There's actually not much on #GroupTheory used for the same, all I could find in a (brief) search was the defunct International Society for Group Theory in Cognitive Science

https://web.archive.org/web/20170618215304/http://www.rci.rutgers.edu/~mleyton/GT.htm

the only name i recognize on there are Michael Leyton, and Jean Petitot (who uses things like #ContactGeometry for neurogeometry). Eloise Carlton's work seems cool: https://www.sciencedirect.com/science/article/abs/pii/002224969090001P "Psychologically simple motions as geodesic paths I. Asymmetric objects"