Neural Networks for Nuclear Reactions in MAESTROeX

TL;DR

This paper introduces neural networks to accelerate nuclear reaction calculations in stellar hydrodynamics simulations, demonstrating improved efficiency and robustness for modeling carbon fusion in supernovae.

Contribution

The study develops a ResNet-based neural network approach for reaction steps in MAESTROeX, including training, validation, and robustness techniques, enabling faster simulations of stellar nuclear reactions.

Findings

Neural networks achieve comparable accuracy to traditional ODE integrators.

The approach generalizes across different flame configurations.

Parallel neural networks improve model robustness.

Abstract

We demonstrate the use of neural networks to accelerate the reaction steps in the MAESTROeX stellar hydrodynamics code. A traditional MAESTROeX simulation uses a stiff ODE integrator for the reactions; here we employ a ResNet architecture and describe details relating to the architecture, training, and validation of our networks. Our customized approach includes options for the form of the loss functions, a demonstration that the use of parallel neural networks leads to increased accuracy, and a description of a perturbational approach in the training step that robustifies the model. We test our approach on millimeter-scale flames using a single-step, 3-isotope network describing the first stages of carbon fusion occurring in Type Ia supernovae. We train the neural networks using simulation data from a standard MAESTROeX simulation, and show that the resulting model can be effectively applied to different flame configurations. This work lays the groundwork for more complex networks, and iterative time-integration strategies that can leverage the efficiency of the neural networks.