Comment by verdverm
5 days ago
Is your project limited in scope to physics equations? The coefficient snapping is interesting, but seems like it would not work well for problems like predator-prey (https://en.wikipedia.org/wiki/Lotka%E2%80%93Volterra_equatio...). I mainly worked with biology and life-sciences data. (real-world, separate from the synthetic benchmark data)
I introduced a new type of "constant" for well known values like this that sit between measured data and free parameters. I think I had some idea similar to your snapping, i.e. to look for places where free parameters could be replaced with const, but multiples of them was not part of that.
Physics and known-constant problems were definitely the focus. My ambition was to create a fast algorithm that could pull out a nice, “natural-looking” equation from (potentially noisy) data, if one existed. Model ranking and selection, coefficient snapping, noise robustness, and the search patterns were all designed to that end.
For that reason, it does terribly on the SRBench black-box track (it doesn’t like to produce long, overfit models), but (to my knowledge) it scores the highest on exact symbolic recovery, and even with noise it can often find the answer in under 10s (single-thread, no GPU).
Does SRBench still run deterministic algorithms 30 times? A more useful measure than wall clock time is the number of equation evaluations and iterations it takes to get there. One of the benefits to deterministic algos is they only need to be run once, whereas you have to run the rng based algos 30+ times for statistical significance.
My algorithm came from frustration at the lack of rigor in the field. There were no standard benchmarks, results were not reproducible, don't get me started on Korns lol