It’s an interesting topic.
There’s a little group of components at the end of this example that calculates the Gaussian curvature of a mesh per vertex:
(it gets the angles between ordered edges and sees how much more or less than 2pi they sum to)
So If you want to base some parameter of a goal on the Gaussian curvature of the starting mesh, that could be done without scripting by feeding this value in.
The custom ‘AngleSum’ goal at the start of that script also shows the calculation of the live angle sum as it changes during simulation. There it tries to make it 2pi everywhere so the mesh is developable, but you could instead take that calculated angle sum and use it as a multiplier for something else, like pressure or edge length.
However…
If this is the ultimate aim, I think a different approach could work better.
For tensile membranes (inflated or not) there are limits to the shapes they can take while remaining all in tension (for instance no membrane will inflate to a bowl shape without some other sort of restraints), but still quite a lot of freedom of form depending on how the tension is distributed (unlike just the minimal surface or CMC surface solutions where tension is constant across it).
Using mesh edges with non zero rest lengths or variable strengths can be a way to adjust these shapes, but it’s not always easy to see how to change these for the input to get the desired shape and without any parts ending up in compression.
I did work some time ago on a goal which would make live adjustments to local tensions of a membrane during form-finding to get it as close as possible to a reference shape while keeping the tension within given bounds. Not sure I ever posted it though. I’ll dig it out and have another look.