Deducing Closed-Form Expressions for Bright-Solitons in Strongly Magnetized Plasmas with Physics Informed Symbolic Regression (PISR)

Abstract: This paper presents a novel approach to finding analytical approximations for bright-soliton solutions in strongly magnetized plasmas. We leverage Physics-Informed Symbolic Regression (PISR) to discover closed-form expressions for the vector potential and number density profiles, governed by a reduced-order model derived from Maxwell-fluid equations. The PISR framework combines symbolic regression with physics-based constraints, boundary conditions, and available simulation data to guide the search for solutions. We demonstrate the effectiveness of the approach by rediscovering approximate solutions consistent with previously published numerical results, showcasing the potential of PISR for reducing simulation costs of reduced-order models in plasma physics.