Some comments on this publication: Their approach is to train a learned downsampler of the boundary and initial conditions, and pass it through a learned coarse-grained "simulator", but the output is only a specified target property, not the full PDE solution. The claim is a decrease in training data needed and faster execution.

The limitation is that you need to have a target property of interest which is not always the case when trying to simulate something.

The paper as it is written is very low quality. They basically ran no real benchmarks and ignored all the other work on this topic. They used a plain NN to act as a baseline and their justification for this was that if you used any of the other published surrogate models to predict a target property you would end up with a NN. This is not a good faith comparison at all. Besides that, they also only ran very tiny experiments which is not where the need for surrogate models lies. And even the layout of the paper is very chaotic.

Unrelated question: Is Nature considered a low quality journal for ML papers?