
Boussinesq approximation
Navier Stokes equations
artificial neural networks
computational methods
computational physics
machine learning
nonlinear systems
reduced dimensions forms
statistical analysis
thermal effects