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 $(\log_{10}p_1,Γ_1,Γ_2,Γ_3,ρ_1,ρ_2)$ -- 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).

Figures (10)

• Figure 1: Energy density versus pressure $\varepsilon(P)$ (log--log) for the valid EoS subset. Each amber trace corresponds to one EoS realization that satisfies our physical filters (stability, causality, and a lower bound on the maximum mass), illustrating the diversity of stiffness/softness across the ensemble. In the axes, $P[\mathrm{geom}]$ and $\varepsilon[\mathrm{geom}]$ denote pressure and energy density expressed in geometric units, where $G = c = 1$; in this system they scale as inverse length squared and relate to cgs units via $P_{\mathrm{geom}} = (G/c^{4})\,P_{\mathrm{cgs}}$ and $\varepsilon_{\mathrm{geom}} = (G/c^{4})\,\varepsilon_{\mathrm{cgs}}$.
• Figure 2: Tidal deformability curves $\Lambda(M)$ for $0.5\!\le\!M/M_\odot\!\le\!2.5$. The amber background shows the valid EoS ensemble, while the vertical band at $M=1.4\,M_\odot$ highlights two EOS-agnostic constraints: a GW-only estimate $\Lambda_{1.4}=222.9^{+420.3}_{-98.9}$ and a multimessenger estimate $\Lambda_{1.4}=265.2^{+237.9}_{-104.4}$.
• Figure 3: Mass–radius relations $M$--$R$ for the valid EoS subset (amber background), overlaid with NICER constraints for PSR J0030+0451 and PSR J0740+6620. Outer contour boundaries are solid; inner credible levels are dashed.
• Figure 4: Conformal prediction pipeline for a multitask surrogate neural network.
• Figure 5: The ROC curve summarizes how the classifier separates physically valid from invalid EoSs across decision thresholds. A trajectory that rises sharply toward the upper-left corner indicates that valid models receive consistently higher predicted probabilities than invalid ones. The resulting AUC $\approx 0.998$ shows that the surrogate captures the underlying physical separability of the EoS space, reflecting the distinct patterns imposed by stability, causal sound-speed behavior, and maximum-mass limits.