@article{QuadeAbelKutzetal.2018,
  author    = {Quade, Markus and Abel, Markus and Kutz, J. Nathan and Brunton, Steven L.},
  title     = {Sparse identification of nonlinear dynamics for rapid model recovery},
  series = {Chaos : an interdisciplinary journal of nonlinear science},
  volume    = {28},
  journal   = {Chaos : an interdisciplinary journal of nonlinear science},
  number    = {6},
  publisher = {American Institute of Physics},
  address   = {Melville},
  issn      = {1054-1500},
  doi       = {10.1063/1.5027470},
  pages     = {10},
  year      = {2018},
  abstract  = {Big data have become a critically enabling component of emerging mathematical methods aimed at the automated discovery of dynamical systems, where first principles modeling may be intractable. However, in many engineering systems, abrupt changes must be rapidly characterized based on limited, incomplete, and noisy data. Many leading automated learning techniques rely on unrealistically large data sets, and it is unclear how to leverage prior knowledge effectively to re-identify a model after an abrupt change. In this work, we propose a conceptual framework to recover parsimonious models of a system in response to abrupt changes in the low-data limit. First, the abrupt change is detected by comparing the estimated Lyapunov time of the data with the model prediction. Next, we apply the sparse identification of nonlinear dynamics (SINDy) regression to update a previously identified model with the fewest changes, either by addition, deletion, or modification of existing model terms. We demonstrate this sparse model recovery on several examples for abrupt system change detection in periodic and chaotic dynamical systems. Our examples show that sparse updates to a previously identified model perform better with less data, have lower runtime complexity, and are less sensitive to noise than identifying an entirely new model. The proposed abrupt-SINDy architecture provides a new paradigm for the rapid and efficient recovery of a system model after abrupt changes.},
  language  = {en}
}
@article{ParezanovicCordierSpohnetal.2016,
  author    = {Parezanovic, Vladimir and Cordier, Laurent and Spohn, Andreas and Duriez, Thomas and Noack, Bernd R. and Bonnet, Jean-Paul and Segond, Marc and Abel, Markus and Brunton, Steven L.},
  title     = {Frequency selection by feedback control in a turbulent shear flow},
  series = {Journal of fluid mechanics},
  volume    = {797},
  journal   = {Journal of fluid mechanics},
  publisher = {Cambridge Univ. Press},
  address   = {New York},
  issn      = {0022-1120},
  doi       = {10.1017/jfm.2016.261},
  pages     = {247 -- 283},
  year      = {2016},
  abstract  = {Many previous studies have shown that the turbulent mixing layer under periodic forcing tends to adopt a lock-on state, where the major portion of the fluctuations in the flow are synchronized at the forcing frequency. The goal of this experimental study is to apply closed-loop control in order to provoke the lock-on state, using information from the flow itself. We aim to determine the range of frequencies for which the closed-loop control can establish the lock-on, and what mechanisms are contributing to the selection of a feedback frequency. In order to expand the solution space for optimal closed-loop control laws, we use the genetic programming control (CPC) framework. The best closed-loop control laws obtained by CPC are analysed along with the associated physical mechanisms in the mixing layer flow. The resulting closed-loop control significantly outperforms open-loop forcing in terms of robustness to changes in the free-stream velocities. In addition, the selection of feedback frequencies is not locked to the most amplified local mode, but rather a range of frequencies around it.},
  language  = {en}
}
@article{ParezanovicLaurentieFourmentetal.2015,
  author    = {Parezanovic, Vladimir and Laurentie, Jean-Charles and Fourment, Carine and Delville, Joel and Bonnet, Jean-Paul and Spohn, Andreas and Duriez, Thomas and Cordier, Laurent and Noack, Bernd R. and Abel, Markus and Segond, Marc and Shaqarin, Tamir and Brunton, Steven L.},
  title     = {Mixing layer manipulation experiment from open-loop forcing to closed-loop machine learning control},
  series = {Flow, turbulence and combustion : an international journal published in association with ERCOFTAC},
  volume    = {94},
  journal   = {Flow, turbulence and combustion : an international journal published in association with ERCOFTAC},
  number    = {1},
  publisher = {Springer},
  address   = {Dordrecht},
  issn      = {1386-6184},
  doi       = {10.1007/s10494-014-9581-1},
  pages     = {155 -- 173},
  year      = {2015},
  language  = {en}
}
@misc{ParezanovićCordierSpohnetal.2016,
  author    = {Parezanović, Vladimir and Cordier, Laurent and Spohn, Andreas and Duriez, Thomas and Noack, Bernd R. and Bonnet, Jean-Paul and Segond, Marc and Abel, Markus and Brunton, Steven L.},
  title     = {Frequency selection by feedback control in a turbulent shear flow},
  series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  number    = {572},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-41369},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-413693},
  pages     = {37},
  year      = {2016},
  abstract  = {Many previous studies have shown that the turbulent mixing layer under periodic forcing tends to adopt a lock-on state, where the major portion of the fluctuations in the flow are synchronized at the forcing frequency. The goal of this experimental study is to apply closed-loop control in order to provoke the lock-on state, using information from the flow itself. We aim to determine the range of frequencies for which the closed-loop control can establish the lock-on, and what mechanisms are contributing to the selection of a feedback frequency. In order to expand the solution space for optimal closed-loop control laws, we use the genetic programming control (CPC) framework. The best closed-loop control laws obtained by CPC are analysed along with the associated physical mechanisms in the mixing layer flow. The resulting closed-loop control significantly outperforms open-loop forcing in terms of robustness to changes in the free-stream velocities. In addition, the selection of feedback frequencies is not locked to the most amplified local mode, but rather a range of frequencies around it.},
  language  = {en}
}