| 03 Sep 2026
PISAS v1.0: A Physics-Informed Neural Surrogate for Earthquake Productivity and Aftershock-Sequence Modeling from Open Seismic Catalogs
Abstract. Rapid estimates of aftershock productivity and temporal decay are valuable immediately after a large earthquake, when sequence-specific observations are still sparse and catalogue completeness may be degraded. Here I present PISAS v1.0, a physics-informed neural surrogate that predicts the quality-controlled number of aftershocks expected during the first 30 d and the Omori–Utsu decay exponent using only information available at mainshock origin time. The model uses mainshock magnitude, hypocentral depth, and three multiscale measures of pre-mainshock seismicity derived from the open U.S. Geological Survey Comprehensive Earthquake Catalog. An analytical decoder converts the neural outputs into a complete mean aftershock-rate history while enforcing positive productivity, bounded decay exponents, monotonic temporal decay, and exact agreement between the predicted event count and the integral of the reconstructed rate. The primary dataset contains 175 independent global sequences from 2000–2025, with model development based on rolling-origin validation and final evaluation on an untouched 2020–2025 temporal test. PISAS reproduced a moderate and transferable component of 30 d productivity variability, with coefficients of determination of 0.454 in out-of-fold validation and 0.534 on the temporal test. Relative to a magnitude-only linear model, productivity root-mean-square error improved by 3.9 % out of fold, 5.0 % on the temporal test, and 4.3 % under leave-one-region-out validation. Prediction of the decay exponent was substantially weaker, with near-zero or negative explained variance in out-of-fold and regional evaluation. Mainshock magnitude was the dominant productivity predictor, whereas hypocentral depth provided the most stable, but limited, information about temporal decay. Compared with an otherwise equivalent unconstrained neural network, PISAS matched or improved predictive accuracy while eliminating all violations of rate normalization and output admissibility. PISAS v1.0 therefore provides a reproducible, physically consistent initial estimate of aftershock productivity and mean temporal evolution, while clearly delimiting the weaker predictability of sequence-specific decay.
In this work, the author builds a global set of 175 aftershock sequences from the USGS ComCat catalog and trains a small neural network to predict the number of aftershocks in the first 30 days and the Omori-Utsu decay exponent p, using the mainshock magnitude, depth and the seismicity rate before the mainshock. The two predictions are converted into an aftershock rate curve, and the model is proposed as a first forecast to use right after a large earthquake. The negative result for p is reported honestly. However, I do not think the current results support the use proposed in the paper, mainly because the model is trained and tested only on sequences that turned out to be productive. I recommend major revisions.
1. The model is trained only on productive sequences.
Only sequences with at least 20 aftershocks are used (L240), which is about a quarter of the M >= 6.5 mainshocks in the author's own data. Right after a mainshock, we do not know whether its sequence will be this productive, so the model is tested on a different population from the one it is meant to forecast. This selection also makes aftershock counts look less sensitive to magnitude than they are: the fitted slope is about 0.5 here (Fig. 2c), compared with about 1 when all mainshocks are included. The sensitivity test already shows the model overpredicting for smaller sequences (Section 6). How does the model perform if it is trained and evaluated on all mainshocks, including those with few or no aftershocks?
2. The improvement over magnitude alone may not be real.
The model reduces the error of a magnitude-only fit by about 4-5% (L25), and the paper describes this as statistically consistent (L881). With 114 validation and 32 test sequences, a difference this small may come from which earthquakes happen to be in the sample. Fig. 6c gives a sense of the uncertainty: removing any of the seismicity-rate inputs changes the error by less than the spread of the full model itself. What are the uncertainties of these improvements? If they are not significant, the conclusions about depth and background seismicity, and the interpretation in Section 8, need to be revised.
3. Comparison with the existing USGS aftershock model.
The USGS already uses regional aftershock parameters for global earthquakes (Page et al., 2016) as the first forecast after a mainshock, which is the same role proposed here. That model also accounts for differences between tectonic regions, which the author's earlier study found to be the most important factor after magnitude (L63). How does PISAS compare with it? Because a first forecast is later updated with observed aftershocks, can the comparison also be made on predicted probabilities rather than only on the error of a single predicted number (the seed spread is not a predictive uncertainty, L455)?
Minor comments: