Mapping the biochemical composition of eukaryotic cells without the use of exogenous labels is a long-sought objective in cell biology. Recently, it has been shown that composition maps on dry single bacterial cells with nanoscale spatial resolution can be inferred from quantitative nanoscale dielectric constant maps obtained with the scanning dielectric microscope. Here, it is shown that this approach can also be applied to the much more challenging case of fixed and dry eukaryotic cells, which are highly heterogeneous and show micrometric topographic variations. More importantly, it is demonstrated that the main bottleneck of the technique (the long computation times required to extract the nanoscale dielectric constant maps) can be shortcut by using supervised neural networks, decreasing them from weeks to seconds in a wokstation computer. This easy-to-use data-driven approach opens the door for in situ and on-the-fly label free nanoscale composition mapping of eukaryotic cells with scanning dielectric microscopy.