Backpropagation algorithms and Reservoir Computing in Recurrent Neural Networks for the forecasting of complex spatiotemporal dynamics.

Journal: Neural networks : the official journal of the International Neural Network Society
Published Date: Mar 21, 2020

Abstract

We examine the efficiency of Recurrent Neural Networks in forecasting the spatiotemporal dynamics of high dimensional and reduced order complex systems using Reservoir Computing (RC) and Backpropagation through time (BPTT) for gated network architectures. We highlight advantages and limitations of each method and discuss their implementation for parallel computing architectures. We quantify the relative prediction accuracy of these algorithms for the long-term forecasting of chaotic systems using as benchmarks the Lorenz-96 and the Kuramoto-Sivashinsky (KS) equations. We find that, when the full state dynamics are available for training, RC outperforms BPTT approaches in terms of predictive performance and in capturing of the long-term statistics, while at the same time requiring much less training time. However, in the case of reduced order data, large scale RC models can be unstable and more likely than the BPTT algorithms to diverge. In contrast, RNNs trained via BPTT show superior forecasting abilities and capture well the dynamics of reduced order systems. Furthermore, the present study quantifies for the first time the Lyapunov Spectrum of the KS equation with BPTT, achieving similar accuracy as RC. This study establishes that RNNs are a potent computational framework for the learning and forecasting of complex spatiotemporal systems.

Authors

  • P R Vlachas
    Computational Science and Engineering Laboratory, ETH Zürich, Clausiusstrasse 33, Zürich CH-8092, Switzerland. Electronic address: vlachas@collegium.ethz.ch.
  • J Pathak
    Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, MD 20742, USA; Department of Physics, University of Maryland, College Park, MD 20742, USA. Electronic address: jpathak@umd.edu.
  • B R Hunt
    Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742, USA; Department of Mathematics, University of Maryland, College Park, MD 20742, USA. Electronic address: bhunt@umd.edu.
  • T P Sapsis
    Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139-4307, USA. Electronic address: sapsis@mit.edu.
  • M Girvan
    Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, MD 20742, USA; Department of Physics, University of Maryland, College Park, MD 20742, USA; Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742, USA. Electronic address: girvan@umd.edu.
  • E Ott
    Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, MD 20742, USA; Department of Physics, University of Maryland, College Park, MD 20742, USA; Department of Electrical and Computer Engineering, University of Maryland, MD 20742, USA. Electronic address: edott@umd.edu.
  • P Koumoutsakos
    Computational Science and Engineering Laboratory, ETH Zürich, Clausiusstrasse 33, Zürich CH-8092, Switzerland. Electronic address: petros@ethz.ch.

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