TY - JOUR A1 - Quade, Markus A1 - Abel, Markus A1 - Kutz, J. Nathan A1 - Brunton, Steven L. T1 - Sparse identification of nonlinear dynamics for rapid model recovery JF - Chaos : an interdisciplinary journal of nonlinear science N2 - 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. Y1 - 2018 U6 - https://doi.org/10.1063/1.5027470 SN - 1054-1500 SN - 1089-7682 VL - 28 IS - 6 PB - American Institute of Physics CY - Melville ER - TY - JOUR A1 - Parezanovic, Vladimir A1 - Cordier, Laurent A1 - Spohn, Andreas A1 - Duriez, Thomas A1 - Noack, Bernd R. A1 - Bonnet, Jean-Paul A1 - Segond, Marc A1 - Abel, Markus A1 - Brunton, Steven L. T1 - Frequency selection by feedback control in a turbulent shear flow JF - Journal of fluid mechanics N2 - 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. KW - free shear layers KW - instability control KW - turbulence control Y1 - 2016 U6 - https://doi.org/10.1017/jfm.2016.261 SN - 0022-1120 SN - 1469-7645 VL - 797 SP - 247 EP - 283 PB - Cambridge Univ. Press CY - New York ER - TY - JOUR A1 - Parezanovic, Vladimir A1 - Laurentie, Jean-Charles A1 - Fourment, Carine A1 - Delville, Joel A1 - Bonnet, Jean-Paul A1 - Spohn, Andreas A1 - Duriez, Thomas A1 - Cordier, Laurent A1 - Noack, Bernd R. A1 - Abel, Markus A1 - Segond, Marc A1 - Shaqarin, Tamir A1 - Brunton, Steven L. T1 - Mixing layer manipulation experiment from open-loop forcing to closed-loop machine learning control JF - Flow, turbulence and combustion : an international journal published in association with ERCOFTAC KW - Shear flow KW - Turbulence KW - Active flow control KW - Extremum seeking KW - POD KW - Machine learning KW - Genetic programming Y1 - 2015 U6 - https://doi.org/10.1007/s10494-014-9581-1 SN - 1386-6184 SN - 1573-1987 VL - 94 IS - 1 SP - 155 EP - 173 PB - Springer CY - Dordrecht ER - TY - GEN A1 - Parezanović, Vladimir A1 - Cordier, Laurent A1 - Spohn, Andreas A1 - Duriez, Thomas A1 - Noack, Bernd R. A1 - Bonnet, Jean-Paul A1 - Segond, Marc A1 - Abel, Markus A1 - Brunton, Steven L. T1 - Frequency selection by feedback control in a turbulent shear flow T2 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - 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. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 572 KW - free shear layers KW - instability control KW - turbulence control Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-413693 SN - 1866-8372 IS - 572 ER -