Inferring the nuclear potential with a neural network via differentiable programming

The interaction between a nucleus and an incident neutron is a many-body interaction between the neutron and each individual nucleon in the target nucleus. While ab initio models for this interaction exist, they are computationally expensive and not as accurate as desired across the nuclear chart. The optical model, in which the neutron is modeled as a quantum mechanical wave refracting from a complex potential, is a fast approximation suited to global modeling of neutron-nucleus interaction. However, existing global optical models such as Koning-Delaroche have a limited number of parameters, necessitated by the hands-on training process and the inaccessibility of the error gradient with respect to these parameters. These models also struggle to reproduce scattering results at backwards scattering angles. We introduce a new, more flexible approach by writing a solver for the quantum scattering problem in a differentiable software framework. Differentiable programming is a method which allows the propagation of derivatives through arbitrary code structures. We use this strategy to propagate the error gradient through a numerical solver of Schrodinger’s equation and train a neural network to predict the optical potential for a wide range of nuclei and incident neutron energies directly from elastic scattering data. Our method demonstrates the exciting potential for the use of differentiable programming to solve inverse problems using experimental data in any number of scientific applications.