AI-based computation method for the Eddington factor in the M1-multigroup model

Radiative hydrodynamics models the interaction between fluid flows and radiation, which is essential for many astrophysical simulations. The M1-multigroup model is widely regarded as the most precise framework for capturing the complex interplay between light and matter, particularly by accounting for the spectral behavior of photons. A critical component of this model is the Eddington factor, which is used in the closure relation linking the radiative pressure to the radiative energy. Although an analytical expression for the Eddington factor does not exist, our research reveals that it depends solely on three parameters: the radiative temperature, the reduced flux, and the group narrowness. To address the challenge of calculating this factor efficiently, we have developed a method that combines neural networks and polynomial approximations. This method achieves computational speeds up to 3000 times faster than traditional line search algorithms while providing precision levels up to 1000 times higher than simplified alternatives based on interpolation or the analytical expression of the M1-gray model. Unlike interpolation-based techniques, it operates without requiring prior knowledge of radiative quantities, offering greater flexibility and applicability in diverse scenarios. Although the test simulations we performed, where radiation pressure is not the dominant factor, demonstrate a limited impact of the precision of the estimation of the Eddington factor on fluid dynamics, our approach lays a solid foundation for future advancements. It is particularly promising for more complex simulations involving out-of-equilibrium, radiative pressure-dominated scenarios. These developments mark a significant step forward in radiative hydrodynamics, offering a robust, accurate, and highly efficient computational tool to advance astrophysical modeling.