Machine learning for radiative hydrodynamics in astrophysics

TL;DR

The work tackles the high computational cost of radiative-hydrodynamics simulations by leveraging AI: first, a neural surrogate for the M1-multigroup closure computes the Eddington factor with accuracy better than $10^{-3}$–$10^{-2}\%$ while delivering about $3{,}000 imes$ speedups over traditional line-search methods; second, Physics-Informed Neural Networks explore extrapolation of hydrodynamic and radiative-hydrodynamic evolutions beyond the training window. The study demonstrates that incorporating spectral resolution via the M1-multigroup model significantly alters radiative shocks, slowing the shock and enlarging the radiative precursor, with diffusion-based jump relations deviating by up to 3–15 ext{%} in density and 1–8 ext{%} in temperature compared with the full multigroup results. PINNs show potential for extrapolating hydrodynamic shocks, but radiative shocks present challenges due to discontinuities and stiff source terms, necessitating further methodological advances. Overall, the AI-assisted framework enables more accurate and efficient radiative-hydrodynamics simulations, opening pathways to high-fidelity investigations of astrophysical phenomena like accretion shocks, stellar formation, and supernova remnants.

Abstract

Radiation hydrodynamics describes the interaction between high-temperature hypersonic plasmas and the radiation they emit or absorb, a coupling that plays a central role in many astrophysical phenomena related to accretion and ejection processes. The HADES code was developed to model such systems by coupling hydrodynamics with M1-gray or M1-multigroup radiative transfer models, which are well suited to optically intermediate media. Despite its accuracy, radiation hydrodynamics simulations remain extremely demanding in terms of computational cost. Two main limitations are responsible for this. First, the M1-multigroup model relies on a closure relation with no analytic expression, requiring expensive numerical evaluations. Second, the Courant-Friedrichs-Lewy condition strongly restricts the time step of the explicit schemes used in HADES. To overcome these difficulties, two complementary Artificial Intelligence based strategies were developed in this thesis. The first approach consists in training a Multi-Layer Perceptron to approximate the M1-multigroup closure relation. This method achieves excellent accuracy while reducing the computational cost by a factor of 3000, making it the most efficient approach currently available for this task. This performance gain enables high-fidelity simulations of radiative shocks, in which radiation directly influences the shock structure. In particular, increasing spectral resolution slows down the shock and enlarges the radiative precursor. The second approach explores the use of Physics-Informed Neural Networks to directly solve the radiation hydrodynamics equations and extrapolate simulations beyond their initial time range. Tests on purely hydrodynamic shocks show accurate handling of discontinuities, but application to radiative shocks remains challenging and requires further investigation.

Figures (52)

• Figure 1: Examples of applications in the field of radiative hydrodynamics.
• Figure 2: Schematic representation of a radiation beam crossing the surface $\overrightarrow{\mathop{}\!\mathrm{d} S}$ and propagating within the solid angle $\mathop{}\!\mathrm{d} \Omega$.
• Figure 3: Types of interactions between light and matter.
• Figure 4: Electromagnetic spectrum. Example of discretization into $\mathcal{G}$ groups: the 1st group includes gamma rays, the 2nd includes X-rays, and the last includes long-wavelength radiation.
• Figure 5: Evolution of the Eddington factor $\chi_g$ at different radiative temperatures $\mathcal{T}_g$, using a group narrowness $\delta_g = 10^{-4}$.