arXiv subjects

Xavier Grundler

Publications and source records attributed to Xavier Grundler.

9 recordsLinked to original sources

arXiv2026

Symbolic Regression for Interpretable Emulation of Proton Collective Flow in Intermediate-Energy Heavy-Ion Collisions

Symbolic regression provides an interpretable machine-learning approach for constructing explicit analytic relations between physical inputs and observables. In this work, we develop symbolic-regression emulators for the isospin-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model and compare their performance with deep neural network (DNN) emulators. Using the same transport-model data employed in our previous emulator studies, we show that symbolic regression can reproduce the proton mid-rapidity slope $F_1$ of transverse flow $v_1$ and elliptic flow $v_2$ with accuracy comparable to that of DNNs, while providing explicit analytic expressions and substantially faster prediction once trained. We further demonstrate the use of symbolic regression in the reverse direction by constructing analytic relations that predict the in-medium nucleon-nucleon cross-section modification factor $X$ from the flow observables. Although the symbolic-regression models require substantially longer training times and exhibit greater run-to-run variation than DNNs, their analytic form and rapid evaluation make them promising tools for future transport-model sensitivity and uncertainty analyses.

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arXiv2026

How Neutron Star Radii Encode the Dense-Matter Equation of State and Hadron-Quark Transition

We investigate how future high-precision neutron star (NS) radius measurements encode microscopic information about the dense-matter equation of state (EOS), focusing on a possible first-order hadron--quark phase transition and the resulting mass--radius topology. Within a Bayesian framework using meta-model EOSs with nine microscopic parameters, we analyze mock radius measurements $R_{1.4}=11.9\pm\sigma_R$ km with $\sigma_R=0.9$ and $0.1$ km for canonical NSs. We introduce inverse EOS--radius mappings that give the posterior mean of each EOS parameter as a function of $R_{1.4}$. Their slope measures radius sensitivity, while their curvature determines the leading precision dependence of the posterior mean through the Jensen expansion. Resolving the mappings into four mass--radius topologies, Connected, Disconnected, Both, and No-Quark-Matter, reveals a clear hierarchy of information. The symmetry-energy parameters $L$ (slope) and $K_{\rm sym}$ (curvature) are strongly encoded in $R_{1.4}$ and their posterior means shift appreciably with improved radius precision, whereas the higher-order hadronic parameters show stronger topology dependence. Among the transition parameters, the transition density $\rho_t$ is the most strongly encoded in $R_{1.4}$, while the energy-density jump and quark-matter sound speed are more strongly associated with the topology of the full mass--radius sequence. Since the different topologies have strongly overlapping $R_{1.4}$ distributions, even precise radius measurements cannot by themselves identify the topology or uniquely determine the high-density transition properties. These results provide a parameter-dependent hierarchy for assessing the scientific return of future high-precision radius measurements and complementary probes of high-density

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arXiv2026

Bayesian Inference of fine-features of dense matter EOS from future high-precision data of neutron star radii

Future high-precision X-ray and gravitational wave observatories are expected to measure the radii of neutron stars (NSs) with an accuracy better than about 0.1 km. However, it remains unclear what particular aspects of the Equation of State (EOS) and to what precision they will be better constrained. Within a Bayesian framework using a meta-model EOS and mock high-precision NS data, the posterior probability distribution functions (PDFs) of NS matter EOS parameters for both hadronic and quark phases and the transition between them were recently studied. We report here a few highlights of these studies.

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arXiv2026

Quantifying the Information Gain from Future High-Precision Radius Measurements for Identifying Twin Neutron Stars

Twin neutron stars (NSs), characterized by identical gravitational masses but different radii, are among the most promising astrophysical signatures of a strong first-order hadron--quark phase transition in supradense matter. We investigate how increasingly precise NS radius measurements improve the Bayesian inference of twin-star observability using mock radius data for a canonical $1.4\,M_\odot$ NS. Radius uncertainties are varied from the current level of about $0.9$ km to the $\approx 0.1$ km precision anticipated from future X-ray and gravitational-wave observations. We quantify the information gained using the posterior distribution of the maximum twin-star radius separation $\Delta R$ together with an analytical model of branch distinguishability and complementary information-theoretic measures based on the branch observational efficiency and the Shannon entropy. The combined analyses reveal three inference regimes: a prior-dominated regime for $\sigma_R \gtrsim 0.6$ km, a rapid information-gain regime for $0.2 \lesssim \sigma_R \lesssim 0.6$ km, and an information-saturation regime for $\sigma_R \lesssim 0.2$ km. These complementary analyses consistently indicate that radius measurements with a precision of about $0.2$ km already extract most of the information available for identifying twin NSs within the present Bayesian framework. Beyond establishing a quantitative observational benchmark for future high-precision radius measurements, this work provides a general Bayesian framework for quantifying the information gain from progressively more precise observations and identifying the point of diminishing scientific returns.

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arXiv2026

Bayesian Constraints on the Neutron Star Equation of State with a Smooth Hadron-Quark Crossover

We perform a Bayesian inference of the dense-matter equation of state (EOS) within a unified framework that incorporates hadronic matter, quark matter, and a smooth hadron-to-quark crossover. The EOS is constrained using physical consistency conditions, gravitational wave data from GW170817, NICER mass versus radius measurements, and hypothetical future high-precision radius observations. In contrast to most previous studies that assume a sharp first-order phase transition or fix part of the EOS, we simultaneously infer hadronic, quark, and crossover parameters within a single statistical framework. We find that current observations strongly constrain the density dependence of the nuclear symmetry energy, particularly its slope and curvature. In contrast, the highest density hadronic parameters and quark-matter properties remain only weakly constrained. We further show that the trace anomaly exhibits a remarkably universal behavior across the accepted EOS ensemble and remains largely insensitive to current observational constraints. This indicates that the present data primarily probe the low to intermediate density EOS. At the same time, robust inference of quark matter and genuinely high-density physics will require next-generation precision radius measurements or complementary observables.

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arXiv2025

Bayesian Quantification of Observability and Equation of State of Twin Stars

The possibility of discovering twin stars, two neutron stars (NSs) with the same mass but different radii, is usually studied in forward modelings by using a restricted number of NS matter equation of state (EOS) encapsulating a first-order phase transition from hadronic to quark matter (QM). Informing our likelihood function with the NS radius data from GW170817 and using a meta-model with 9-parameters capable of mimicking most NS EOSs available in the literature, we conduct a Bayesian quantification of the observability and underlying EOSs of twin stars. Of the accepted EOSs, between 12-18\% yield twin stars, depending on the restrictions we place on the second branch. The possibility of twin stars remains robust even under recent observational constraints. We show that many of these twin star scenarios are observable with currently available levels of accuracy in measuring NS radii. We also present the marginalized posterior probability density functions (PDFs) of every EOS parameter for each of four mass-radius correlation topologies. We find that the inferred EOS depends sensitively on not only whether twin stars are present, but also the category of twin stars, indicating that the observation of twin stars would provide a strong constraint on the underlying EOS. In particular, for two coexisting hybrid stars having QM cores at different densities, the PDF for QM speed of sound squared $c_{\rm qm}^2$ has two peaks, one below and another above the conformal limit $c_{\rm qm}^2=1/3$ predicted by perturbative QCD.

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arXiv2025

Bayesian Inference of Hybrid Star Properties from Future High-Precision Measurements of Their Radii

Future high-precision X-ray and gravitational-wave observations of neutron stars (NSs) are expected to constrain NS radii with uncertainties as small as $\sigma \simeq 0.1$~km. Such unprecedented precision offers a unique opportunity to extract new information about the nature and equation of state (EOS) of supradense matter in NS cores. Using mock radius data with uncertainties ranging from $\sigma = 1.0$ to $0.1$~km, together with a flexible meta-model NS EOS that allows for a first-order hadron-quark phase transition, we perform a Bayesian statistical analysis to assess the impact of radius measurements on EOS constraints. We find that high-precision radius measurements, particularly for massive NSs, significantly tighten constraints on the hadron-quark transition density $\rho_t$, the quark matter mass fraction in NS cores, and several parameters characterizing the EOS of supranuclear hadronic matter, although the degree of improvement depends on the assumed prior range of $\rho_t$. In contrast, even with the highest precision considered, NS radii -- including those of massive stars -- remain largely insensitive to the stiffness of quark matter, independent of the measurement accuracy or the prior range adopted for $\rho_t$.

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arXiv2024

Bayesian Inference of Fine-Features of Nuclear Equation of State from Future Neutron Star Radius Measurements to 0.1km Accuracy

To more precisely constrain the Equation of State (EOS) of supradense neutron-rich nuclear matter, future high-precision X-ray and gravitational wave observatories are proposed to measure the radii of neutron stars (NSs) with an accuracy better than about 0.1 km. However, it remains unclear what particular aspects (other than the stiffness generally spoken of in the literature) of the EOS and to what precision they will be better constrained. In this work, within a Bayesian framework using a meta-model EOS for NSs, we infer the posterior probability distribution functions (PDFs) of incompressibility $K_{0}$ and skewness $J_{0}$ of symmetric nuclear matter (SNM) as well as the slope $L$, curvature $K_{\rm{sym}}$, and skewness $J_{\rm{sym}}$ characterizing the density dependence of nuclear symmetry energy $E_{\rm{sym}}(ρ)$, respectively, from mean values of NS radii consistent with existing observations and an expected accuracy $ΔR$ ranging from about 1.0 km to 0.1 km. We found that (1) the $ΔR$ has little effect on inferring the stiffness of SNM at suprasaturation densities, (2) smaller $ΔR$ reveals more accurately not only the PDFs but also pairwise correlations among parameters characterizing high-density $E_{\rm{sym}}(ρ)$, (3) a double-peak feature of the PDF($K_{\rm{sym}}$) corresponding to the strong $K_{\rm{sym}}-J_{\rm{sym}}$ and $K_{\rm{sym}}-L$ anti-correlations is revealed when $ΔR$ is less than about 0.2 km, and the locations of the two peaks are sensitive to the maximum value of $J_{\rm{sym}}$ reflecting the stiffness of $E_{\rm{sym}}(ρ)$ above about 3 times the saturation density $ρ_0$ of SNM, (4) the high-precision radius measurement for canonical NSs is more useful than that for massive ones for constraining the EOS of nucleonic matter around $(2-3)ρ_0$.

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arXiv2024

Neural Network Emulation of Flow in Heavy-Ion Collisions at Intermediate Energies

Applications of new techniques in machine learning are speeding up progress in research in various fields. In this work, we construct and evaluate a deep neural network (DNN) to be used within a Bayesian statistical framework as a faster and more reliable alternative to the Gaussian Process (GP) emulator of an isospin-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model simulator of heavy-ion reactions at intermediate beam energies. We found strong evidence of DNN being able to emulate the IBUU simulator's prediction on the strengths of protons' directed and elliptical flow very efficiently even with small training datasets and with accuracy about ten times higher than the GP. Limitations of our present work and future improvements are also discussed.

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