  Given an unknown dynamic system such as a coupled harmonic oscillator with
$n$ springs and point masses. We are often interested in gaining insights into
its physical parameters, i.e. stiffnesses and masses, by observing trajectories
of motion. How do we achieve this from video frames or time-series data and
without the knowledge of the dynamics model? We present a neural framework for
estimating physical parameters in a manner consistent with the underlying
physics. The neural framework uses a deep latent variable model to disentangle
the system physical parameters from canonical coordinate observations. It then
returns a Hamiltonian parameterization that generalizes well with respect to
the discovered physical parameters. We tested our framework with simple
harmonic oscillators, $n=1$, and noisy observations and show that it discovers
the underlying system parameters and generalizes well with respect to these
discovered parameters. Our model also extrapolates the dynamics of the system
beyond the training interval and outperforms a non-physically constrained
baseline model. Our source code and datasets can be found at this URL:
https://github.com/gbarber94/ConSciNet.
