Constraining Axion-Like Particle mediated Dark Matter with Observational Constraints: A Statistical and Machine Learning Approach

We present a comprehensive study of axion-like particle (ALP) mediated dark matter (DM) effects on neutron star (NS) structure within a relativistic mean-field framework with non-linear mesonic interactions constrained by nuclear and astrophysical data. We explore DM masses $m_χ\in [0,1000]\,\mathrm{GeV}$ and Fermi momenta $q_f \in [0,0.06]\,\mathrm{GeV}$, generating over 30{,}000 equations of state using two representative hadronic models, a stiff EoS (EoS1) and a soft EoS (EoS18), including a consistent crust description. A multi-level statistical filtering scheme based on voting, likelihood, and kernel density estimation is applied using constraints from radio and X-ray pulsars, GW170817, and the low-mass compact object HESS~J1731$-$347. We find that models satisfying the PSR~J0614$-$3329 radius constraint automatically comply with the HESS bound, allowing ALP-mediated DM to explain low-mass compact objects while remaining consistent with $2\,M_\odot$ NSs. For the stiff EoS, we obtain a lower bound $m_χ\gtrsim 43\,\mathrm{GeV}$, with preferred values $q_f = 0.034^{+0.020}_{-0.012}$ and $m_χ\in [101,949]\,\mathrm{GeV}$, while the soft EoS yields no strict lower bound, though large $m_χ$ and $q_f$ are disfavored. We also develop a supervised interpolation model using \texttt{AutoGluon} to infer DM parameters from NS mass--radius curves, achieving $R^2>0.998$, and show that $m_χ$ is mainly constrained by global radius ratios, whereas $q_f$ is driven by the tidal deformability $Λ_{1.4}$.

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