Mesprit moves around the world at random so it could potentially be anywhere after it runs away. To find where he is, use the map on the Poketch.
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You can't I don't think.
mesprit is a wandering Pokemon, so after it runs away, it goes somewhere out in sinnoh. if you switch locations at certain places, mesprit will eventually get to where you are. do not fly to a nearby location with mesprit, or it will run away to a different place. hope this helps =D
You always start form twinleaf town right? So go to the lake closest to twinleaf, and use surf to go to a cave in the middle of nowhere, go inside, and you'll hopefully find a mesprit. Mesprit runs away from you, so I suggest you have a Pokemon with Mean Look.
Instead of flying to the nearest city, which makes it run away, walk or bike to its icon on poketch app Marker Map and look around in the nearest patch of tall grass. Mesprit often runs away, so be careful!
mesprit is at the descon wold and then it will be at verity lakefront and then it will start going around sihhoh in Pokemon platinum