I read "An elementary introduction to information geometry" of Frank Nielsen (https://arxiv.org/pdf/1808.08271.pdf), and I am very impressed by this theory.
Now, I am searching for some theory about manifolds that defined by solutions of partial differential equations (PDE). I suppose, Laplace equation with undetermined boundary condition defines some manifold of possible solutions.
I need a help from community, because Google Scholar and Google propose me articles about solution of PDE on manifolds, but not about manifolds defined by PDE solutions.