Large earthquakes pose significant challenges due to their destructive power and unpredictability. While numerical wave propagation offers high-resolution ground motion simulations, the computational cost is prohibitive for real-time disaster mitigation. Even with High-Performance Computing (HPC), simulations are sensitive to model inputs, particularly for large events. Recent HPC workflows can produce synthetic solutions within an hour, but this is still too slow for near real-time societal alerts. Empirical GMMs offer a faster alternative, providing mean and variability values for intensity measures (IMs) like peak ground acceleration (PGA) or pseudo-spectral acceleration (PSA) as functions of seismic observations. However, the limited size and variability of earthquake catalogs compromise their predictive capacity, particularly for large-magnitude events. This research proposes a Machine Learning (ML) methodology that combines the speed of empirical GMMs with the precision of physics-based simulations. The proposed ML-based estimator for ground-shaking maps (MLESmap) aims to leverage the accuracy of well-curated simulations while maintaining fast evaluation times, creating the next generation of shaking maps.

Numerous studies have explored ML applications in earthquake seismology, often using seismic observations to train ML-based GMMs and infer IMs. While these approaches show improvements over traditional regression-based GMMs when sufficient data is available, data scarcity, particularly for large-magnitude events, remains a limitation. ML models also tend to struggle with extrapolation beyond the training data's range. Synthetic datasets, generated from physics-based simulations, offer a solution by providing data on a dense and uniform grid, overcoming spatial sparsity. Withers et al. (2020) presented promising results using an artificial neural network (ANN) GMM trained on CyberShake synthetics, but used predictor variables similar to empirical GMMs. This study differs by using only elementary information (location and magnitude) as predictor variables to maximize applicability and minimize uncertainty in rapid estimations.

The MLESmap methodology uses two supervised ML algorithms: Random Forest (RF) and Deep Neural Networks (DNN). It was trained using a CyberShake Study 15.4 (CSS-15.4) database containing over 150,000 physics-based simulations for Southern California. The dataset encompasses IMs for 153,628 scenarios, covering a wide range of magnitudes (predominantly around Mw 7.6, with a magnitude cutoff of 6.5 in CyberShake). The dataset was divided into training and validation subsets. Eight independent ML models were generated (four periods per algorithm: T = 2, 3, 5, and 10 seconds). Predictor variables included the event's hypocentral location (latitude, longitude, depth), magnitude, site latitude, longitude, Euclidean distance, and azimuth between hypocenter and site. The logarithm of RotD50 (median pseudo-spectral acceleration across all azimuths) served as the target variable due to its high dynamic range. The Random Forest model utilized the dislib library in Python for efficient handling of large datasets, with hyperparameters optimized via grid search and k-folds cross-validation. The Deep Neural Networks (DNNs) consisted of fully connected MLPs, with architectures optimized to avoid issues such as non-generalization, vanishing/exploding gradients, and local minima. Regularization, data normalization, batch normalization, different learning rate schedulers, dropout, and activation functions were carefully considered in the network topology design. TensorFlow and Keras libraries were used for the DNN implementation. The models were validated using several regression metrics (MAE, MSE, RMSE, MAPE, R², Pearson's correlation) on the validation dataset. For comparisons with empirical GMMs, RMSE and the geometric mean ratio of Aida's number K were used to assess both accuracy and prediction bias.

MLESmap models demonstrated high predictive power, with an average R² of 0.86, indicating a high likelihood of correct predictions for unseen samples. The average MAPE was below 15%. Comparisons with the ASK-14 empirical GMM showed that MLESmap models significantly outperformed ASK-14 for synthetic earthquakes compatible with the training data, achieving up to a 45% reduction in median RMSE. The MLESmap predictions exhibited less bias than ASK-14, which tended to underpredict RotD50 for larger events and overpredict for smaller events. Similar improvements were observed for five real historical earthquakes in Southern California (Landers, Hector Mine, Northridge, North Palm Springs, Whittier). For 'inside' stations (within the training data's spatial extent), RMSE reductions of 14-73% (RF) and 19-88% (DNN) relative to ASK-14 were observed for events within the training data's magnitude range. However, for the Whittier earthquake (Mw 5.9), which fell outside the training data's magnitude range, the ML models underperformed compared to ASK-14. This highlights the importance of the training data's range in model performance. The spatial distribution of RotD50 predicted by MLESmap better captured local amplification effects, especially for larger events, compared to ASK-14.

The MLESmap methodology successfully combines the accuracy of physics-based simulations with the speed of empirical GMMs. The superior performance of MLESmap over ASK-14, achieved using only readily available earthquake parameters, demonstrates its potential as a valuable tool for rapid post-disaster analysis. The results strongly suggest that the CyberShake synthetic database accurately represents the underlying physics of ground motion in the study region. The limitations are primarily due to the scope of the training data. MLESmap models perform optimally for earthquakes with parameters (magnitude, location) within the bounds of the training dataset. Extrapolation outside this range leads to reduced accuracy. Future research could focus on expanding the training dataset, incorporating additional earthquake parameters (focal mechanism, rupture extent), or employing hybrid approaches that combine MLESmap with empirical GMMs to enhance generalizability. Transfer learning techniques could also be explored to leverage knowledge from one region to improve predictions in other areas.

MLESmap offers a promising new approach for real-time earthquake ground-shaking predictions. Its superior accuracy compared to empirical GMMs, coupled with its fast evaluation time, makes it a valuable tool for rapid post-disaster assessment. The limitations related to the training data's range highlight the importance of continued data development and model refinement. Future research could investigate the incorporation of additional parameters, hybrid approaches, transfer learning, and expanded datasets to increase the robustness and broader applicability of MLESmap.

The primary limitation of MLESmap is its reliance on the training data's parameter range. Predictions outside this range (in terms of magnitude and location) may be less accurate. The study focuses on RotD50 as the IM, and extending it to other IMs might require further model training and validation. The accuracy of the predictions is highly dependent on the quality and representativeness of the CyberShake synthetic database. Finally, the current implementation does not provide temporal information about the events.