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 $m_{\chi }\in [0,1000]\mathrm{G}\mathrm{e}\mathrm{V}$ and Fermi momenta $q_f\in [0,0.06]\mathrm{G}\mathrm{e}\mathrm{V}$, 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 $2M_{\odot }$ NSs. For the stiff EoS, we obtain a lower bound $m_{\chi }\gtrsim 43\mathrm{G}\mathrm{e}\mathrm{V}$, with preferred values $q_f=0.034_{-0.012}^{+0.020}$ and $m_{\chi }\in [101,949]\mathrm{G}\mathrm{e}\mathrm{V}$, while the soft EoS yields no strict lower bound, though large $m_{\chi }$ and $q_f$ are disfavored. We also develop a supervised interpolation model using $\mathtt{\text{AutoGluon}}$ to infer DM parameters from NS mass–radius curves, achieving $R^2>0.998$, and show that $m_{\chi }$ is mainly constrained by global radius ratios, whereas $q_f$ is driven by the tidal deformability ${\mathrm{\Lambda }}_{1.4}$.