as one of the authors, I might be able to answer some of the questions raised in this discussion
cba9 - In theory given sufficient amount of data (which can be generated), any physics engine can be approximated by a machine learning algorithm, however it might be tricky to make it faster than an existing solver. We got to the conclusion NN can not beat the fastest solvers (PBF). This might change with the newest development of the hardware.
krapht - The feature vector is based on N-S equations, so there is a potential to approximate the solver to any precision
david_ar - We tried to analyze the model, and as for many learning approaches it seem kinda impossible to see what is going on.
fenomas - Instead of solving diff equations, we train a regression model, which predicts the same thing as a numerical solver.
lifeformed - any regression is a machine learning approach by definition
daniel-levin - at the time we wrote the paper, we were not sure about the generalization properties. We didn't find any failure case either (if we did, we would just include such simulations in the training set). However, in the last week before the conference we tried various different forms of additional forces to simulate sand/ash/whatever and to do so we used the model trained only on water simulations. Surprisingly, it generalized quite well. However, not extrapolating outside the training set has some advantages - our method is stable and simply never diverges even if we try really hard.
irascible - after we do some optimizations (I guess it can be sped up by a factor of 10 or so) and finish/publish all kinds of other materials (smoke, fire, foam, elastic bodies, fractures, cloth, ..), we plan to do library, a plugin for Unity, etc and licence it