Super-resolving sparse observations in partial differential equations: A
  physics-constrained convolutional neural network approach
Daniel Kelshaw Luca Magri
We propose the physics-constrained convolutional neural network (PC-CNN) to
infer the high-resolution solution from sparse observations of spatiotemporal
and nonlinear partial differential equations. Results are shown for a chaotic
and turbulent fluid motion, whose solution is high-dimensional, and has fine
spatiotemporal scales. We show that, by constraining prior physical knowledge
in the CNN, we can infer the unresolved physical dynamics without using the
high-resolution dataset in the training. This opens opportunities for
super-resolution of experimental data and low-resolution simulations.