Emulating Brown Dwarf Star Cooling: A Surrogate Model for MESA-Generated L(t) Curves
Akeyla Rizkyazzahra Vardiny (a*), Dr. Muhamad Irfan Hakim, S.Si., M.Si. (b)

a) Astronomy Study Program, FMIPA, Institut Teknologi Bandung, Jl. Ganesa 10, Bandung 40132, Indonesia
*akeylavardiny[at]gmail.com
b) Astronomy Study Program, FMIPA, Institut Teknologi Bandung, Jl. Ganesa 10, Bandung 40132, Indonesia

Abstract

Brown dwarfs are considered unique due to their mass range below the minimum mass of hydrogen burning. Hence, they often cool down with age as a consequence of electron degeneracy pressure, which will result in the failure of nuclear fusion in the stellar core. The degeneracy of the mass, age, and metallicity-where a single luminosity can correspond to multiple combinations of mass, age, and composition-complicates the interpretation of observational data from facilities such as JWST.

This paper demonstrates surrogate models that emulate MESA (Modules for Experiments in Stellar Astrophysics) calculations of brown dwarf cooling curves, predicting the luminosity-age relation L(t, M, [Fe/H]) from 1 Myr to 1 Gyr (the full range of the MESA brown dwarf simulation). The training set is constructed from a real MESA brown dwarf model (20 M_J, [Fe/H] = -1.0, evolved to 1 Gyr), with physically motivated perturbations across mass (13-75 M_J) and metallicity ([Fe/H] = -0.5 to +0.5). Unlike conventional approaches that interpret the cooling curves as functional outputs, we explicitly model age as an independent input feature, enabling individual age predictions without re-running the entire cooling curve. We train and compare three surrogate methods: a Gaussian Process regressor with a radial basis function kernel, a Random Forest with 300 trees, and an Ensemble model combining GP and RF predictions (70% GP, 30% RF). We find that with small training sets (n=600), Random Forest unexpectedly outperforms Gaussian Process (MAE = 0.032 vs 0.236), contrary to common expectations for smooth regression tasks. The Random Forest achieves the best performance with a mean absolute error of 0.032 in log_10(L/L_Sun) (R^2 = 0.9997), while the Gaussian Process yields MAE = 0.236 (R^2 = 0.989). The superior performance of the Random Forest is attributed to its effectiveness with the relatively small training set (600 samples). Group-based cross-validation prevents data leakage, confirming model robustness.

Keywords: Brown dwarfs - methods: numerical - stars: evolution - stars: low-mass - machine learning - surrogate modeling

Topic: Instrumentation and Computational Physics