Application of Neural Networks for Determine the Radiation Pressure in Two-Moment Radiation Hydrodynamics in Slab Geometry

Abstract

In two-moment radiation transport, the closure is the constitutive relation that maps the energy and momentum to the radiation-pressure tensor. Among available closures, the maximum-entropy (ME) approach is the most reliable. However, it is associated with a high computational cost. In this paper, we propose a machine-learning approach for the rapid evaluation of the ME closure for bosonic, classical and fermionic radiation. We generate ME reference data using Gauss–Legendre angular quadrature combined with a robust bisection-based inversion of the moment constraints. Next, we train a small physics-constrained multilayer perceptron (MLP) with output restricted to the physically admissible range (between one third and one). Monotonicity in the reduced flux is enforced, and the derivative is matched to the ME reference. The neural network (NN)-based closure achieves a mean absolute error (MAE) of 9.0×10⁻⁴ over the range ϕ ∈ [0, 0.98], which yields a latency reduction of about ∼10³× per closure evaluation. In the Marshak wave benchmark the full simulation runs about 247 × faster while the hyperbolicity indicator remains strictly positive (minimum 5.1 · 10⁻²). Compared with the analytic Kershaw closure for bosonic and classical radiation, our model is substantially more accurate and faster. For practical adoption, we also provide a lightweight rational approximation (MAE 1.01× ∼10⁻³), and in the bosonic and classical cases we confirm positivity of the hyperbolicity indicator for degeneracy parameters between −5 and 5.