Dynamics　of　the　dissociative　chemisorption　of　H2　(D2)　and　the　subsequent　H*　(D*)　diffusion　on　the　Pt　doped　Cu(111)　surface　are　investigated　using　both　quasi-classical　trajectory　(QCT)　and　ring　polymer　molecular　dynamics　(RPMD)　approaches.　The　classical　dynamics　is　also　studied　with　electronic　friction　to　simulate　the　nonadiabatic　interaction　with　surface　electron-hole　pairs.　These　dynamics　calculations　were　made　possible　by　a　high-dimensional　potential　energy　surface,　machine　learned　from　density　functional　theory　data.　It　is　shown　that　the　diffusion　of　adsorbed　H*　at　moderate　temperatures　can　be　largely　characterized　by　classical　mechanics,　as　evidenced　by　roughly　the　same　diffusion　coefficients　obtained　from　QCT　and　RPMD　calculations.　In　the　long-time　limit,　the　diffusion　coefficient　computed　by　averaging　classical　trajectories　with　electronic　friction　is　in　reasonably　good　agreement　with　the　latest　experimental　data,　underscoring　the　importance　of　the　nonadiabatic　interaction　for　H*　diffusion　on　metal　surfaces.