Certified Uncertainty for Surrogate Models of Neutron Star Equations of State via Mondrian Conformal Prediction
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 $(\log_{10}p_1,Γ_1,Γ_2,Γ_3,ρ_1,ρ_2)$ -- with fixed transition densities $ρ_1$ and $ρ_2$ -- and jointly performs (i) validity classification under physical/observational constraints and (ii) regression of $M_{\max}$, $R(M_{\max})$, $R_{1.4}$, and $Λ_{1.4}$. 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 $α\in[0.05,0.25]$, empirical coverages closely track $1-α$ 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).