Radiative transfer is a fundamental process in astrophysics, essential for both interpreting observations and modeling thermal and dynamical feedback in simulations via ionizing radiation and photon pressure. However, numerically solving the underlying radiative transfer equation is computationally intensive due to the complex interaction of light with matter and the disparity between the speed of light and the typical gas velocities in astrophysical environments, making it particularly expensive to include the effects of on-the-fly radiation in hydrodynamic simulations. This motivates the development of surrogate models that can significantly accelerate radiative transfer calculations while preserving high accuracy. We present a surrogate model based on a Fourier Neural Operator architecture combined with U-Nets. Our model approximates three-dimensional, monochromatic radiative transfer in time-dependent regimes, in absorption-emission approximation, achieving speedups of more than 2 orders of magnitude while maintaining an average relative error below 3%, demonstrating our approach's potential to be integrated into state-of-the-art hydrodynamic simulations.

We propose a novel machine learning algorithm for simulating radiative transfer. Our algorithm is based on physics informed neural networks (PINNs), which are trained by minimizing the residual of the underlying radiative tranfer equations. We present extensive experiments and theoretical error estimates to demonstrate that PINNs provide a very easy to implement, fast, robust and accurate method for simulating radiative transfer. We also present a PINN based algorithm for simulating inverse problems for radiative transfer efficiently.