# Inferring the dynamics of oscillatory systems using recurrent neural networks

## TL;DR

This paper demonstrates that recurrent neural networks can effectively predict and analyze the dynamics of various oscillatory systems, including bifurcations and response curves, even with limited training data.

## Contribution

It introduces a method for using RNNs to infer detailed dynamical properties of oscillatory systems, extending beyond simple prediction.

## Key findings

- RNNs accurately predict system evolution in perturbed oscillatory systems.
- Effective estimation of bifurcations and dynamical response curves using RNNs.
- Quantitative analysis of training data requirements for LSTM and GRU networks.

## Abstract

We investigate the predictive power of recurrent neural networks for oscillatory systems not only on the attractor, but in its vicinity as well. For this we consider systems perturbed by an external force. This allows us to not merely predict the time evolution of the system, but also study its dynamical properties, such as bifurcations, dynamical response curves, characteristic exponents etc. It is shown that they can be effectively estimated even in some regions of the state space where no input data were given. We consider several different oscillatory examples, including self-sustained, excitatory, time-delay and chaotic systems. Furthermore, with a statistical analysis we assess the amount of training data required for effective inference for two common recurrent neural network cells, the long short-term memory and the gated recurrent unit.