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Control of Oscillator Networks with Symbolic Regression
Held by Dr. Markus Abel (Universität Potsdam)
10.05.2016, 16:00 Uhr
The control of a network of oscillators is not only important due to the obvious application for neural diseases, but as well interesting from a scientific point of view. Such ensembles of oscillators can show a variety of complex states. Some might be wanted, others are not favored, depending on the objectives of the investigator. An example is the fully synchronized state, where all oscillators follow the mean-field, this conincides with observations of Parkinson disease. So, one control objective could be to suppress synchronization of oscillators, but more complicated scenarios can be designed easily for more complex networks, more complex dynamics, etc. We present a machine-learning-based approach, where the control law is obtained by an optimization procedure. Instead of using the now famous neural networks we focus on symbolic regression which has the advantage to obtain analytic expressions. The approach involves the formulation of the problem in terms of measurement function and actuation functions, that are very important for eventual practical applications. We demonstrate the method by some easy test scenarios and a network of FitzHugh-Nagumo or Hindmarsh-Rose oscillators.
The implementation of the methods is done using several python modules, and a proprietary implementation of the genetic programming using functional design. That way modularity allows a very flexible use of the modules and easy use of our software.