Hamiltonian GAN
Christine Allen-Blanchette
A growing body of work leverages the Hamiltonian formalism as an inductive
bias for physically plausible neural network based video generation. The
structure of the Hamiltonian ensures conservation of a learned quantity (e.g.,
energy) and imposes a phase-space interpretation on the low-dimensional
manifold underlying the input video. While this interpretation has the
potential to facilitate the integration of learned representations in
downstream tasks, existing methods are limited in their applicability as they
require a structural prior for the configuration space at design time. In this
work, we present a GAN-based video generation pipeline with a learned
configuration space map and Hamiltonian neural network motion model, to learn a
representation of the configuration space from data. We train our model with a
physics-inspired cyclic-coordinate loss function which encourages a minimal
representation of the configuration space and improves interpretability. We
demonstrate the efficacy and advantages of our approach on the Hamiltonian
Dynamics Suite Toy Physics dataset.