this functionality has been broken on goproblems.com for a long time, but it's working again here:
https://www.goproblems.com/startsearch.php

you can use this to search for problems of a given partial position. this revamped version is using jGoBoard instead of a Java applet, finally! it's also much faster, has a nicer UI, gives results without leaving the page, and remembers your search position.

while testing this feature, i had a couple of interesting thoughts, which seem to almost contradict eachother:
1) it's starting to feel like every known "basic" problem is already in the database. by basic, i mean a classical life and death problem, in a corner, that is well structured and not too crazily difficult. the type of problem you think of in a typical go problem book. i was trying to add a couple problems and it felt like all of these were already in the 12k problem database at this point.
2) how few results you get in a search with just a couple of stones on the board. for example, searching for this position:

i would naively imagine lots of hits over the 12k problems. but it's just a single hit.

so this gives me hope that many many more interesting problems are yet to be created!