A holomorphic neural network framework for 3D boundary value problems governed by harmonic potentials

ArXi:2605.31231v1 Announce Type: cross We present a neural-network-based framework for the solution of three-dimensional boundary value problems where the solution is expressible in terms of harmonic potentials. The approach leverages the Whittaker integral formula, which allows representing the solution through functions that are holomorphic with respect to a suitable complex variable. These functions are subsequently approximated using holomorphic neural networks, which guaranty fulfillment of the holomorphicity requirement.