This paper concerns solving the steady radiative transfer equation with diffusive scaling, using physics informed neural networks (PINNs). The idea of PINNs is to minimize a least-square loss function, that consists residual from governing equation, mismatch boundary conditions, and other physical constraints such as conservation. It advantageous being flexible easy execute, brings potential fo...

The modified two-stream approximation is derived from the radiative transfer equation using a two-point gaussian quadrature and neglecting terms of order 2 > 3 in the Legendre expansion of the phase function. The results are compared with the Eddington approximation and with exact results for the special cases of perfect absorption, perfect scattering, and a semi-infinite layer with isotropic s...

A stabilized weak formulation of the radiative transfer equation is presented, which is stable independent of the scattering coeecient. This enables the use of standard nite element discretizations without further algebraic constraints. Furthermore, a weighted residual-based a posteriori error estimate is derived for the discrete solution. An example demonstrates the eeciency of the new method.