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Several techniques have been proposed over the years for automatic hypocenterlocalization. While those techniques have pros and cons that trade-offcomputational efficiency and the susceptibility of getting trapped in localminima, an alternate approach is needed that allows robust localizationperformance and holds the potential to make the elusive goal of real-timemicroseismic monitoring possible. Physics-informed neural networks (PINNs) haveappeared on the scene as a flexible and versatile framework for solving partialdifferential equations (PDEs) along with the associated initial or boundaryconditions. We develop HypoPINN -- a PINN-based inversion framework forhypocenter localization and introduce an approximate Bayesian framework forestimating its predictive uncertainties. This work focuses on predicting thehypocenter locations using HypoPINN and investigates the propagation ofuncertainties from the random realizations of HypoPINN's weights and biasesusing the Laplace approximation. We train HypoPINN to obtain the optimizedweights for predicting hypocenter location. Next, we approximate the covariancematrix at the optimized HypoPINN's weights for posterior sampling with theLaplace approximation. The posterior samples represent various realizations ofHypoPINN's weights. Finally, we predict the locations of the hypocenterassociated with those weights' realizations to investigate the uncertaintypropagation that comes from those realisations. We demonstrate the features ofthis methodology through several numerical examples, including using the Otwayvelocity model based on the Otway project in Australia.

Laplace HypoPINN: Physics-Informed Neural Network for hypocenter localization and its predictive uncertainty