  Extracting Hamiltonian parameters from available experimental data is a
challenge in quantum materials. In particular, real-space spectroscopy methods
such as scanning tunneling spectroscopy allow probing electronic states with
atomic resolution, yet even in those instances extracting effective Hamiltonian
is an open challenge. Here we show that impurity states in modulated systems
provide a promising approach to extracting non-trivial Hamiltonian parameters
of a quantum material. We show that by combining the real-space spectroscopy of
different impurity locations in a moire topological superconductor, modulations
of exchange and superconducting parameters can be inferred via machine
learning. We demonstrate our strategy with a physically-inspired harmonic
expansion combined with a fully-connected neural network that we benchmark
against a conventional convolutional architecture. We show that while both
approaches allow extracting exchange modulations, only the former approach
allows inferring the features of the superconducting order. Our results
demonstrate the potential of machine learning methods to extract Hamiltonian
parameters by real-space impurity spectroscopy as local probes of a topological
state.
