@article{QuadeIseleAbel2020, author = {Quade, Markus and Isele, Thomas and Abel, Markus}, title = {Machine learning control}, series = {Physica : D, Nonlinear phenomena}, volume = {412}, journal = {Physica : D, Nonlinear phenomena}, publisher = {Elsevier}, address = {Amsterdam}, issn = {0167-2789}, doi = {10.1016/j.physd.2020.132582}, pages = {11}, year = {2020}, abstract = {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.}, language = {en} } @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{GoutQuadeShafietal.2017, author = {Gout, Julien and Quade, Markus and Shafi, Kamran and Niven, Robert K. and Abel, Markus}, title = {Synchronization control of oscillator networks using symbolic regression}, series = {Nonlinear Dynamics}, volume = {91}, journal = {Nonlinear Dynamics}, number = {2}, publisher = {Springer}, address = {Dordrecht}, issn = {0924-090X}, doi = {10.1007/s11071-017-3925-z}, pages = {1001 -- 1021}, year = {2017}, abstract = {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.}, language = {en} } @article{QuadeAbelShafietal.2016, author = {Quade, Markus and Abel, Markus and Shafi, Kamran and Niven, Robert K. and Noack, Bernd R.}, title = {Prediction of dynamical systems by symbolic regression}, series = {Physical review : E, Statistical, nonlinear and soft matter physics}, volume = {94}, journal = {Physical review : E, Statistical, nonlinear and soft matter physics}, publisher = {American Society for Pharmacology and Experimental Therapeutics}, address = {Bethesda}, issn = {2470-0045}, doi = {10.1103/PhysRevE.94.012214}, pages = {15}, year = {2016}, abstract = {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.}, language = {en} } @misc{McQuadeO'BrienDoerretal.2013, author = {McQuade, D. Tyler and O'Brien, Alexander G. and D{\"o}rr, Markus and Rajaratnam, Rajathees and Eisold, Ursula and Monnanda, Bopanna and Nobuta, Tomoya and L{\"o}hmannsr{\"o}ben, Hans-Gerd and Meggers, Eric and Seeberger, Peter H.}, title = {Continuous synthesis of pyridocarbazoles and initial photophysical and bioprobe characterization}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-95214}, pages = {4067 -- 4070}, year = {2013}, abstract = {Pyridocarbazoles when ligated to transition metals yield high affinity kinase inhibitors. While batch photocyclizations enable the synthesis of these heterocycles, the non-oxidative Mallory reaction only provides modest yields and difficult to purify mixtures. We demonstrate here that a flow-based Mallory cyclization provides superior results and enables observation of a clear isobestic point. The flow method allowed us to rapidly synthesize ten pyridocarbazoles and for the first time to document their interesting photophysical attributes. Preliminary characterization reveals that these molecules might be a new class of fluorescent bioprobe.}, language = {en} } @phdthesis{Quade2018, author = {Quade, Markus}, title = {Symbolic regression for identification, prediction, and control of dynamical systems}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-419790}, school = {Universit{\"a}t Potsdam}, pages = {xiii, 134}, year = {2018}, abstract = {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.}, language = {en} } @article{TodtSanderHainichetal.2015, author = {Todt, Helge Tobias and Sander, Angelika and Hainich, Rainer and Hamann, Wolf-Rainer and Quade, Markus and Shenar, Tomer}, title = {Potsdam Wolf-Rayet model atmosphere grids for WN stars}, series = {Astronomy and astrophysics : an international weekly journal}, volume = {579}, journal = {Astronomy and astrophysics : an international weekly journal}, publisher = {EDP Sciences}, address = {Les Ulis}, issn = {0004-6361}, doi = {10.1051/0004-6361/201526253}, pages = {6}, year = {2015}, abstract = {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.}, language = {en} }