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.

翻译：贝叶斯神经网络（BNN）是一种结合神经网络与随机过程优势的概率模型，能够有效防止过拟合，并在数据有限的场景中表现出色。地震破裂研究正是典型的数据不充分问题，科学家需要依赖大量试错性的数值或物理模型。由于资源匮乏和计算成本高昂，解析地震破裂的成因常面临困难。本研究采用BNN（1）应对小数据问题，（2）识别导致地震破裂的参数组合，以及（3）估计地震破裂相关的不确定性。使用2000次破裂模拟数据训练和测试模型，采用简单的二维破裂几何模型，其中断层中心存在高斯几何异质性，每次模拟涉及8个变量参数。BNN的测试F1分数为0.8334，比普通神经网络高2.34%。结果表明：破裂传播参数的不确定性高于破裂终止参数；正应力在破裂传播中起决定性作用，同时也是最大的不确定性来源，其次为动态摩擦系数；剪应力作用中等，而断层宽度、高度等几何特征的重要性和不确定性最低。