Nanoscale thermally assisted hydrodynamic melt perturbations induced by ultrafast laser energy deposition in noble-metal films produce irreversible nanoscale translative mass redistributions and results in formation of radially-symmetric frozen surface structures. We demonstrate that the final three-dimensional (3D) shape of the surface structures formed after re-solidification of the molten part of the film is governed by incident laser fluence and, more importantly, predicted theoretically via molecular dynamics modeling. Considering the underlying physical processes associated with laser-induced energy absorption, electron-ion energy exchange, acoustic relaxation and hydrodynamic flows, the theoretical approach separating "slow" and "fast" physical processes and combining hybrid analytical two-temperature calculations, scalable molecular-dynamics simulations, and a semi-analytical thin-shell model was shown to provide accurate prediction of the final nanoscale solidified morphologies, fully consistent with direct electron-microscopy visualization of nanoscale focused ion-beam cuts of the surface structures produced at different incident laser fluences. Finally, these results are in reasonable quantitative agreement with mass distribution profiles across the surface nanostructures, provided by their noninvasive and non-destructive nanoscale characterization based on energy-dispersive x-ray fluorescence spectroscopy, operating at variable electron-beam energies.