# Inferring the dynamics of oscillatory systems using recurrent neural networks

arXiv: https://arxiv.org/abs/1904.03026 · HTML: https://mlsanity.com/paper/1904.03026/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Apr 2019.

## Built on by (most cited first, 8 of 8)

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- [Almost-Linear RNNs Yield Highly Interpretable Symbolic Codes in Dynamical Systems Reconstruction](https://mlsanity.com/paper/2410.14240/) (2024)
- [Detecting Invariant Manifolds in ReLU-Based RNNs](https://mlsanity.com/paper/2510.03814/) (2025)
- [Learning Hamiltonian dynamics by reservoir computer](https://mlsanity.com/paper/2104.14474/) (2021)
- [Next-Generation Reservoir Computing for Dynamical Inference](https://mlsanity.com/paper/2509.11338/) (2025)
- [Deep Learning Surrogates for Emulating Stochastic Climate Tipping Dynamics](https://mlsanity.com/paper/2605.20580/) (2026)

## Abstract (arXiv)

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.