  Resolving the locations and discriminating the spin states of individual
trapped ions with high fidelity is critical for a large class of applications
in quantum computing, simulation, and sensing. We report on a method for
high-fidelity state discrimination in large two-dimensional (2D) crystals with
over 100 trapped ions in a single trapping region, combining a hardware
detector and an artificial neural network. A high-data-rate, spatially
resolving, single-photon sensitive timestamping detector performs efficient
single-shot detection of 2D crystals in a Penning trap, exhibiting rotation at
about $25\,\mathrm{kHz}$. We then train an artificial neural network to process
the fluorescence photon data in the rest frame of the rotating crystal in order
to identify ion locations with a success rate of $~90\%$, accounting for
substantial illumination inhomogeneity across the crystal. Finally, employing a
time-binned state detection method, we arrive at an average spin-state
detection fidelity of $94(2)\%$. This technique can be used to analyze spatial
and temporal correlations in arrays of hundreds of trapped-ion qubits.
