Machine and Deep Learning Regression Techniquesfor the Inverse Stellar Structure Problem

Introduction
Understanding the equation of state (EoS) of dense nuclear matter remains a key challenge
in nuclear astrophysics, with direct implications for the structure and observable properties
of neutron stars and quark stars. Despite strong constraints from nuclear theory, heavy-ion
collisions, and astrophysical observations, the high-density regime of the EoS is still subject
to significant uncertainties. This motivates the development of inverse approaches that infer
microscopic properties from macroscopic observables.
Methodology
In this work, we investigate the inverse stellar structure problem by reconstructing the
EoS from mass–radius relations using a data-driven framework. A comprehensive set of
physically consistent equations of state is constructed covering hadronic and quark matter
regimes. For the low-density sector, we employ HLPS2/HLPS3 and tabulated Com-
pOSE equations of state for cold neutron stars. The high-density extension depends on the
underlying low-density baseline: for HLPS-based models, we use multimodal
parametrizations, while for CompOSE-based models, we apply speed-of-sound parametriza-
tions, ensuring thermodynamic consistency across the matching density region. Quark mat-
ter is modeled using MIT bag and color-flavor-locked (CFL) equations of state.
The inverse mapping is performed using tree-based regression models (Decision Trees,
Random Forest, Gradient Boosting, and XGBoost) and Deep Neural Networks with (at least)
three hidden layers. Model optimization and fine-tuning are carried out using GroupKFold
cross-validation combined with Grid Search.
Results
The reconstruction of the EoS from mass–radius data is found to be robust across all
model classes. XGBoost and the Deep Neural Network models consistently achieve the highest ac-
curacy, while the ensemble tree methods provide stable intermediate performance. Remarkably, the
use of only eight mass–radius points yields comparable accuracy to denser sampling, indicating
strong information efficiency in the inverse problem.
Conclusions
Our results demonstrate that inverse modeling techniques provide a powerful and efficient
framework for constraining the EoS of dense matter. The approach offers a complementary
methodology to traditional theory-driven studies and highlights the capability of modern
regression techniques to extract physical information from sparse astrophysical observations.