This might be a soft question, and may also demonstrate some misunderstanding on my part.
M. Gromov's $h$-principle is a powerful characterization on when general classes of PDEs and PDRs (specifically under-determined ones) admit solutions. Specifically if a problem admits the h-principle generic solutions can be deformed to true (holonomic) solutions.
Now we have a very similar sounding semi-analytical method of solving PDEs called homotopy analysis method which given an initial guess solution uses series expansion and homotopy methods to converge to solutions.
I understand the two methods are of completely different flavors, but I was wondering if there is any relationship between these two methods? My gut instinct would be that the second can be interpreted as a special case of the first, but I couldn't find any resources that made any connections whatsoever, so they might not be related.