Backpropagation algorithms and Reservoir Computing in Recurrent Neural Networks for the forecasting of complex spatiotemporal dynamics
Name
1910.05266.pdf
Description
Submitted version
Size
15.97 MB
Format
Adobe PDF
Checksum (MD5)
db466f215746b625ee471cd23ad5e30d
Author(s)
Vlachas, P.R.
Pathak, J.
Hunt, B.R.
Sapsis, Themistoklis Panagiotis
Girvan, M.
Ott, E.
Koumoutsakos, P.
Date Issued
June 2020
Journal
Neural Networks
Publisher
Elsevier BV
Citation
Vlachas, P. R. et al. "Backpropagation algorithms and Reservoir Computing in Recurrent Neural Networks for the forecasting of complex spatiotemporal dynamics." Neural Networks 126 (June 2020): 191-217 © 2020 Elsevier Ltd
Version
Original manuscript
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.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
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Creative Commons Attribution-NonCommercial-NoDerivs License
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DOI of Published Version
https://doi.org/10.1016/j.neunet.2020.02.016
