  We adapt a machine-learning approach to study the many-body localization
transition in interacting fermionic systems on disordered 1D and 2D lattices.
We perform supervised training of convolutional neural networks (CNNs) using
labelled many-body wavefunctions at weak and strong disorder. In these limits,
the average validation accuracy of the trained CNNs exceeds 99.95%. We use the
disorder-averaged predictions of the CNNs to generate energy-resolved phase
diagrams, which exhibit many-body mobility edges. We provide finite-size
estimates of the critical disorder strengths at $W_c\sim2.8$ and $9.8$ for 1D
and 2D systems of 16 sites respectively. Our results agree with the analysis of
energy-level statistics and inverse participation ratio. By examining the
convolutional layer, we unveil its feature extraction mechanism which
highlights the pronounced peaks in localized many-body wavefunctions while
rendering delocalized wavefunctions nearly featureless.
