The OED entry for ansatz lists it as a regular noun in English. That means it takes -es for the plural here.
On the other hand, its earliest citation almost looks invariant:
- 1942 Jrnl. Indian Math. Soc. 6 41 (title) Studies in Fourier ansatz and
The other citations, through 1990, all look completely singular. There are no clear examples of a plural. It just isn’t marked as irregular, and they always do that if it is.
There are extremely few words in the OED of German derivation that retain their German plural in English, perhaps a half-dozen odd ones, and seldom as the dominant form. For example, there is one citation from 1962 of bratwurst > bratwürste:
- 1962 Punch 11 July 51/2 We ate two delicious Bratwürste apiece.
In contrast, Wandervogel is definitely marked Wandervögel in the plural, and the plural forms Wandervogel and Wandervogeln are marked catachrestic — that is, erroneous. Here are two examples of the word as an irregular plural:
- 1967 Listener 30 Nov. 705/3 Around 1930, alienated and disaffected youth was being manufactured mainly in Germany, where the First War had produced the biggest earthquake. Some of them called themselves the Wandervögel, and wandered around Europe with their guitars and their interchangeable girlfriends, living on what they could get wherever sympathisers would accept them.
- 1978 J. I. M. Stewart Full Term xxi. 241 A bunch of juvenile Wandervögel.
You can tell those uses aren’t assimilated because they’re still written in italic in the original. And they’re still capitalized, unlike most (but not all) citations of ansatz.
One more example with an irregular German plural in English is Land, “a semi-autonomous unit of local government in Germany and Austria”, whose plural is given as any of Länder
/ˈlɛndər/, Laender, Lands, and in that order.