From the abstract.
This statement is patently false. The "boring solvers" are computationally expensive, to the point that some applications, such as structural optimization, are practically impossible to employ. We're talking about models which might take hours to run a single simulation.
Not to mention the fact that the computational cost of running high resolution models typically grows exponentially with regards to refinement level.
Boring old solvers were adequate to provide approximate solutions without having to resort to precalculated tables, but times moved on and so did the tech applications.
Again, the abstract does not appear to claim a performance benefit, so I'd love it if you could explain where that's coming from.