Informative Ensemble Learning for Seismic Location and Association

Hazard assessment and treaty verification rely on detecting weak or clustered seismic events. Locating an unknown number of events from unassociated teleseismic arrivals within a brief time window, especially when phase labels are absent, remains a difficult joint-inference task. Particle-based variational methods that maximise conditional entropy (i.e., choose the most informative event sets) now are much closer to recovering the full posterior: number of events, non-Gaussian location uncertainties, arrival-event association probabilities, and phase labels. They typically scale only after a high-recall neural network restricts the global search to seismic “hot spots.” Yet that network is usually hand-tuned and blind to its own uncertainty. Similar issues pervade nearly every machine learning approach to phase-association today.

We introduce the Informative Ensemble Kalman Learner (IEKL), an uncertainty-driven framework that learns both the weights and the structure of this network in one loop. IEKL treats an ensemble of networks as the state of a low-rank Gaussian process and applies an ensemble Kalman update, a simple data-assimilation step, to the weights at each iteration. The update produces a sharp posterior without back-propagating through every member. Resulting weight uncertainties spotlight redundant connections, so IEKL prunes uninformative weights and subnetworks on the fly. Because the update bypasses gradients, the same mechanism works for differentiable and non-differentiable networks and has already uncovered governing equations and physical models in other domains.

Embedded in the seismic location-association pipeline, IEKL yields a fully probabilistic solution: it reports event locations, associations, and phase labels while continuously refining its own neural core. Uncertainty thus becomes a resource that guides both inference and model design, enabling faster, more interpretable, and self-optimising seismic monitoring. In this talk, we will show how this approach benefits nearly every type of network from simple perceptrons to foundation models, and demonstrate us on UGEB and LEB data in the IDC network. We will addictionally show case its benefits in learning operators for neural dynamical systems, and in neuro-physical inversion.