He is solving differential equations but with an analogue computer.
Doing it faster and with less doubts over fidelity and existence of a solution too.
Solving partial differential equations numerically and vetting the solution so obtained is not a trivial matters. Many things can go wrong in non obvious ways.
Analogue computers are a worthy alternative when applicable.
Relatedly, a common confusion is the use of probability in ergodic and non ergodic processes. The best example I have come across is that of a million people playing Russian Roulette with a six chamber revolver, in repeat mode.
At any instant, only about 1/6th will get shot. However, your own probability will rapidly converge to 1 of being shot.
I have forever been confused by 'left' and 'right'. It takes me a few seconds of deliberate thinking to get it right.
So in one of my first piece of software that I wrote for real money I had two functions. One called create_scene_left(), the other called create_scene_rght().
I was very pleased with myself for sneaking in creating_a_scene, but the left and right versions did the opposite of what their names indicated. Users of the software had no problems, but I am sure it would confuse any maintainer.
It even took me an year to even realize that the names were wrong.
In my interview, several decades ago, a binary search over the bitwise representation of integers is the solution that I came up with. To the interviewers credit, who was caught by surprise by a solution he had not anticipated, he played along very sportily. He was very intrigued and happy that we came up with a solution he hadn't encountered.
Later I felt stupid after reading about quick select.
I agree and I vehemently share your concern about profusion of tweakable parameters in the model.
There is some misconception in the wild about epicycles models that need not be shared by you specifically. There weren't that many epicycles per orbiting body, but every orbiting body had a few that had to be 'trained' specifically for them.
My fear, and I suspect yours too is that good curve fits done one at a time with mathematical models that are universal approximators (*) rarely, if at all lead to causally explanatory models. In Physics it's the latter that we seek.
(*) Epicycloidal models are a form of Fourier analysis and are a class of universal approximators for periodic trajectories.
I would argue that Kepler's success influenced the choice of the inductive bias. In that case the claim that Kepler took years what this can do in seconds is not an unbiased position to take.
I do see a great value in conjecturing possible solutions that needs to be verified with domain specific knowledge.
Recall that Ptolemaic epicycles were a great fit, in fact a better fit than Copernicus's heliocentric model. This makes me wary of deep NNs in Physics.
This is not surprising at all and depends on the inductive bias hardcoded in the search.
There are infinite number of curves that agree on those 8 points and deviate from Kepler 's law everywhere else. On such 'trajectories' this algorithm would have performed badly.
I loved how the Fortress language was coming slong till Oracle killed it. It was an interesting mix if Fortran and functional programming ideas with thoughtful ideas on parallelization.