Recovering missing CFD data for high-order discretizations using deep neural networks and dynamics learning

@article{Carlberg2018RecoveringMC,
  title={Recovering missing CFD data for high-order discretizations using deep neural networks and dynamics learning},
  author={Kevin T. Carlberg and Antony Jameson and Mykel J. Kochenderfer and Jeremy Morton and Liqian Peng and Freddie D. Witherden},
  journal={ArXiv},
  year={2018},
  volume={abs/1812.01177}
}
View PDF on arXiv
42 Citations
Highly Influential Citations
2
Background Citations
12
Methods Citations
12

Figures from this paper

42 Citations

Enabling Nonlinear Manifold Projection Reduced-Order Models by Extending Convolutional Neural Networks to Unstructured Data

A nonlinear manifold learning technique based on deep autoencoders that is appropriate for model order reduction of physical systems in complex geometries and shows better than an order of magnitude improvement in accuracy over linear subspace methods.

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

A nonlinear manifold learning technique based on deep convolutional autoencoders that is appropriate for model order reduction of physical systems in complex geometries and shows better than an order of magnitude improvement in accuracy over linear methods.

Assessment of unsteady flow predictions using hybrid deep learning based reduced-order models

Two deep learning-based hybrid data-driven reduced order models for the prediction of unsteady fluid flows are presented, and an observer-corrector method for the calculation of integrated pressure force coefficients on the fluid-solid boundary on a reference grid is introduced.

Machine learning for fluid flow reconstruction from limited measurements

Shallow Learning for Fluid Flow Reconstruction with Limited Sensors and Limited Data

This work proposes a shallow neural network-based learning methodology for fluid flow reconstruction that learns an end-to-end mapping between the sensor measurements and the high-dimensional fluid flow field, without any heavy preprocessing on the raw data.

Non-intrusive reduced-order modeling using uncertainty-aware Deep Neural Networks and Proper Orthogonal Decomposition: Application to flood modeling

Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders

Shallow neural networks for fluid flow reconstruction with limited sensors

This work proposes a shallow neural network-based learning methodology for fluid flow reconstruction that learns an end-to-end mapping between the sensor measurements and the high-dimensional fluid flow field, without any heavy preprocessing on the raw data.

Non-intrusive nonlinear model reduction via machine learning approximations to low-dimensional operators

This work proposes a method that enables traditionally intrusive reduced-order models to be accurately approximated in a non-intrusive manner using modern machine-learning regression techniques, and demonstrates the effectiveness of the proposed technique on two types of PDEs.

Non-intrusive Nonlinear Model Reduction via Machine Learning Approximations to Low-dimensional Operators

This work proposes a method that enables traditionally intrusive reduced-order models to be accurately approximated in a non-intrusive man-ner, and demonstrates the effectiveness of the proposed technique on two types of PDEs.

References

SHOWING 1-10 OF 64 REFERENCES

Latent Space Physics: Towards Learning the Temporal Evolution of Fluid Flow

It is demonstrated for the first time that dense 3D+time functions of physics system can be predicted within the latent spaces of neural networks, and the method arrives at a neural‐network based simulation algorithm with significant practical speed‐ups.

Parallel implementation of large-scale CFD data compression toward aeroacoustic analysis

Galerkin v. least-squares Petrov-Galerkin projection in nonlinear model reduction

A Kernel-Based Approach to Data-Driven Koopman Spectral Analysis

The resulting approximations of the leading Koopman eigenvalues, eigenfunctions, and modes are both more accurate and less sensitive to the distribution of the data used in the computation than those produced by Dynamic Mode Decomposition.

Deep learning for universal linear embeddings of nonlinear dynamics

It is often advantageous to transform a strongly nonlinear system into a linear one in order to simplify its analysis for prediction and control, so the authors combine dynamical systems with deep learning to identify these hard-to-find transformations.

A study on CFD data compression using hybrid supercompact wavelets

A hybrid method with supercompact multiwavelets is suggested as an efficient and practical method to compress CFD dataset and allows high data compression ratio for fluid simulation data.

Gappy data and reconstruction procedures for flow past a cylinder

This work investigates the possibility of using proper orthogonal decomposition (POD) in reconstructing complete flow fields from gappy data and finds that for the two lower levels of gappiness both the temporal and spatial POD modes can be recovered accurately leading to a very accurate representation of the velocity field.

Linearly-Recurrent Autoencoder Networks for Learning Dynamics

A new neural network architecture combining an autoencoder with linear recurrent dynamics in the encoded state is used to learn a low-dimensional and highly informative Koopman-invariant subspace of observables.

Deep Dynamical Modeling and Control of Unsteady Fluid Flows

The proposed approach, grounded in Koopman theory, is shown to produce stable dynamical models that can predict the time evolution of the cylinder system over extended time horizons and is able to find a straightforward, interpretable control law for suppressing vortex shedding in the wake of the cylinders.

Optimization Methods for Large-Scale Machine Learning

A major theme of this study is that large-scale machine learning represents a distinctive setting in which the stochastic gradient method has traditionally played a central role while conventional gradient-based nonlinear optimization techniques typically falter, leading to a discussion about the next generation of optimization methods for large- scale machine learning.
...