Machine Learning S-Wave Scattering Phase Shifts Bypassing the Radial Schr\"odinger Equation

TL;DR

This paper introduces a machine learning approach using convolutional neural networks to predict s-wave scattering phase shifts directly from potentials, bypassing the radial Schrödinger equation, and demonstrates its effectiveness.

Contribution

The work presents a novel ML model that accurately predicts scattering phase shifts from potentials, guided by the Hamiltonian, even with bound states in the data.

Findings

Model accurately predicts phase shifts

Effective even with bound states present

Guided by Hamiltonian for physical relevance

Abstract

We present a proof of concept machine learning model resting on a convolutional neural network capable to yield accurate scattering s-wave phase shifts caused by different three-dimensional spherically symmetric potentials at fixed collision energy thereby bypassing the radial Schr\"{o}dinger equation. In out work, we discuss how the Hamiltonian can serve as a guiding principle in the construction of a physically-motivated descriptor. The good performance, even in presence of bound states in the data sets, exhibited by our model that accordingly is trained on the Hamiltonian through each scattering potential, demonstrates the feasibility of this proof of principle.