---
_id: '16290'
abstract:
- lang: eng
  text: The control of complex systems is of critical importance in many branches
    of science, engineering, and industry, many of which are governed by nonlinear
    partial differential equations. Controlling an unsteady fluid flow is particularly
    important, as flow control is a key enabler for technologies in energy (e.g.,
    wind, tidal, and combustion), transportation (e.g., planes, trains, and automobiles),
    security (e.g., tracking airborne contamination), and health (e.g., artificial
    hearts and artificial respiration). However, the high-dimensional, nonlinear,
    and multi-scale dynamics make real-time feedback control infeasible. Fortunately,
    these high- dimensional systems exhibit dominant, low-dimensional patterns of
    activity that can be exploited for effective control in the sense that knowledge
    of the entire state of a system is not required. Advances in machine learning
    have the potential to revolutionize flow control given its ability to extract
    principled, low-rank feature spaces characterizing such complex systems.We present
    a novel deep learning modelpredictive control framework that exploits low-rank
    features of the flow in order to achieve considerable improvements to control
    performance. Instead of predicting the entire fluid state, we use a recurrent
    neural network (RNN) to accurately predict the control relevant quantities of
    the system, which are then embedded into an MPC framework to construct a feedback
    loop. In order to lower the data requirements and to improve the prediction accuracy
    and thus the control performance, incoming sensor data are used to update the
    RNN online. The results are validated using varying fluid flow examples of increasing
    complexity.
article_type: original
author:
- first_name: Katharina
  full_name: Bieker, Katharina
  id: '32829'
  last_name: Bieker
- first_name: Sebastian
  full_name: Peitz, Sebastian
  id: '47427'
  last_name: Peitz
  orcid: https://orcid.org/0000-0002-3389-793X
- first_name: Steven L.
  full_name: Brunton, Steven L.
  last_name: Brunton
- first_name: J. Nathan
  full_name: Kutz, J. Nathan
  last_name: Kutz
- first_name: Michael
  full_name: Dellnitz, Michael
  last_name: Dellnitz
citation:
  ama: Bieker K, Peitz S, Brunton SL, Kutz JN, Dellnitz M. Deep model predictive flow
    control with limited sensor data and online learning. <i>Theoretical and Computational
    Fluid Dynamics</i>. 2020;34:577–591. doi:<a href="https://doi.org/10.1007/s00162-020-00520-4">10.1007/s00162-020-00520-4</a>
  apa: Bieker, K., Peitz, S., Brunton, S. L., Kutz, J. N., &#38; Dellnitz, M. (2020).
    Deep model predictive flow control with limited sensor data and online learning.
    <i>Theoretical and Computational Fluid Dynamics</i>, <i>34</i>, 577–591. <a href="https://doi.org/10.1007/s00162-020-00520-4">https://doi.org/10.1007/s00162-020-00520-4</a>
  bibtex: '@article{Bieker_Peitz_Brunton_Kutz_Dellnitz_2020, title={Deep model predictive
    flow control with limited sensor data and online learning}, volume={34}, DOI={<a
    href="https://doi.org/10.1007/s00162-020-00520-4">10.1007/s00162-020-00520-4</a>},
    journal={Theoretical and Computational Fluid Dynamics}, author={Bieker, Katharina
    and Peitz, Sebastian and Brunton, Steven L. and Kutz, J. Nathan and Dellnitz,
    Michael}, year={2020}, pages={577–591} }'
  chicago: 'Bieker, Katharina, Sebastian Peitz, Steven L. Brunton, J. Nathan Kutz,
    and Michael Dellnitz. “Deep Model Predictive Flow Control with Limited Sensor
    Data and Online Learning.” <i>Theoretical and Computational Fluid Dynamics</i>
    34 (2020): 577–591. <a href="https://doi.org/10.1007/s00162-020-00520-4">https://doi.org/10.1007/s00162-020-00520-4</a>.'
  ieee: K. Bieker, S. Peitz, S. L. Brunton, J. N. Kutz, and M. Dellnitz, “Deep model
    predictive flow control with limited sensor data and online learning,” <i>Theoretical
    and Computational Fluid Dynamics</i>, vol. 34, pp. 577–591, 2020.
  mla: Bieker, Katharina, et al. “Deep Model Predictive Flow Control with Limited
    Sensor Data and Online Learning.” <i>Theoretical and Computational Fluid Dynamics</i>,
    vol. 34, 2020, pp. 577–591, doi:<a href="https://doi.org/10.1007/s00162-020-00520-4">10.1007/s00162-020-00520-4</a>.
  short: K. Bieker, S. Peitz, S.L. Brunton, J.N. Kutz, M. Dellnitz, Theoretical and
    Computational Fluid Dynamics 34 (2020) 577–591.
date_created: 2020-03-13T12:40:09Z
date_updated: 2022-01-06T06:52:48Z
department:
- _id: '101'
doi: 10.1007/s00162-020-00520-4
intvolume: '        34'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://link.springer.com/content/pdf/10.1007/s00162-020-00520-4.pdf
oa: '1'
page: 577–591
project:
- _id: '52'
  name: Computing Resources Provided by the Paderborn Center for Parallel Computing
publication: Theoretical and Computational Fluid Dynamics
publication_identifier:
  issn:
  - 0935-4964
  - 1432-2250
publication_status: published
status: public
title: Deep model predictive flow control with limited sensor data and online learning
type: journal_article
user_id: '47427'
volume: 34
year: '2020'
...