Predicting 2D coordinate of 'optimum' connection point of 3 points with neural networks

I have some data which represent a tree-like structure with many branches extending from it. A new point to be connected to the existing tree is found and an 'optimum' connection point (to minimize branch volume & obey some physical constraints) is currently found using some iterative calculations.

I want to make a machine learning model that can predict this optimum connection point but I'm struggling to think of how to do this.

The data I have is the xy coordinates of the 3 points that are to be joined and the corresponding optimum point that joints the points together. I also have the 'thickness' of each branch. I tried making a regression model with the xy coordinates as output, but the predictions aren't very accurate...

Diagram of problem:

Can anyone think of some approaches to solving this problem?

https://stackoverflow.com/questions/65957480/predicting-2d-coordinate-of-optimum-connection-point-of-3-points-with-neural-n January 29, 2021 at 11:40PM