  Quantum-disordered models provide a versatile platform to explore the
emergence of quantum excitations in many-body systems. The engineering of spin
models at the atomic scale with scanning tunneling microscopy and the local
imaging of excitations with electrically driven spin resonance has risen as a
powerful strategy to image spin excitations in finite quantum spin systems.
Here, focusing on $S=1/2$ lattices as realized by Ti in MgO, we show that
dynamical spin excitations provide a robust strategy to infer the nature of the
underlying Hamiltonian. We show that finite-size interference of the dynamical
many-body spin excitations of a generalized long-range Heisenberg model allows
the underlying spin couplings to be inferred. We show that the spatial
distribution of local spin excitations in Ti islands and ladders directly
correlates with the underlying ground state in the thermodynamic limit. Using a
supervised learning algorithm, we demonstrate that the different parameters of
the Hamiltonian can be extracted by providing the spatially and
frequency-dependent local excitations that can be directly measured by
electrically driven spin resonance with scanning tunneling microscopy. Our
results put forward local dynamical excitations in confined quantum spin models
as versatile witnesses of the underlying ground state, providing an
experimentally robust strategy for Hamiltonian inference in complex real spin
models.
