Bayesian neural networks (BNN) are the probabilistic model that combines the strengths of both neural network (NN) and stochastic processes. As a result, BNN can combat overfitting and perform well in applications where data is limited. Earthquake rupture study is such a problem where data is insufficient, and scientists have to rely on many trial and error numerical or physical models. Lack of resources and computational expenses, often, it becomes hard to determine the reasons behind the earthquake rupture. In this work, a BNN has been used (1) to combat the small data problem and (2) to find out the parameter combinations responsible for earthquake rupture and (3) to estimate the uncertainty associated with earthquake rupture. Two thousand rupture simulations are used to train and test the model. A simple 2D rupture geometry is considered where the fault has a Gaussian geometric heterogeneity at the center, and eight parameters vary in each simulation. The test F1-score of BNN (0.8334), which is 2.34% higher than plain NN score. Results show that the parameters of rupture propagation have higher uncertainty than the rupture arrest. Normal stresses play a vital role in determining rupture propagation and are also the highest source of uncertainty, followed by the dynamic friction coefficient. Shear stress has a moderate role, whereas the geometric features such as the width and height of the fault are least significant and uncertain.

Damage due to earthquakes poses a threat to humans worldwide. To estimate the hazard, scientists use historical earthquake data and ground motion recorded by seismometers at different locations. However, the current approaches are mostly empirical and may not capture the full range of ground shaking in future large earthquakes due to a lack of historical geological data. This leads to significant uncertainties in hazard estimates. Not only that, due to the lack of sufficient historical data, scientists mostly rely on simulated data, which is computationally expensive.

Damage due to earthquakes poses a threat to humans worldwide. To estimate the hazard, scientists use historical earthquake data and ground motion recorded by seismometers at different locations. However, the current approaches are mostly empirical and may not capture the full range of ground shaking in future large earthquakes due to a lack of historical geological data. This leads to significant uncertainties in hazard estimates. Not only that, due to the lack of sufficient historical data, scientists mostly rely on simulated data, which is computationally expensive.

Simulating dynamic rupture propagation is challenging due to the uncertainties involved in the underlying physics of fault slip, stress conditions, and frictional properties of the fault. A trial and error approach is often used to determine the unknown parameters describing rupture, but running many simulations usually requires human review to determine how to adjust parameter values and is thus not very efficient. To reduce the computational cost and improve our ability to determine reasonable stress and friction parameters, we take advantage of the machine learning approach. We develop two models for earthquake rupture propagation using the artificial neural network (ANN) and the random forest (RF) algorithms to predict if a rupture can break a geometric heterogeneity on a fault. We train the models using a database of 1600 dynamic rupture simulations computed numerically. Fault geometry, stress conditions, and friction parameters vary in each simulation. We cross-validate and test the predictive power of the models using an additional 400 simulated ruptures, respectively. Both RF and ANN models predict rupture propagation with more than 81% accuracy, and model parameters can be used to infer the underlying factors most important for rupture propagation. Both of the models are computationally efficient such that the 400 testings require a fraction of a second, leading to potential applications of dynamic rupture that have previously not been possible due to the computational demands of physics-based rupture simulations.