Deep Learning of the Eddington Tensor in the Core-collapse Supernova Simulation

TL;DR

This paper develops deep neural network-based closure relations for neutrino transport in core-collapse supernova simulations, improving accuracy over traditional methods and enabling more efficient modeling.

Contribution

The authors introduce DNN-based closure relations for the Eddington tensor, outperforming analytical closures in CCSN simulations and offering a new approach for neutrino transport modeling.

Findings

DNNs better reproduce the Eddington tensor than M1 closure.

TBNN slightly outperforms CWNN in accuracy.

DNN-based closures are computationally more efficient.

Abstract

We trained deep neural networks (DNNs) as a function of the neutrino energy density, flux, and the fluid velocity to reproduce the Eddington tensor for neutrinos obtained in our first-principles core-collapse supernova (CCSN) simulations. Although the moment method, which is one of the most popular approximations for neutrino transport, requires a closure relation, none of the analytical closure relations commonly employed in the literature captures all aspects of the neutrino angular distribution in momentum space. In this paper, we developed a closure relation by using the DNN that takes the neutrino energy density, flux, and the fluid velocity as the input and the Eddington tensor as the output. We consider two kinds of DNNs: a conventional DNN named a component-wise neural network (CWNN) and a tensor-basis neural network (TBNN). We found that the diagonal component of the Eddington tensor is reproduced better by the DNNs than the M1-closure relation especially for low to intermediate energies. For the off-diagonal component, the DNNs agree better with the Boltzmann solver than the M1 closure at large radii. In the comparison between the two DNNs, the TBNN has slightly better performance than the CWNN. With the new closure relations at hand based on the DNNs that well reproduce the Eddington tensor with much smaller costs, we opened up a new possibility for the moment method.