Feed forward neural network parametrization of the mean radiative properties of the mixture

Abstract

Fast evaluated and highly accurate parametrization of the radiative properties has important applications where opacity evaluations in situ are frequently needed. Feed forward neural network (FFNN) is successfully developed to fit the average ionization degree, Planck and Rosseland mean opacities of the mixture from the opacity project. Three typical cases are shown: (a) for pure C, FFNNs with different sizes provide low to high representations, and with hundreds of parameters, the root mean square error (RMSE) decreases within 1%. Properties of the complex element such as Fe are also fitted successfully; (b) the mean properties of the CH mixture are fitted with the RMSE less than 2.7% by a 3×30×30×1 FFNN (1081 parameters). Analytical relations between the properties of mixture and each species are discussed; (c) the Rosseland mean opacities of the mixtures from solar model are reconstructed by a 4×20×20×1 FFNN (541 parameters) with the RMSE less than 0.7%, where the mass fractions of H and He are used as the reduced variables to distinguish the compositions at different solar radius. These cases illustrate the key points in the fitting and suggest FFNN as a feasible and powerful tool in the parametrization of mixture properties. This work is essential for practical application and further modelization of the mixture.