Fold Bifurcation Identification through Scientific Machine Learning

TL;DR

This paper introduces a physics-informed CNN approach for identifying fold bifurcations in dynamical systems from transient time series, demonstrating strong generalization across different complex systems with minimal data.

Contribution

It presents a novel CNN training method that incorporates physics-based data pre-processing, enabling accurate bifurcation detection with limited data and high generalization.

Findings

CNN accurately classifies bifurcation trajectories in multiple systems

Physics-based pre-processing improves feature extraction and generalization

Method shows potential for real-life safety monitoring applications

Abstract

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.