  Graphene quantum dots provide a platform for manipulating electron behaviors
in two-dimensional (2D) Dirac materials. Most previous works were of the
"forward" type in that the objective was to solve various confinement,
transport and scattering problems with given structures that can be generated
by, e.g., applying an external electrical field. There are applications such as
cloaking or superscattering where the challenging problem of inverse design
needs to be solved: finding a quantum-dot structure according to certain
desired functional characteristics. A brute-force search of the system
configuration based directly on the solutions of the Dirac equation is
computational infeasible. We articulate a machine-learning approach to
addressing the inverse-design problem where artificial neural networks subject
to physical constraints are exploited to replace the rigorous Dirac equation
solver. In particular, we focus on the problem of designing a quantum dot
structure to generate both cloaking and superscattering in terms of the
scattering efficiency as a function of the energy. We construct a physical loss
function that enables accurate prediction of the scattering characteristics. We
demonstrate that, in the regime of Klein tunneling, the scattering efficiency
can be designed to vary over two orders of magnitudes, allowing any scattering
curve to be generated from a proper combination of the gate potentials. Our
physics-based machine-learning approach can be a powerful design tool for 2D
Dirac material-based electronics.
