Our work addresses the challenge of estimating spin polarization in high-energy electron and positron storage rings, such as the Electron Storage Ring (ESR) of the Electron-Ion Collider (EIC) at Brookhaven National Lab (BNL) and those in the electron/positron Future Circular Collider (FCC-ee) at CERN. We model the spin and orbital motion of particle bunches using the recently introduced spin-orbit Fokker-Planck (SOFP) equation, a linear time-evolution partial differential equation (PDE). In this paper, we propose a novel machine learning (ML) approach leveraging a randomized Fourier neural network (rFNN) framework, specifically designed to solve linear PDEs. We will discuss the SOFP highlight its relevance to spin polarization studies, and share preliminary results demonstrating the network’s performance on the Poisson problem.
Agudelo et al. (Thu,) studied this question.