Flexible Seismicity Modeling With Neural Modulated Renewal Processes

Neural point processes (NPPs) have recently been applied to seismicity modeling, but their theoretical connections to classical point processes models remain elusive. Moreover, two fundamental questions remain unresolved: (a) how much historical information is sufficient for NPPs to effectively model seismicity, and (b) what is the differential impact between inter‐event times and magnitudes on the model predictive performance? To answer these questions, we reinterpret a class of NPPs within the framework of neural modulated renewal processes (NMRPs), which generalize conventional modulated renewal processes by integrating deep learning architectures. We develop and analyze four variants: the unmodulated neural renewal process (NRP), the inter‐event times modulated NMRP (I‐NMRP), the magnitude modulated NMRP (M‐NMRP), and the jointly modulated NMRP (J‐NMRP). Their performance is systematically evaluated against the epidemic‐type aftershock sequence (ETAS) model using the EarthquakeNPP benchmark. Results demonstrate that I‐NMRP and J‐NMRP not only match, but in some cases surpass, ETAS in terms of log‐likelihood, while requiring substantially less historical input. Furthermore, the analysis reveals that inter‐event times play a more critical role than magnitudes in enhancing predictive performance. These findings establish NMRP as a flexible and efficient framework for seismicity modeling, with strong potential to incorporate diverse contextual information and to deepen our understanding of earthquake triggering processes.