An Extended Closure Relation by LightGBM for Neutrino Radiation Transport in Core-collapse Supernovae

Abstract We developed a machine learning model using LightGBM, one of the most popular gradient-boosting decision tree methods these days, to predict the Eddington tensor, or the second-order angular moment, for neutrino radiation transport in core-collapse supernova simulations. We use not only the zeroth and first moments of the neutrino distribution function in momentum space as in ordinary closure relations, but also information on the background matter configuration extensively. For training the model, we utilize some post-bounce snapshots from one of our previous Boltzmann radiation–hydrodynamics simulations; the Eddington tensor, as well as the zeroth and first angular moments, are calculated from the neutrino distribution function obtained in the simulation. LightGBM is light indeed, and its high efficiency in training enables us to feed a large number of features and figure out which features are more important than others. In this paper, we report the results of this feature engineering in addition to those of the training, validation, and generalization of our model. We find that the flux factor and nonlocal features are among the most relevant features; our LightGBM model can reproduce the Eddington factor better in general than the M1 closure relation, one of the most commonly employed algebraic closure relations at present; the generalization performance is also much improved from our previous model based on the deep neural network.