## 3 Results
### Early Earthquake Magnitude Estimation as a Regression Task
The input consists of a combination of acceleration, velocity, and displacement waveforms with a length of 3 s after the P-wave arrival. The architecture includes an input block, a convolutional-based feature extractor, a bidirectional gated recurrent unit (Bi-GRU) with an AM for sequential learning, and an output layer for final magnitude estimation. Compared to traditional \(\tau_{c}\) and \(P_{d}\) methods, MEANet demonstrates superior accuracy, achieving an error of \(\pm\)0.25 magnitude units at a single station. Tests indicate that extending the time window from 3 to 10 s improves magnitude prediction, as additional waveform data enhances event characterization, particularly for larger earthquakes. The study also highlights the importance of certain physical parameters, such as \(P_{d}\), \(P_{v}\), and \(P_{u}\), in improving robustness. By leveraging a physics-guided approach combined with deep learning, MEANet reduces the underestimation of large magnitudes, a common issue in early warning models. This hybrid strategy suggests potential applications in early warning systems, particularly in regions where rapid and precise magnitude estimation is critical, highlighting its ability to generalize across different seismic scenarios. Ref. [44] introduced MagNet, a fully convolutional network (FCN) designed for magnitude estimation. The architecture consists of two main components, namely, a compression module for feature extraction and an expansion module for magnitude prediction. The compression module applies sequential convolutional and pooling layers to extract key features from 2D waveform data, reducing dimensionality while increasing feature depth. The expansion module uses upsampling and convolutional layers to generate a Gaussian probability distribution representing the magnitude. Unlike conventional CNNs, MagNet employs a probability distribution approach rather than a single value estimation, enhancing robustness against noise and outliers. The model was trained on 700 real seismic events from the China Seismic Experimental Site (CSES) and augmented to 21,700 datasets using synthetic data generation techniques. It processes waveform records from multiple seismic stations to generate probabilistic magnitude estimates. MagNet performs well for moderate earthquakes (magnitudes 3 to 5.9), achieving an average error of \(-\)0.017 and a standard deviation of 0.21, with a 99.8% recovery rate. For small earthquakes (magnitudes 2.3 to 3.5), the model maintains high accuracy with an error of \(-\)0.011 and a standard deviation of 0.14, demonstrating its capability for lower-magnitude events. The model also shows resilience against anomalous noise, outperforming traditional magnitude estimation methods. However, the model struggles with large earthquakes (\(M>6.5\)), as the dataset lacks sufficient high-magnitude training samples. This limitation suggests the need for future improvements, such as transfer learning or hybrid models incorporating physical constraints. Ref. [56] proposed AIMag, a deep learning model for single-station magnitude estimation based on the MagNet architecture. AIMag employs a CRNN structure that integrates convolutional layers for feature extraction and recurrent layers for temporal modeling. Unlike traditional approaches, AIMag estimates magnitudes using the first P-waves without requiring location information or instrument response corrections. It was tested across various time window lengths ranging from 1 to 114 s, revealing that performance improves as the window length increases. At its optimal configuration (114 s), AIMag achieves a median estimation error within \(\pm\)0.5 magnitude units for events ranging from \(M2.3\) to \(M7.6\). However, for magnitudes above \(M7\), the model tends to underestimate, likely due to P-wave saturation and the scarcity of large-magnitude events in the training set. To enhance generalization, data augmentation techniques were applied, including P-phase shifting, noise injection, and random channel removal.