) where x i and x j are the doping concentrations in regions i and j, respectively and s is written in spherical coordinates. While the probability of energy transfer between two dopants is actually proportional to distance -6 , we chose to represent this probability as a sum of Gaussian functions because they are continuous at x = 0 and can be integrated multiple times while still capturing the decaying nature of energy transfer with increasing distance between two ions. Adjusting the σ parameters within the Gaussians allows for the modulation of the effective interaction distance of dopants. When used in the ML model, the integrated interaction module is parameterized by n learnable weights (here n = 5) each corresponding to a σ value of one of the Gaussians in the sum.