  Seismic phase association is the task of grouping phase arrival picks across
a seismic network into subsets with common origins. Building on recent
successes in this area with machine learning tools, we introduce a neural
mixture model association algorithm (Neuma), which incorporates
physics-informed neural networks and mixture models to address this challenging
problem. Our formulation assumes explicitly that a dataset contains real phase
picks from earthquakes and noise picks resulting from phase picking mistakes
and fake picks. The problem statement is then to assign each observation to
either an earthquake or noise. We iteratively update a set of hypocenters and
magnitudes while determining the optimal class assignment for each pick. We
show that by using a physics-informed Eikonal solver as the forward model, we
can impose stringent quality control on surviving picks while maintaining high
recall. We evaluate the performance of Neuma against several baseline
algorithms on a series of challenging synthetic datasets and the 2019
Ridgecrest, California sequence. Neuma outperforms the baselines in precision
and recall for each of the synthetic datasets. Furthermore, it detects an
additional 3285 more earthquakes than the best baseline on the Ridgecrest
dataset (13.5%), while substantially improving the hypocenters.
