SyMetric: Measuring the Quality of Learnt Hamiltonian Dynamics Inferred from Vision
This work addresses a critical evaluation gap for Hamiltonian-based models in fields like robotics and autonomous driving, though it is incremental as it builds on prior methods.
The authors tackled the problem of evaluating models that learn latent dynamics from images using Hamiltonian mechanics, by developing new measures including SyMetric, which more accurately assesses the quality of learnt dynamics than existing methods. They used SyMetric to improve a model, resulting in HGN++, which achieves stable, infinite-length rollouts on some datasets and interpretable latents.
A recently proposed class of models attempts to learn latent dynamics from high-dimensional observations, like images, using priors informed by Hamiltonian mechanics. While these models have important potential applications in areas like robotics or autonomous driving, there is currently no good way to evaluate their performance: existing methods primarily rely on image reconstruction quality, which does not always reflect the quality of the learnt latent dynamics. In this work, we empirically highlight the problems with the existing measures and develop a set of new measures, including a binary indicator of whether the underlying Hamiltonian dynamics have been faithfully captured, which we call Symplecticity Metric or SyMetric. Our measures take advantage of the known properties of Hamiltonian dynamics and are more discriminative of the model's ability to capture the underlying dynamics than reconstruction error. Using SyMetric, we identify a set of architectural choices that significantly improve the performance of a previously proposed model for inferring latent dynamics from pixels, the Hamiltonian Generative Network (HGN). Unlike the original HGN, the new HGN++ is able to discover an interpretable phase space with physically meaningful latents on some datasets. Furthermore, it is stable for significantly longer rollouts on a diverse range of 13 datasets, producing rollouts of essentially infinite length both forward and backwards in time with no degradation in quality on a subset of the datasets.