Regressing Dynamic System Parameters from Poincare Maps

Preprint link ($5 CAD prize if you can help us figure out a better title)

(I know this page is low on text and a bit eye-burning right now, I’m hoping to come back to this soon! The paper is still going through the journal submission process with all of its wonders)

Figure 1: Real-time construction of Poincare maps for the Swinging Atwood's Machine (SAM) in a stable (red) and chaotic (green) configuration. On the left is the system configuration, on the right is the Poincare-Map representation of the system.	Figure 2: Sampled Poincare maps for the Swinging Atwood's Machine (colours correspond to trajectories from different initial configurations) for various values of the system's mass-ratio parameter, μ.

Figure 3: An example input-output for a deep learning model I developed which estimates the mass ratio parameter of the SAM system which produced the Poincare map (left) input to the network. On the right is the parameter estimate, along with a higher quality Poincare map corresponding to the estimated parameter.

Figure 4: Pixel-wise classification of the chaoticity of trajectories using a U-Net style architecture with a standard semantic segmentation approach. Left: ground truth, right: predictions. Note the blob-like artifacts in the prediction (right) which imply multiple classifications for the same trajectory.	Figure 5: Trajectory chaos classifications obtained from a physics-based modification of the U-Net architecture which makes classifications at the trajectory level.