Thermodynamics-informed super-resolution of scarce temporal dynamics
  data
Carlos Bermejo-Barbanoj Beatriz Moya Alberto Badías Francisco Chinesta Elías Cueto
We present a method to increase the resolution of measurements of a physical
system and subsequently predict its time evolution using thermodynamics-aware
neural networks. Our method uses adversarial autoencoders, which reduce the
dimensionality of the full order model to a set of latent variables that are
enforced to match a prior, for example a normal distribution. Adversarial
autoencoders are seen as generative models, and they can be trained to generate
high-resolution samples from low-resoution inputs, meaning they can address the
so-called super-resolution problem. Then, a second neural network is trained to
learn the physical structure of the latent variables and predict their temporal
evolution. This neural network is known as an structure-preserving neural
network. It learns the metriplectic-structure of the system and applies a
physical bias to ensure that the first and second principles of thermodynamics
are fulfilled. The integrated trajectories are decoded to their original
dimensionality, as well as to the higher dimensionality space produced by the
adversarial autoencoder and they are compared to the ground truth solution. The
method is tested with two examples of flow over a cylinder, where the fluid
properties are varied between both examples.