Earthquake aftershock forecasting with conditional generative models

<title>Abstract</title> <p>Forecasting how aftershocks evolve in space and time after a large earthquake is a central problem in statistical seismology and underpins operational earthquake forecasting. Existing forecasting methods rest on statistical point-process models such as the epidemic-type aftershock sequence (ETAS) and Reasenberg–Jones models, which prescribe a fixed decay in time and an isotropic kernel in space. They match the average Omori–Utsu and Gutenberg–Richter statistics well but do not capture the fault-controlled spatial patterns of real sequences or the productivity that varies among sequences. Rather than modeling individual events as a point process, we recast aftershock forecasting as conditional generation of a spatiotemporal field. We develop QuakeGen, a diffusion model that generates the evolving fields of aftershock rate and maximum magnitude conditioned on recent seismicity and the forecasting horizon. On global sequences, the data-driven approach outperforms the operational Reasenberg–Jones forecast, recovering the fault-controlled, anisotropic spatial structure that fixed kernels cannot express. On daily forecasting, QuakeGen also matches the well-tuned ETAS baselines, which neural point-process models have yet to surpass on the regional benchmark. Conditional generative modeling, which has transformed prediction in fields from weather forecasting to protein structure, could forecast more accurately how earthquake sequences unfold in space and time.</p>