Discovering new solutions to century-old problems in fluid dynamics

>The pattern was visible in two of the equations studied, the Incompressible Porous Media (IPM) and Boussinesq equations.

Wait until they get into porous media of variable porosity at pressures up to 20,000 psi or more. You get compressibility factors up the wazoo. Plus anywhere near critical points, physical density can take on almost new meaning so one of the holiest grails was to pray for digital densitometry and live to have it come true :)

In oil & gas exploration research back in 1981 we had one of the early experts working on this but it required a mainframe. He was tied into the big iron by time-sharing dial-up from the same lab where I had helped build the facilities for the physical modeling. Using the actual subsurface core samples and reservoir fluids in question where enhanced oil recovery was contemplated. I was doing advanced data handling for the oil & gas analyzers using new benchtop HP systems where it previously required a mainframe, so until then it only had been possible within the major oil companies' own labs, not any technology startup.

>Unlike conventional neural networks that learn from vast datasets, we trained our models to match equations which model the laws of physics.

We had models but not neural networks, but already thought that AI was probably going to be good as it matures, so that's what we were preparing for every day. There was still great room for improvement in the equations for the exact reasons these modern researchers have worked to pinpoint, so that kept us plenty busy. Plus we were invoicing oil companies and making money on our experiments as we went along, where I absolutely love delighting clients and giving them their money's worth, and "busyness" there matches the description most appropriately. I guess I turned out to always favor computer modeling where you have a physical lab to check advancements against, as well as invoice from.

The oil bust hit in 1982 and all groups like this were scattered, followed by decades of depression in research after which it has never been comparable. Nobody cared about this kind of thing any more, at least not anybody that could afford it.

What these researchers have elegantly pursued in automated discovery of these type snafus using modern powerful computers is what's basically been on my mind since I heard about LLM's to begin with. Things like this that I've always wanted to do, mere language models still wont help me now, or no matter how much better they get at language.