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  -