Forecasting Fold Bifurcations through Physics-Informed Convolutional
  Neural Networks
Giuseppe Habib Ádám Horváth
This study proposes a physics-informed convolutional neural network (CNN) for
identifying dynamical systems' time series near a fold bifurcation. The
peculiarity of this work is that the CNN is trained with a relatively small
amount of data and on a single, very simple system. In contrast, the CNN is
validated on much more complicated systems. A similar task requires significant
extrapolation capabilities, which are obtained by exploiting physics-based
information. Physics-based information is provided through a specific
pre-processing of the input data, consisting mostly of a transformation into
polar coordinates, normalization, transformation into the logarithmic scale,
and filtering through a moving mean. The results illustrate that such data
pre-processing enables the CNN to grasp the important features related to
approaching a fold bifurcation, namely, the trend of the oscillation amplitude,
and neglect other characteristics that are not particularly relevant, such as
the vibration frequency. The developed CNN was able to correctly classify
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 obtained pave the way for the
development of similar CNNs effective in real-life applications.