Hamiltonian GAN
This work addresses the limitation of requiring structural priors in Hamiltonian-based video generation, offering a more flexible approach for researchers in physics-informed machine learning, though it is incremental as it builds on existing Hamiltonian methods.
The paper tackles the problem of learning a configuration space representation from data for physically plausible video generation, by introducing a GAN-based pipeline with a learned map and Hamiltonian neural network, achieving improved interpretability on the Hamiltonian Dynamics Suite Toy Physics dataset.
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.