As per object, what is the current state of the art? Last year we had some work on approximating both the solution and the PDE using neural networks:

https://arxiv.org/abs/1801.06637

This year (well, actually last year, too, but then the preprint kept being revised until recently) we had the paper from Google on approximating the solution given knowledge of the PDE (whose results are frankly not as impressive as advertised, solving the 1D Burgers equation with 1024 convolutions is not gonna give the scare to commercial CFD codes producers)

https://arxiv.org/abs/1808.04930

There must have been something else, of course, or NeurIPS wouldn’t have accepted a workshop on Machine Learning and the Physical Sciences. What’s the current state of the art? I’m especially interested in fluid dynamics, but I wouldn’t mind learning about using Deep Learning to solve PDEs stemming from other branches of physics.