Vicsek GNN

Trying to uncover pairwise potentials symbolically of birds flights using GNNs

Real flight data projected into 2D space.

Corrolated movement

Some birds corrolated movement

Vicsek model for 10 birds moving at 3m/s in 3d space projected into 2D space.

3D Model (mathematical description)

Visulaliztion:

Perameters:

• Noise = 0.25
• Velocity = 20 (m/s)
• Radius = 200 m

Perameters:

• Noise = 0.25
• Velocity = 20 (m/s)
• Radius = 100 m

Limitations:

• Birds all have same velocity

Lenored Jones Potential to model the birds with a pairwise potential:

The GNN couldnot learn from this simulation and could not reduce its loss at all!

Perameters:

• epsilon
• sigma

Extension:

Using spring as a baseline: GNN works perfectly. However pairwise rules are very rigid and simple...

Using 95 videos of collective motion flights:

Apply this to real flight data to try to uncover some symbolic model.

We assume that there is some potential between pairs of birds in the flock related to their hierarcical value difference.

References:

• Nagy, Máté, et al. "Hierarchical group dynamics in pigeon flocks." Nature 464.7290 (2010): 890-893.

• Cranmer, Miles, et al. "Discovering symbolic models from deep learning with inductive biases." Advances in Neural Information Processing Systems 33 (2020): 17429-17442.

• https://arxiv.org/pdf/1904.09584.pdf