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 \(Λ_{1.4}\).