TY - JOUR A1 - Quade, Markus A1 - Isele, Thomas A1 - Abel, Markus T1 - Machine learning control BT - explainable and analyzable methods JF - Physica : D, Nonlinear phenomena N2 - Recently, the term explainable AI came into discussion as an approach to produce models from artificial intelligence which allow interpretation. For a long time, symbolic regression has been used to produce explainable and mathematically tractable models. In this contribution, we extend previous work on symbolic regression methods to infer the optimal control of a dynamical system given one or several optimization criteria, or cost functions. In earlier publications, network control was achieved by automated machine learning control using genetic programming. Here, we focus on the subsequent path continuation analysis of the mathematical expressions which result from the machine learning model. In particular, we use AUTO to analyze the solution properties of the controlled oscillator system which served as our model. As a result, we show that there is a considerable advantage of explainable symbolic regression models over less accessible neural networks. In particular, the roadmap of future works may be to integrate such analyses into the optimization loop itself to filter out robust solutions by construction. KW - Explainable AI KW - Machine learning control KW - Dynamical systems KW - Synchronization control KW - Genetic programming Y1 - 2020 U6 - https://doi.org/10.1016/j.physd.2020.132582 SN - 0167-2789 SN - 1872-8022 VL - 412 PB - Elsevier CY - Amsterdam ER - 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 - Gout, Julien A1 - Quade, Markus A1 - Shafi, Kamran A1 - Niven, Robert K. A1 - Abel, Markus T1 - Synchronization control of oscillator networks using symbolic regression JF - Nonlinear Dynamics N2 - Networks of coupled dynamical systems provide a powerful way to model systems with enormously complex dynamics, such as the human brain. Control of synchronization in such networked systems has far-reaching applications in many domains, including engineering and medicine. In this paper, we formulate the synchronization control in dynamical systems as an optimization problem and present a multi-objective genetic programming-based approach to infer optimal control functions that drive the system from a synchronized to a non-synchronized state and vice versa. The genetic programming-based controller allows learning optimal control functions in an interpretable symbolic form. The effectiveness of the proposed approach is demonstrated in controlling synchronization in coupled oscillator systems linked in networks of increasing order complexity, ranging from a simple coupled oscillator system to a hierarchical network of coupled oscillators. The results show that the proposed method can learn highly effective and interpretable control functions for such systems. KW - Dynamical systems KW - Synchronization control KW - Genetic programming Y1 - 2017 U6 - https://doi.org/10.1007/s11071-017-3925-z SN - 0924-090X SN - 1573-269X VL - 91 IS - 2 SP - 1001 EP - 1021 PB - Springer CY - Dordrecht ER - TY - JOUR A1 - Quade, Markus A1 - Abel, Markus A1 - Shafi, Kamran A1 - Niven, Robert K. A1 - Noack, Bernd R. T1 - Prediction of dynamical systems by symbolic regression JF - Physical review : E, Statistical, nonlinear and soft matter physics N2 - We study the modeling and prediction of dynamical systems based on conventional models derived from measurements. Such algorithms are highly desirable in situations where the underlying dynamics are hard to model from physical principles or simplified models need to be found. We focus on symbolic regression methods as a part of machine learning. These algorithms are capable of learning an analytically tractable model from data, a highly valuable property. Symbolic regression methods can be considered as generalized regression methods. We investigate two particular algorithms, the so-called fast function extraction which is a generalized linear regression algorithm, and genetic programming which is a very general method. Both are able to combine functions in a certain way such that a good model for the prediction of the temporal evolution of a dynamical system can be identified. We illustrate the algorithms by finding a prediction for the evolution of a harmonic oscillator based on measurements, by detecting an arriving front in an excitable system, and as a real-world application, the prediction of solar power production based on energy production observations at a given site together with the weather forecast. Y1 - 2016 U6 - https://doi.org/10.1103/PhysRevE.94.012214 SN - 2470-0045 SN - 2470-0053 VL - 94 PB - American Society for Pharmacology and Experimental Therapeutics CY - Bethesda ER - TY - THES A1 - Quade, Markus T1 - Symbolic regression for identification, prediction, and control of dynamical systems T1 - Symbolische Regression zur Identifikation, Vorhersage und Regelung dynamischer Systeme N2 - In the present work, we use symbolic regression for automated modeling of dynamical systems. Symbolic regression is a powerful and general method suitable for data-driven identification of mathematical expressions. In particular, the structure and parameters of those expressions are identified simultaneously. We consider two main variants of symbolic regression: sparse regression-based and genetic programming-based symbolic regression. Both are applied to identification, prediction and control of dynamical systems. We introduce a new methodology for the data-driven identification of nonlinear dynamics for systems undergoing abrupt changes. Building on a sparse regression algorithm derived earlier, the model after the change is defined as a minimum update with respect to a reference model of the system identified prior to the change. The technique is successfully exemplified on the chaotic Lorenz system and the van der Pol oscillator. Issues such as computational complexity, robustness against noise and requirements with respect to data volume are investigated. We show how symbolic regression can be used for time series prediction. Again, issues such as robustness against noise and convergence rate are investigated us- ing the harmonic oscillator as a toy problem. In combination with embedding, we demonstrate the prediction of a propagating front in coupled FitzHugh-Nagumo oscillators. Additionally, we show how we can enhance numerical weather predictions to commercially forecast power production of green energy power plants. We employ symbolic regression for synchronization control in coupled van der Pol oscillators. Different coupling topologies are investigated. We address issues such as plausibility and stability of the control laws found. The toolkit has been made open source and is used in turbulence control applications. Genetic programming based symbolic regression is very versatile and can be adapted to many optimization problems. The heuristic-based algorithm allows for cost efficient optimization of complex tasks. We emphasize the ability of symbolic regression to yield white-box models. In contrast to black-box models, such models are accessible and interpretable which allows the usage of established tool chains. N2 - In der vorliegenden Arbeit nutzen wird symbolische Regression zur automatisierten Modellierung dynamischer Systeme. Symbolische Regression ist eine mächtige und vielseitige Methode, welche zur Daten-getriebenen Identifikation von mathematischen Ausdrücken geeignet ist. Insbesondere werden dabei Struktur und Parameter des gesuchten Ausdrucks parallel ermittelt. Zwei Varianten der symbolischen Regression werden im Rahmen dieser Arbeit in Betracht gezogen: sparse regression und symbolischer Regression basierend auf genetischem Programmieren. Beide Verfahren werden für die Identifikation, Vor- hersage und Regelung dynamischer Systeme angewandt. Wir führen eine neue Methodik zur Identifikation von dynamischen Systemen, welche eine spontane Änderung erfahren, ein. Die Änderung eines Modells, wel- ches mit Hilfe von sparse regression gefunden wurde, ist definiert als sparsamste Aktualisierung im Hinblick auf das Modell vor der Änderung. Diese Technik ist beispielhaft am chaotischem Lorenz System und dem van der Pol Oszillator demonstriert. Aspekte wie numerische Komplexität, Robustheit gegenüber Rauschen sowie Anforderungen an Anzahl von Datenpunkten werden untersucht. Wir zeigen wie symbolische Regression zur Zeitreihenvorhersage genutzt wer- den kann. Wir nutzen dem harmonischen Oszillator als Beispielmodell, um Aspekte wie Robustheit gegenüber Rauschen sowie die Konvergenzrate der Optimierung zu untersuchen. Mit Hilfe von Einbettungsverfahren demonstrieren wir die Vorhersage propagierenden Fronten in gekoppelten FitzHugh-Nagumo Oszillatoren. Außerdem betrachten wir die kommerzielle Stromproduktionsvorhersage von erneuerbaren Energien. Wir zeigen wie man diesbezügliche die numerische Wettervorhersage mittels symbolischer Regression verfeinern und zur Stromproduktionsvorhersage anwenden kann. Wir setzen symbolische Regression zur Regelung von Synchronisation in gekoppelten van der Pol Oszillatoren ein. Dabei untersuchen wir verschiedene Topologien und Kopplungen. Wir betrachten Aspekte wie Plausibilität und Stabilität der gefundenen Regelungsgesetze. Die Software wurde veröffentlicht und wird u. a. zur Turbulenzregelung eingesetzt. Symbolische Regression basierend auf genetischem Programmieren ist sehr vielseitig und kann auf viele Optimierungsprobleme übertragen werden. Der auf Heuristik basierenden Algorithmus erlaubt die effiziente Optimierung von komplexen Fragestellungen. Wir betonen die Fähigkeit von symbolischer Regression, sogenannte white-box Modelle zu produzieren. Diese Modelle sind – im Gegensatz zu black-box Modellen – zugänglich und interpretierbar. Dies ermöglicht das weitere Nutzen von etablierten Methodiken. KW - dynamical systems KW - symbolic regression KW - genetic programming KW - identification KW - prediction KW - control KW - Dynamische Systeme KW - Symbolische Regression KW - Genetisches Programmieren KW - Identifikation KW - Vorhersage KW - Regelung Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-419790 ER - TY - JOUR A1 - Todt, Helge Tobias A1 - Sander, Angelika A1 - Hainich, Rainer A1 - Hamann, Wolf-Rainer A1 - Quade, Markus A1 - Shenar, Tomer T1 - Potsdam Wolf-Rayet model atmosphere grids for WN stars JF - Astronomy and astrophysics : an international weekly journal N2 - We present new grids of Potsdam Wolf-Rayet (PoWR) model atmospheres for Wolf-Rayet stars of the nitrogen sequence (WN stars). The models have been calculated with the latest version of the PoWR stellar atmosphere code for spherical stellar winds. The WN model atmospheres include the non-LTE solutions of the statistical equations for complex model atoms, as well as the radiative transfer equation in the co-moving frame. Iron-line blanketing is treated with the help of the superlevel approach, while wind inhomogeneities are taken into account via optically thin clumps. Three of our model grids are appropriate for Galactic metallicity. The hydrogen mass fraction of these grids is 50%, 20%, and 0%, thus also covering the hydrogen-rich late-type WR stars that have been discovered in recent years. Three grids are adequate for LMC WN stars and have hydrogen fractions of 40%, 20%, and 0%. Recently, additional grids with SMC metallicity and with 60%, 40%, 20%, and 0% hydrogen have been added. We provide contour plots of the equivalent widths of spectral lines that are usually used for classification and diagnostics. KW - stars: evolution KW - stars: mass-loss KW - stars: winds, outflows KW - stars: Wolf-Rayet KW - stars: atmospheres KW - stars: massive Y1 - 2015 U6 - https://doi.org/10.1051/0004-6361/201526253 SN - 0004-6361 SN - 1432-0746 VL - 579 PB - EDP Sciences CY - Les Ulis ER -