One of the most important unsolved problems in seismology is accurate aftershock prediction, which has critical societal consequences for public safety and infrastructure resilience following large earthquakes. Statistical methods, like Epidemic-Type Aftershock-Sequences (ETAS) model and Omori’s law, are based on empirical regularities but fail to model complex interactions and physical mechanisms. Recent progress of machine learning has already been seen in modeling seismicity that nurture nonlinear patterns using deep neural networks though these techniques are risk of overfitting and cannot be interpretable, particularly when confronted with data sparsity or transfer learning to new regions. In this work, we systematically benchmark ETAS, Multilayer Perceptron (MLP), Long Short-Term Memory (LSTM), Physics-Informed Neural Networks (PINNs), Liquid Time-Constant (LTC) Networks, and our novel hybrid Physic-Informed LTC on a real-world catalog of 1250 mainshock–aftershock pairs (1980–2013). By embedding Omori’s and Gutenberg–Richter laws into the loss function and comparing on standard (MAE) and operational (late warning fraction) metrics, we show that Physic-Informed LTC achieves the lowest MAE (20.1367) and the highest timely-warning fraction (61.4%), outperforming pure LTC (MAE = 20.2051, late warning = 40.4%) and PINN (MAE = 20.2344, late warning = 51.8%). These results demonstrate that physics-informed hybrid AI can deliver both state-of-the-art accuracy and actionable lead times for earthquake early warning systems.

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Using a Liquid Time-Constant Network with Physics-Informed Neural Network to Predict Aftershocks

  • Shakurov Timur,
  • Kim Pavel,
  • Iskander Akhmetov,
  • Talgat Mazakov,
  • Gulzat Ziyatbekova,
  • Sholpan Jomartova,
  • Aigerim Mazakova

摘要

One of the most important unsolved problems in seismology is accurate aftershock prediction, which has critical societal consequences for public safety and infrastructure resilience following large earthquakes. Statistical methods, like Epidemic-Type Aftershock-Sequences (ETAS) model and Omori’s law, are based on empirical regularities but fail to model complex interactions and physical mechanisms. Recent progress of machine learning has already been seen in modeling seismicity that nurture nonlinear patterns using deep neural networks though these techniques are risk of overfitting and cannot be interpretable, particularly when confronted with data sparsity or transfer learning to new regions. In this work, we systematically benchmark ETAS, Multilayer Perceptron (MLP), Long Short-Term Memory (LSTM), Physics-Informed Neural Networks (PINNs), Liquid Time-Constant (LTC) Networks, and our novel hybrid Physic-Informed LTC on a real-world catalog of 1250 mainshock–aftershock pairs (1980–2013). By embedding Omori’s and Gutenberg–Richter laws into the loss function and comparing on standard (MAE) and operational (late warning fraction) metrics, we show that Physic-Informed LTC achieves the lowest MAE (20.1367) and the highest timely-warning fraction (61.4%), outperforming pure LTC (MAE = 20.2051, late warning = 40.4%) and PINN (MAE = 20.2344, late warning = 51.8%). These results demonstrate that physics-informed hybrid AI can deliver both state-of-the-art accuracy and actionable lead times for earthquake early warning systems.