Deep Neural Networks for Modeling Astrophysical Nuclear Reacting Flows

TL;DR

Stellar and explosive astrophysical flows require coupling hydrodynamics to stiff nuclear reaction networks, which makes direct integration expensive. The authors adopt DeePODE, a neural network surrogate framework trained with Evolutionary Monte Carlo Sampling, to learn a fast, generalizable mapping of nuclear evolution over a fixed time step across broad thermodynamic conditions. The resulting Net-3Sp and Net-13Sp surrogates achieve sub-percent accuracy relative to semi-implicit solvers and provide up to ≈2.6× CPU speedups, with a temperature-thresholded deployment ensuring stability in extreme regimes. Validation spans zero-, one-, and two-dimensional tests, including flame propagation and Kelvin-Helmholtz instabilities, demonstrating scalable, high-fidelity modeling of astrophysical nuclear reacting flows. This work offers a practical path toward accelerating high-resolution simulations while preserving key thermonuclear behavior.

Abstract

In astrophysical simulations, nuclear reacting flows pose computational challenges due to the stiffness of reaction networks. We introduce neural network-based surrogate models using the DeePODE framework to enhance simulation efficiency while maintaining accuracy and robustness. Our method replaces conventional stiff ODE solvers with deep learning models trained through evolutionary Monte Carlo sampling from zero-dimensional simulation data, ensuring generalization across varied thermonuclear and hydrodynamic conditions. Tested on 3-species and 13-species reaction networks, the models achieve $\lesssim 1\%$ accuracy relative to semi-implicit numerical solutions and deliver a $\sim 2.6\times$ speedup on CPUs. A temperature-thresholded deployment strategy ensures stability in extreme conditions, sustaining neural network utilization above 75\% in multi-dimensional simulations. These data-driven surrogates effectively mitigate stiffness constraints, offering a scalable approach for high-fidelity modeling of astrophysical nuclear reacting flows.

Figures (14)

• Figure 1: The reaction diagrams of two nuclear reaction networks, both generated by pynucastro, with the arrows for exothermic reactions marked in blue. (a) Reaction schematic of the Net-3Sp, includes two forward reactions and two reverse reactions. (b) Reaction schematic of the Net-13Sp, includes sixteen forward reactions and sixteen reverse reactions.
• Figure 2: The phase diagrams of two nuclear reaction networks illustrate the temperature gradient (ordinate) against the temperature (abscissa). Gray points represent sampling data, while orange points are part of the calibrations data in §\ref{['sec:results']}. (a) Phase diagram of the Net-3Sp. (b) Phase diagram of the Net-13Sp.
• Figure 3: L1 loss of two nuclear reaction networks, each training session consisted of 5000 epochs. The top panel is the loss of Net-3Sp. The bottom panel is the loss of Net-13Sp.
• Figure 4: Two zero-dimensional calibrations for Net-3Sp. We compare the temperature and mass fractions of various isotopes between neural network solutions (dashed lines) and direction integration solutions (solid lines) in simulations of 2 ms each. (a) Zero-dimensional calibration i@ for Net-3Sp. (b) Zero-dimensional calibration ii@ for Net-3Sp.
• Figure 5: Two zero-dimensional calibration for Net-13Sp. We compare the temperature and mass fractions of various isotopes between neural network solutions (dashed lines) and direction integration solutions (solid lines) in simulations of 0.1 ms each. (a) Zero-dimensional calibration i@ for Net-13Sp. (b) Zero-dimensional calibration ii@ for Net-13Sp.