Certified Uncertainty for Surrogate Models of Neutron Star Equations of State via Mondrian Conformal Prediction

Abstract

We present a multitask surrogate for neutron-star equations of state (EoSs) that delivers \emph{distribution-free}, certified uncertainty via split conformal prediction (CP) and its Mondrian variant. The surrogate ingests a six-parameter piecewise-polytropic representation $({\log }_{10}{p}_1,{\Gamma }_1,{\Gamma }_2,{\Gamma }_3,{\rho }_1,{\rho }_2)$ -- with fixed transition densities ${\rho }_1$ and ${\rho }_2$ -- and jointly performs (i) validity classification under physical/observational constraints and (ii) regression of $M_{\max }$, $R(M_{\max })$, $R_{1.4}$, and ${\Lambda }_{1.4}$. Trained on a balanced set of $40,000$ EoSs, the model attains near-perfect discrimination (AUC $\approx 0.997$) and sub-percent relative errors for masses and radii, with few-percent error for tidal deformability. Across $\alpha \in [0.05,0.25]$, empirical coverages closely track $1-\alpha$ for both Standard and Mondrian CP; in conservative regimes, Mondrian yields narrower average physical widths at comparable coverage. To our knowledge, this is the first application of class-conditioned (Mondrian) conformal calibration to neutron-star EoS surrogates, enabling efficient, reproducible, and uncertainty-aware inference; the framework is readily extensible to functional targets (e.g., full $R(M)$ curves).