Physical Constraint Embedded Neural Networks for inference and noise regulation

Neural networks often require large amounts of data to generalize and can be ill-suited for modeling small and noisy experimental datasets. Standard network architectures trained on scarce and noisy data will return predictions that violate the underlying physics. In this paper, we present methods for embedding even--odd symmetries and conservation laws in neural networks and propose novel extensions and use cases for physical constraint embedded neural networks. We design an even--odd decomposition architecture for disentangling a neural network parameterized function into its even and odd components and demonstrate that it can accurately infer symmetries without prior knowledge. We highlight the noise resilient properties of physical constraint embedded neural networks and demonstrate their utility as physics-informed noise regulators. Here we employed a conservation of energy constraint embedded network as a physics-informed noise regulator for a symbolic regression task. We showed that our approach returns a symbolic representation of the neural network parameterized function that aligns well with the underlying physics while outperforming a baseline symbolic regression approach.

Joint Parameter Discovery and Generative Modeling of Dynamic Systems

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.