Physics-enhanced Gaussian Process Variational Autoencoder
Thomas Beckers Qirui Wu George J. Pappas
Variational autoencoders allow to learn a lower-dimensional latent space
based on high-dimensional input/output data. Using video clips as input data,
the encoder may be used to describe the movement of an object in the video
without ground truth data (unsupervised learning). Even though the object's
dynamics is typically based on first principles, this prior knowledge is mostly
ignored in the existing literature. Thus, we propose a physics-enhanced
variational autoencoder that places a physical-enhanced Gaussian process prior
on the latent dynamics to improve the efficiency of the variational autoencoder
and to allow physically correct predictions. The physical prior knowledge
expressed as linear dynamical system is here reflected by the Green's function
and included in the kernel function of the Gaussian process. The benefits of
the proposed approach are highlighted in a simulation with an oscillating
particle.