Scaling-law-informed neural point processes for earthquake sequence forecasting
Earthquake sequence forecasting requires models that can learn nonlinear history dependence while retaining robust statistical structure. We develop a scaling-law-informed neural marked point process, termed Fusion, that combines neural representations of catalog history with temporal features derived from the Epidemic-Type Aftershock Sequence model and magnitude information derived from the Gutenberg--Richter law. The model separates the magnitude cutoff applied to the input catalog from the fixed target-event threshold, allowing lower-magnitude earthquakes to inform forecasts without changing the target-event set. For the 2016--2017 Amatrice--Visso--Norcia sequence, Fusion achieves the highest target-event temporal likelihood when lower-magnitude events are retained, outperforming both ETAS and a purely neural point-process baseline. Event-wise and cumulative analyses show sustained timing gains through substantial portions of the Visso and Norcia sequences. Across five benchmark catalogs, catalog-specific neural training with a fixed ETAS prior yields the highest temporal likelihood at the minimum evaluated magnitude cutoff. Magnitude likelihood shows no consistent predictive gain beyond the Gutenberg--Richter-based ETAS reference, indicating that the additional information captured by Fusion is primarily temporal. These results show that lower-magnitude catalog histories and empirical scaling-law information complement neural sequence learning for target-event timing.