A Spatio‐Temporal Neural Kernel Function Model for Earthquake Clustering: Bridging ETAS and Neural Point Processes

Abstract Modeling earthquake clustering in space and time is central to understanding seismicity patterns and improving forecasting. The Epidemic‐Type Aftershock Sequence (ETAS) model, grounded in the Hawkes process, has long been the standard approach for describing aftershock triggering through fixed, empirically defined kernel functions. However, these functional forms may limit flexibility in representing the full diversity of real seismic behavior. In this study, we introduce the Spatio‐Temporal Neural Kernel Function (ST‐NKF) model, a neural extension of the ETAS model that replaces empirical kernels with data‐driven function approximators while retaining physical interpretability. Specifically, three fully connected neural networks are used to learn the productivity, temporal, and spatial kernel components directly from earthquake catalogs, enabling flexible estimation of triggering patterns under the same probabilistic structure as ETAS. We evaluate ST‐NKF on the EarthquakeNPP benchmark for California and compare its performance with the ETAS model using marginal temporal and conditional spatial log‐likelihoods. Results show that ST‐NKF achieves comparable performance with ETAS model, demonstrating that neural networks can reproduce empirical ETAS behavior within a unified, interpretable point process framework. Importantly, this represents the first neural model to match ETAS in spatiotemporal seismicity modeling, marking a promising step toward integrating seismological interpretability with the flexibility of deep learning. Future extensions may further improve performance by incorporating nonstationary background rates, multimodal geophysical information, or more expressive neural architectures beyond the Hawkes paradigm.