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Given an unknown dynamic system such as a coupled harmonic oscillator with$n$ springs and point masses. We are often interested in gaining insights intoits physical parameters, i.e. stiffnesses and masses, by observing trajectoriesof motion. How do we achieve this from video frames or time-series data andwithout the knowledge of the dynamics model? We present a neural framework forestimating physical parameters in a manner consistent with the underlyingphysics. The neural framework uses a deep latent variable model to disentanglethe system physical parameters from canonical coordinate observations. It thenreturns a Hamiltonian parameterization that generalizes well with respect tothe discovered physical parameters. We tested our framework with simpleharmonic oscillators, $n=1$, and noisy observations and show that it discoversthe underlying system parameters and generalizes well with respect to thesediscovered parameters. Our model also extrapolates the dynamics of the systembeyond the training interval and outperforms a non-physically constrainedbaseline model. Our source code and datasets can be found at this URL:https://github.com/gbarber94/ConSciNet.

Joint Parameter Discovery and Generative Modeling of Dynamic Systems