Machine-learning discovery potential for a heavy Higgs boson in $e^+e^-\to ZH$ at a future lepton collider

We study the discovery potential for a CP-even heavy neutral Higgs boson $H$ in the Type-I two-Higgs-doublet model (2HDM) at a future $e^+e^-$ collider with $\sqrt{s}=500~\mathrm{GeV}$, focusing on the process $e^+e^-\to ZH$ with $H\to WW$, and with $Z\to\ell\ell$ or $Z\toνν$. The final states are four jets plus two leptons ($4j2\ell$) and four jets plus missing transverse momentum ($4j2ν$). We compare a cut-based analysis with two multivariate strategies: a one-dimensional Boosted Decision Tree (BDT) trained per mass point, and a two-dimensional (BDT $\times$ $m_H$) template analysed with a profile likelihood. The 2D template improves the expected discovery significance by a factor of $2.5$--$3.6$ in the $4j2\ell$ channel and by a factor of $5$--$18$ in the $4j2ν$ channel relative to the cut-based analysis, with the largest gains at high $m_H$ where the cut-based mass window loses efficiency. We translate the expected exclusions into $95\%$ CL upper limits on $σ\times$ BR and discuss the implications for the Type-I 2HDM parameter space.