Real progress on machine learning for density functional theory

(Sorry about the slow pace of posting.  The end of the semester has been very intense, including a faculty retreat for our department last week.)

I've written before (here, here, and here) about density functional theory, arguably one of the most impactful intellectual physics results of 20th century physics.   DFT is one approach to trying to solve the quantum electronic structure problem for molecules or solids containing many electrons.  As explained in the links above, the idea is powerful.  It turns out that the ground state (lowest energy state) electronic density as a function of position \(n(\mathbf{r})\), contains all the information needed to calculate basically anything you could want to know about the ground state.  There is a functional \(E[n(\mathbf{r})]\), for example, that will give you the energy of the full-on, interacting many-electron ground state.  It's possible to do a non-interacting electron model that can get you arbitrarily close to the true, correct \(n(\mathbf{r})\), The tricky bit is, there is no exact analytical expression for the functional \(E[n(\mathbf{r})]\), which includes a particularly tricky contribution called the exchange-correlation part of the functional, \(E_{\mathrm{xc}}[n(\mathbf{r})]\).  Because we are talking about functionals rather than functions,  \(E_{\mathrm{xc}}[n(\mathbf{r})]\) might depend in a non-local way on \(n(\mathbf{r})\) and its derivatives at all points in space - there is no reason to think it will be simple to write down.  

From deepmind.com

I wrote six years ago about the idea that machine learning techniques might make it possible to get a working version of something close to the exact \(E_{\mathrm{xc}}[n(\mathbf{r})]\) , even if we can't readily write it down in some closed form.  Now it seems that real progress has been made in this direction.  Here is a blog post from the DeepMind team about their paper in Science this week where they demonstrate a new functional that they claim is very good and accurate vs exact calculations on test systems, computationally tractable, and satisfies fundamental properties that have to hold for the true exact functional.  They argue that their code is more than just a fancy look-up table and that it contains generalizable knowledge so that it's useful well beyond their specific training test cases.  

If this is so, then it could be a major step forward in (for some definitions of the term) first-principles calculations of molecular and material properties.  I'm curious about whether the new functional will actually let us gain some physical insight into why physics requires that particular underlying mathematical structure.  Still, even if we end up with a "black box" that allows greatly improved calculations, that would really be something.  I'd appreciate it if knowledgable DFT/electronic structure experts could comment here on how excited we should be about this.