# Fold Bifurcation Identification through Scientific Machine Learning

arXiv: https://arxiv.org/abs/2312.14210 · HTML: https://mlsanity.com/paper/2312.14210/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 83 references that are in the map.
- First posted on arXiv 21 Dec 2023.

## Builds on (most cited first, 9 of 9)

- [A Survey of Convolutional Neural Networks: Analysis, Applications, and Prospects](https://mlsanity.com/paper/2004.02806/) (2020)
- [A Primer on Neural Network Models for Natural Language Processing](https://mlsanity.com/paper/1510.00726/) (2015)
- [Reliable extrapolation of deep neural operators informed by physics or sparse observations](https://mlsanity.com/paper/2212.06347/) (2022)
- [Using Machine Learning to Anticipate Tipping Points and Extrapolate to Post-Tipping Dynamics of Non-Stationary Dynamical Systems](https://mlsanity.com/paper/2207.00521/) (2022)
- [Anticipating synchronization with machine learning](https://mlsanity.com/paper/2103.13358/) (2021)
- [Convolutional Recurrent Neural Networks for Electrocardiogram Classification](https://mlsanity.com/paper/1710.06122/) (2017)
- [Predicting discrete-time bifurcations with deep learning](https://mlsanity.com/paper/2303.09669/) (2023)
- [Universal Early Warning Signals of Phase Transitions in Climate Systems](https://mlsanity.com/paper/2206.00060/) (2022)
- [Classification of chaotic time series with deep learning](https://mlsanity.com/paper/1908.06848/) (2019)

## Abstract (arXiv)

This study employs scientific machine learning to identify transient time series of dynamical systems near a fold bifurcation of periodic solutions. The unique aspect of this work is that a convolutional neural network (CNN) is trained with a relatively small amount of data and on a single, very simple system, yet it is tested on much more complicated systems. This task requires strong generalization capabilities, which are achieved by incorporating physics-based information. This information is provided through a specific pre-processing of the input data, which includes transformation into polar coordinates, normalization, transformation into the logarithmic scale, and filtering through a moving mean. The results demonstrate that such data pre-processing enables the CNN to grasp the important features related to transient time-series near a fold bifurcation, namely, the trend of the oscillation amplitude, and disregard other characteristics that are not particularly relevant, such as the vibration frequency. The developed CNN was able to correctly classify transient trajectories near a fold for a mass-on-moving-belt system, a van der Pol-Duffing oscillator with an attached tuned mass damper, and a pitch-and-plunge wing profile. The results contribute to the progress towards the development of similar CNNs effective in real-life applications such as safety monitoring of dynamical systems.