Controlling Dynamical Systems Using a Deep Reservoir Computer

Mon, Dec 9, 2019, 4:30 pm to 5:30 pm
Speaker(s): 
Sponsor(s): 
Electrical Engineering

Abstract:

Reservoir computing is a new type of machine learning that is well suited to tasks involving deterministic dynamical systems, such as forecasting, prediction, and data assimilation. It relies on a “reservoir” of artificial neurons with recurrent connections. Each neuron is characterized by a differential equation and hence the reservoir naturally has memory. Importantly, the connection weights that projects information into the reservoir and the connection within the reservoir are chosen randomly and held fixed; only the output-layer weights are trained. The output layer is often just a linear combination of the variables characterizing each neuron and hence optimizing the reservoir computer for a task only involves linear optimization, which can be done quickly. It is found that reservoir computers perform equally well on dynamical system tasks in comparison to deep-learning approaches, but can be trained with vastly less data. I will review the general properties of reservoir computers and will discuss our recent work on using them as a full nonlinear controller for dynamical systems. Here, the reservoir computer learns how to perform so-called inverse control, where it learns the perturbations that need to be applied to the system so that it follows a desired behavior. The controller can be trained quickly, potentially in real time. I give a numerical example of controlling a quadcopter (drone) after an in-flight damage event and experimental results of controlling a chaotic electronic circuit. We find that a layered or deep reservoir computer architecture gives the lowest controller error and gives a systematic way of improving control error as layers are added.

  • D.J. Gauthier, ‘Reservoir computing: Harnessing a universal dynamical system,’ SIAM News 51:2, 12 (2018).
  • D. Canaday, A. Griffith, and D.J. Gauthier, ‘Rapid Time Series Prediction with a Hardware-Based Reservoir Computer,’ Chaos 28, 123119 (2018).
  • N. D. Haynes, M. C. Soriano, D. P. Rosin, I. Fischer, D. J. Gauthier, 'Reservoir computing with a single time-delay autonomous Boolean node,' Phys. Rev. E 91, 020801 (2015).

Bio:

Daniel J. Gauthier is a Professor of Physics and Electrical and Computer Engineering at The Ohio State University. He received the B.S., M.S., and Ph.D. degrees in Optics from the University of Rochester, Rochester, NY, in 1982, 1983, and 1989, respectively. His Ph.D. research on “Instabilities and chaos of laser beams propagating through nonlinear optical media” was supervised by Prof. R.W. Boyd and supported in part through a University Research Initiative Fellowship. From 1989 to 1991, he developed the first CW two-photon optical laser as a Post-Doctoral Research Associate under the mentorship of Prof. T.W. Mossberg at the University of Oregon. In 1991, he joined the faculty of Duke University, Durham, NC, as an Assistant Professor of Physics and was named a Young Investigator of the U.S. Army Research Office in 1992 and the National Science Foundation in 1993. He was the Robert C. Richardson Professor of Physics at Duke from 2011- 2015, chair of the Duke Physics Department from 2005 – 2011, interim chair in spring 2015. He moved to The Ohio State University in 2016. His research interests include high-rate quantum communication, quantum repeaters, nonlinear quantum optics, synchronization and control of the dynamics of complex networks, and reservoir computing. Prof. Gauthier is a Fellow of the Optical Society of America and the American Physical Society.

This seminar is supported by the Korhammer Lecture Series Funds