  The development of two-dimensional materials has resulted in a diverse range
of novel, high-quality compounds with increasing complexity. A key requirement
for a comprehensive quantitative theory is the accurate determination of these
materials' band structure parameters. However, this task is challenging due to
the intricate band structures and the indirect nature of experimental probes.
In this work, we introduce a general framework to derive band structure
parameters from experimental data using deep neural networks. We applied our
method to the penetration field capacitance measurement of trilayer graphene,
an effective probe of its density of states. First, we demonstrate that a
trained deep network gives accurate predictions for the penetration field
capacitance as a function of tight-binding parameters. Next, we use the fast
and accurate predictions from the trained network to automatically determine
tight-binding parameters directly from experimental data, with extracted
parameters being in a good agreement with values in the literature. We conclude
by discussing potential applications of our method to other materials and
experimental techniques beyond penetration field capacitance.
