Flow-Based Generative Emulation of Grids of Stellar Evolutionary Models

TL;DR

This work tackles the challenge of modeling high-dimensional grids of stellar evolution by introducing conditional normalizing flows to learn $p_N(\mathbf{y}|\mathbf{x})$ across multiple grids, enabling both accurate forward emulation and probabilistic inference. By training CNFs on MESA dwarf, MESA giant, and AsfGrid models, the authors achieve flexible, density-based interpolation and sampling that naturally account for degeneracies in stellar parameters. They demonstrate a Bayesian parameter estimation workflow using these flows on Kepler red giants, including stars in clusters NGC 6791 and NGC 6819, and a large field-star sample, revealing that age and mass inferences can be biased without priors on initial helium and mixing-length parameters and that previous asteroseismic scaling may overestimate masses by 5–10%. The approach provides a scalable, physics-informed tool for rapid, probabilistic exploration of stellar grids with wide applicability to galactic archaeology and asteroseismology.

Abstract

We present a flow-based generative approach to emulate grids of stellar evolutionary models. By interpreting the input parameters and output properties of these models as multi-dimensional probability distributions, we train conditional normalizing flows to learn and predict the complex relationships between grid inputs and outputs in the form of conditional joint distributions. Leveraging the expressive power and versatility of these flows, we showcase their ability to emulate a variety of evolutionary tracks and isochrones across a continuous range of input parameters. In addition, we describe a simple Bayesian approach for estimating stellar parameters using these flows and demonstrate its application to asteroseismic datasets of red giants observed by the Kepler mission. By applying this approach to red giants in open clusters NGC 6791 and NGC 6819, we illustrate how large age uncertainties can arise when fitting only to global asteroseismic and spectroscopic parameters without prior information on initial helium abundances and mixing length parameter values. We also conduct inference using the flow at a large scale by determining revised estimates of masses and radii for 15,388 field red giants. These estimates show improved agreement with results from existing grid-based modelling, reveal distinct population-level features in the red clump, and suggest that the masses of Kepler red giants previously determined using the corrected asteroseismic scaling relations have been overestimated by 5-10%.

Figures (2)

• Figure 1: A schematic of conditional normalizing flows. The flow maps random variates $\mathbf{z}$ from a base probability density $\mathbf{p_0(\mathbf{z})}$ (here shown as a 2D normal distribution) to another variable $\mathbf{y}$. The mapping occurs over a series of $N$ invertible transformations $f = f_{\theta_i}, i \in [1, 2, \cdots, N]$, where $\theta_i$ is learned by a neural network and is conditioned by contextual inputs $\mathbf{x}$. The probability density of $\mathbf{y}$ is subsequently conditioned by $\mathbf{x}$, such that $y_N \sim p_N(\mathbf{y}|\mathbf{x})$. In this work, the $\mathbf{y}$ corresponds to the output stellar properties of an evolutionary grid of models, while $\mathbf{x}$ corresponds to the input parameters of the grid.
• Figure 2: (a) Corner plot showing the original distribution (black) of output parameters $\mathbf{y}$ in the MESA grid of dwarf models and the emulated grid from CNF$_{\mathrm{dwarf}}$ in red. (b) Same as (a), except the comparison is between the MESA grid of giant models and the emulated grid from CNF$_{\mathrm{giant}}$. Descriptions of each parameter are listed in Table \ref{['table:mesa']}.