Spherical Fourier Neural Operators for Modelling Electrostatic Potential and Ion Transport in Electrolyte Solutions

We introduce the Spherical Fourier Neural Operator (SFNO), a new computational framework that efficiently solves two equations describing electrostatic potential and ion movement dynamics in electrolyte solutions. Implementing Spherical Harmonic Transform and SFNO models allows researchers to accurately understand complex dynamical processes in spherical geometries using minimal computational resources compared to Finite Difference and Finite Element Methods. The model received training with synthetic inputs derived from numerical solutions representing various initial conditions across different parameter intensities from governing PDEs. The training process employed a two-stage protocol: A single-step autoregressive training period initiates the process before multiple-step autoregressive training completes the process jointly to develop better stability alongside extended prediction accuracy. Across all scenarios, the SFNO model provided accurate predictions of electrostatic potential and ionic fluxes while displaying minimal errors and maintaining fundamental physical consistency. Further development of this method requires better generalization performance and solutions for variance-based issues, as demonstrated by the negative R-square scores. The results of SFNO-based modeling have showcased their potential to transform the simulation of complex electrolyte structures by delivering a flexible solution that works efficiently for present-day scientific applications and industrial production requirements.