Artificial Derivation of Schrödinger Equation Driven by Artificial Neural Networks

Abstract

Starting from the idea that artificial intelligent might be able to derive known as well as unknown equations of physics and other different branches of basic science, the concept of perceptron was used to derive the the well-known Schrödinger equation. The physics scenario has consisted in the case of a massive particle with an electric charge. While inputs have been defined as a family of polynomials dependent on the system energy, weights are characterized by having a direct dependence on unphysical variables. With this, wavefunction was reconstructed and it turned out to be the perceptron output. Also, Hamiltonian and evolution operator were reconstructed. The square of probability have displayed to exhibit up to two well-defined regions, situation that would come from perceptron methodology than derived from physics itself.