Collective motion is a fascinating form of emergent behavior, observed in e.g. the flocking of birds and schooling of fish. The Vicsek Model (CLICK HERE for a good summary) aims at reproducing this form of complex behavior through a short-range velocity-aligning force. The phase diagram of this model is similar to that of a liquid-gas transition, and is marked by a region of coexistence between disorderly and collectively moving particles. It can be seen as a non-equilibrium version of the XY-model, where the moving spins now have continuous positions, rather than being stationary on a lattice. These continuous positions make a treatment with machine learning more difficult, as most neural networks are designed for grid-based data.
A first objective for this thesis would hence be developing a machine learning algorithm to work with these continuous positions and identifying the phases of the Vicsek model. For this, the student can build on the experience our group has with machine learning of the Active Ising Model , a grid-based version of the Vicsek Model. Once this has been achieved, possible extensions are e.g. looking into the temporal evolution of the Vicsek Model and Active Ising Model, or developing a machine learning algorithm to accelerate simulations for models of collective motion (CLICK HERE for a good summary).