Reservoir computing is a best-in-class machine learning algorithm for processing information generated by dynamical systems using observed time-series data. Importantly, it requires very small training data sets, uses linear optimization, and thus requires minimal computing resources. However, the algorithm uses randomly sampled matrices to define the underlying recurrent neural network and has a multitude of metaparameters that must be optimized. Recent results demonstrate the equivalence of reservoir computing to nonlinear vector autoregression, which requires no random matrices, fewer metaparameters, and provides interpretable results. I will give examples that nonlinear vector autoregression excels at reservoir computing benchmark tasks and requires even shorter training data sets and up to a million times shorter training, heralding the next generation of reservoir computing. I will begin with a brief introduction to using machine learning for forecasting dynamical systems, then describe traditional reservoir computing, and then discuss the next generation of reservoir computing.
Daniel 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 continuous-wave 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, and was a founding member of the Duke Fitzpatrick Institute for Photonics. He moved to The Ohio State University in 2016. His research interests include: reservoir computing; synchronization and control of the dynamics of complex networks in electronic and optical systems; quantum communication; and nonlinear quantum optics. Prof. Gauthier is a Fellow of the Optical Society of America and the American Physical Society.