Well, you are not alone. As a Math PhD, I want to believe that there is something less trivial than glorified linear regression to this whole AI/ML mess, but well, there isn't... It's non-linear transforms + holy Mary's all the way.
Otter, N., Porter, M.A., Tillmann, U. et al. A roadmap for the computation of persistent homology. EPJ Data Sci. 6, 17 (2017). https://doi.org/10.1140/epjds/s13688-017-0109-5