  We use physics informed neural networks (PINNs) to solve the radiative
transfer equation and calculate a synthetic spectrum for a Type Ia supernova
(SN~Ia) SN 2011fe. The calculation is based on local thermodynamic equilibrium
(LTE) and 9 elements are included. Physical processes included are approximate
radiative equilibrium, bound-bound transitions, and the Doppler effect. A PINN
based gamma-ray scattering approximation is used for radioactive decay energy
deposition. The PINN synthetic spectrum is compared to an observed spectrum, a
synthetic spectrum calculated by the Monte-Carlo radiative transfer program
TARDIS, and the formal solution of the radiative transfer equation. We discuss
the challenges and potential of this deep-learning based radiative transfer
equation solver. In fact, PINNs offer the prospect of simultaneous solution of
the atmosphere problem for both radiation field and thermal state throughout
spacetime. We have made modest steps to realizing that prospect with our
calculations which required many approximations in order to be feasible at this
point in the development of PINN atmosphere solutions.
