How do I clean the bottom of a porcelain pan?
You can't, mostly if it is unglazed/porous

(most) Porcelain dishes have porous bottoms, anything that touches it will be sucked in the small pores, and if baked in, will be more difficult to remove.

If the glazed part of the dish is clean, I would not think much about the bottom.

Some people will see it as a good sign that you are using it.

On the other hand, you could try using products like Bar Keepers and a plastic scouring pad to clean it.

Anecdotal, I keep the glazed part as clean as possible, and don't really care about the unglazed bottom.