@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{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}
}