'Next Generation' Reservoir Computing: an Empirical Data-Driven Expression of Dynamical Equations in Time-Stepping Form

Next generation reservoir computing based on nonlinear vector autoregression (NVAR) is applied to emulate simple dynamical system models and compared to numerical integration schemes such as Euler and the 2nd order Runge-Kutta. It is shown that the NVAR emulator can be interpreted as a data-driven method used to recover the numerical integration scheme that produced the data. It is also shown that the approach can be extended to produce high-order numerical schemes directly from data. The impacts of the presence of noise and temporal sparsity in the training set is further examined to gauge the potential use of this method for more realistic applications.

[1]  K. Emanuel,et al.  Optimal Sites for Supplementary Weather Observations: Simulation with a Small Model , 1998 .

[2]  Jonathan Demaeyer,et al.  The Modular Arbitrary-Order Ocean-Atmosphere Model: MAOOAM v1.0 , 2016, 1603.06755.

[3]  H. Abarbanel,et al.  Reduced Dimension, Biophysical Neuron Models Constructed From Observed Data , 2021, bioRxiv.

[4]  E. Lorenz.  Deterministic nonperiodic flow , 1963 .

[5]  Leisheng Jin,et al.  Model-Free Prediction of Chaotic Systems Using High Efficient Next-generation Reservoir Computing , 2021, ArXiv.

[6]  Sebastian Scher,et al.  Toward Data‐Driven Weather and Climate Forecasting: Approximating a Simple General Circulation Model With Deep Learning , 2018, Geophysical Research Letters.

[7]  Erik Bollt,et al.  On explaining the surprising success of reservoir computing forecaster of chaos? The universal machine learning dynamical system with contrast to VAR and DMD. , 2020, Chaos.

[8]  R. Brockett,et al.  Reservoir observers: Model-free inference of unmeasured variables in chaotic systems. , 2017, Chaos.

[9]  Jaideep Pathak,et al.  Model-Free Prediction of Large Spatiotemporally Chaotic Systems from Data: A Reservoir Computing Approach. , 2018, Physical review letters.

[10]  Daniel J. Gauthier,et al.  Forecasting Chaotic Systems with Very Low Connectivity Reservoir Computers , 2019, Chaos.

[11]  Marc Bocquet,et al.  Data assimilation as a learning tool to infer ordinary differential equation representations of dynamical models , 2019, Nonlinear Processes in Geophysics.

[12]  Erik Bollt,et al.  Next generation reservoir computing , 2021, Nature Communications.

[13]  S. Brunton,et al.  Discovering governing equations from data by sparse identification of nonlinear dynamical systems , 2015, Proceedings of the National Academy of Sciences.

[14]  F. Takens.  Detecting strange attractors in turbulence , 1981 .

[15]  Fourier Reservoir Computing for data-driven prediction of multi-scale coupled quasi-geostrophic dynamics , 2021 .

[16]  Daniel R. Creveling.  Parameter and state estimation in nonlinear dynamical systems , 2008 .

[17]  Sebastian Scher,et al.  Weather and climate forecasting with neural networks: using general circulation models (GCMs) with different complexity as a study ground , 2019, Geoscientific Model Development.

[18]  Ankit B. Patel,et al.  Domain-driven models yield better predictions at lower cost than reservoir computers in Lorenz systems , 2021, Philosophical Transactions of the Royal Society A.

[19]  Jaideep Pathak,et al.  A Machine Learning‐Based Global Atmospheric Forecast Model , 2020 .

[20]  Daniel J. Gauthier,et al.  Stabilizing unstable steady states using extended time-delay autosynchronization. , 1998, Chaos.

[21]  Hsin-Yi Lin,et al.  Integrating Recurrent Neural Networks With Data Assimilation for Scalable Data‐Driven State Estimation , 2021, Journal of Advances in Modeling Earth Systems.