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Inferring the dynamics of oscillatory systems using recurrent neural networks.

Rok Cestnik¹, Markus Abel¹

¹Department of Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Str. 24/25, 14476 Potsdam-Golm, Germany.

Chaos (Woodbury, N.Y.)

|July 4, 2019

Summary

Recurrent neural networks accurately predict oscillatory systems, even estimating dynamical properties in unobserved regions. This study assesses data needs for common recurrent neural network cells.

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Area of Science:

Dynamical systems theory
Computational neuroscience
Machine learning

Background:

Recurrent neural networks (RNNs) show promise in modeling complex time-series data.
Oscillatory systems are fundamental in various scientific domains, exhibiting rich dynamical behaviors.
Predicting system behavior beyond observed data is a significant challenge.

Purpose of the Study:

To evaluate the predictive capabilities of RNNs for oscillatory systems, including their vicinity.
To explore the estimation of dynamical properties like bifurcations and characteristic exponents using RNNs.
To determine the data requirements for effective RNN-based inference in oscillatory systems.

Main Methods:

Utilizing recurrent neural networks, including Long Short-Term Memory (LSTM) and Gated Recurrent Unit (GRU) cells.
Perturbing oscillatory systems with external forces to analyze their response and dynamical properties.
Applying statistical analysis to assess the impact of training data volume on prediction accuracy.

Main Results:

RNNs demonstrate effective prediction of oscillatory systems' time evolution and dynamical properties.
Accurate estimation of system behavior was achieved even in regions with no input data.
The study quantified the amount of training data necessary for reliable inference using LSTM and GRU cells.

Conclusions:

Recurrent neural networks are powerful tools for analyzing and predicting the behavior of oscillatory systems.
RNNs can generalize predictions to unobserved regions, offering insights into system dynamics.
Understanding data requirements is crucial for optimizing RNN performance in modeling oscillatory phenomena.