Physics-Informed Machine Learning for Short-Term Aftershock Forecasting: A Comparative Study with ETAS

Aftershock forecasting is non-negotiable for controlling possible subsequent natural disasters. Previous models like the Epidemic-Type Aftershock Sequence (ETAS) have proved to be effective but they require intensive complex calculations including proper estimation of suitable parameters. Machine learning is a data-based study and is flexible, but can lose reliability due to noise or bias. In this study, we take help of a physics-based feature—the Boussinesq Stress Index —that uses seismic magnitude and depth to utilize its forecasting power to determine a binary decision—if an earthquake will be followed by a larger event (∆M ≥ 1.0) within 7 days of the event, and within 50 km radius. Using a simulated but realistic seismicity event data with a depth-dependent probabilistic forecasting, we compare performances of Random Forest models with and without the stress index, a logistic regression model with the index, using an oracle ETAS forecast. Our results show that the stress index does not satisfactorily improve the Random Forest’s discrimination (∆AUC = +0.0012, 95% CI -0.0199, 0.0221), but it improves the logistic regression’s performance by a meaningful extent, which achieves an AUC of 0.744—outperforming both Random Forest models and approaching the ETAS oracle (AUC 0.730). SHAP analysis confirms that the stress index acts as one of the most deciding factors for this study. These findings highlight that the value of a physics-informed feature may depend critically on the choice of machine learning model, and that a simple linear model can sometimes exploit such features more effectively than complex ensembles. Our study makes a unique contribution in integrating light-weight machine learning techniques with physics-based feature for an aftershock probabilistic forecast.