PHASE performance with independently varying viscous and resistive scales

Determine the performance of the PHASE physics-adapted neural operator for incompressible magnetohydrodynamics when the kinetic Reynolds number Re and magnetic Reynolds number Rm vary independently, rather than being constrained to Re = Rm.

Background

PHASE is developed and evaluated only for two-dimensional incompressible magnetohydrodynamics under the restriction Re = Rm, corresponding to magnetic Prandtl number Pm = 1. Consequently, the reported experiments do not test regimes in which viscous and resistive dissipation act at independently varying scales.

The unresolved problem is to assess whether the model maintains accurate predictions when Re and Rm are decoupled, thereby extending its multi-regime modeling capability to varying magnetic Prandtl numbers and independently controlled viscous and resistive scales.