The main problem is the mesh that you use for the simulation!
It features only 4 faces, which is not enough resolution. You can fix that by defining a smaller (Target Edge) Length for the TriRemesher. In general, the higher the mesh resolution, the more accurate the result of resolution that you get, but also the longer the computation time.
Another issue is how you define the anchor points. For the inclusion check of the vertices in the middle region, it is best to use the closed, planar curve, called Pattern1 instead of the individual line segments that the C (Creases) output of the TriRemesher spits out. Individual lines do not define a closed region.
You do also need to define the naked boundary vertices as anchors. Generally speaking you always define nodes, corresponding to mesh vertices as anchors, not any other random point that has nothing to do with the mesh that you want to define the anchors for. More simply put, the anchors are mesh vertices!
And last but not least, you absolutely need a force that drives the simulation. The anchors define what vertices get fixed in place, the edge length define the plasticity of the mesh edges - meaning how they stretch or contract -, and all of these parameters interact with a certain force or multitude of forces, and produce the simulation!
test inflate_anchor_v2.gh (15.9 KB)