Chair of Computational Science
Clausiusstrasse 33
ETH-Zentrum, CLT C 14
CH-8092 Zürich

Contact Information


Pantelis R. Vlachas

Post-doctoral Fellow

Research and Interests

  • Data-driven modeling of complex dynamical systems (chaotic, high-dimensional, stochastic, etc.)
  • Developing a framework for learning the effective dynamics across scales, with applications to complex systems, from fluid dynamics to molecules
  • Machine learning algorithms
  • Neural network architectures – LSTM – CNN
  • (Reinforcement learning, Bayesian and variational inference)


  • Ph. D. ETH Zurich on “Learning effective dynamics of complex dynamical systems across scales”, 2022
  • M. Sc., Electrical Engineering, Technical University of Munich (TUM), 2016
  • B. Sc., Electrical Engineering, Technical University of Munich (TUM), 2014

Publications (see scholar page)


  • P. R. Vlachas, J. Pathak, B. R. Hunt, T. P. Sapsis, M. Girvan, E. Ott, and P. Koumoutsakos, “Backpropagation algorithms and reservoir computing in recurrent neural networks for the forecasting of complex spatiotemporal dynamics,” Neural Networks, vol. 126, pp. 191-217, 2020.
    [BibTeX] [Abstract] [PDF] [DOI]

    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.

    author = {P.R. Vlachas and J. Pathak and B.R. Hunt and T.P. Sapsis and M. Girvan and E. Ott and P. Koumoutsakos},
    doi = {},
    issn = {0893-6080},
    journal = {{Neural Networks}},
    keywords = {Time series forecasting, RNN, LSTM, GRU, Reservoir Computing, Kuramoto{\textendash}Sivashinsky, Lorenz-96, Complex systems},
    pages = {191 - 217},
    title = {Backpropagation algorithms and Reservoir Computing in Recurrent Neural Networks for the forecasting of complex spatiotemporal dynamics},
    url = {},
    volume = {126},
    year = {2020}


  • P. R. Vlachas, W. Byeon, Z. Y. Wan, T. P. Sapsis, and P. Koumoutsakos, “Data-driven forecasting of high-dimensional chaotic systems with long short-term memory networks,” P. Roy. Soc. A-Math. Phy., vol. 474, iss. 2213, p. 20170844, 2018.
    [BibTeX] [PDF] [DOI]
    author = {Pantelis R. Vlachas and Wonmin Byeon and Zhong Y. Wan and Themistoklis P. Sapsis and Petros Koumoutsakos},
    doi = {10.1098/rspa.2017.0844},
    journal = {{P. Roy. Soc. A-Math. Phy.}},
    month = {may},
    number = {2213},
    pages = {20170844},
    publisher = {The Royal Society},
    title = {Data-driven forecasting of high-dimensional chaotic systems with long short-term memory networks},
    url = {},
    volume = {474},
    year = {2018}

  • Z. Y. Wan, P. R. Vlachas, P. Koumoutsakos, and T. P. Sapsis, “Data-assisted reduced-order modeling of extreme events in complex dynamical systems,” PLoS ONE, vol. 13, iss. 5, pp. 1-22, 2018.
    [BibTeX] [PDF] [DOI]
    author = {Zhong Y. Wan and Pantelis R. Vlachas and Petros Koumoutsakos and Themistoklis P. Sapsis},
    doi = {10.1371/journal.pone.0197704},
    journal = {{PL}o{S} {ONE}},
    month = {may},
    number = {5},
    pages = {1-22},
    publisher = {Public Library of Science},
    title = {Data-assisted reduced-order modeling of extreme events in complex dynamical systems},
    url = {},
    volume = {13},
    year = {2018}


Download curriculum vitae here.