Accurate and efficient evaluation of singular integrals is of crucial importance for the successful implementation of the boundary element method (BEM). In most traditional methods, complex mathematical operations or expensive computation cost is required to achieve high accuracy of singular integral. To solve this problem, a new machine learning-based prediction framework is proposed in this paper from the perspective of data analysis. Using the framework, an effective prediction model can be constructed by various supervised machine learning algorithms. The prediction model is fed into the BEM program to predict the results of singular integrals directly according to the given coordinates of the elements. In this process, a transformation method is proposed to bridge the gap between the training space in which the prediction model is constructed and the application space in which the prediction model is applied. We take the singular integrals in 3D elastostatics as an example to evaluate the performance of the proposed framework with 5 typical machine learning algorithms. The results demonstrate that, the prediction method has less cost time while getting identical computational accuracy with the traditional method. More importantly, the prediction accuracy is numerically stable and not sensitive to the position of source points.

准确有效地评估奇异积分对于成功实施边界元方法（BEM）至关重要。在大多数传统方法中，需要复杂的数学运算或昂贵的计算成本才能实现奇异积分的高精度。为了解决这个问题，本文从数据分析的角度提出了一种新的基于机器学习的预测框架。使用该框架，可以通过各种监督的机器学习算法来构建有效的预测模型。将预测模型输入到BEM程序中，以根据给定的元素坐标直接预测奇异积分的结果。在这个过程中 提出了一种变换方法，以弥补构造预测模型的训练空间与应用预测模型的应用空间之间的差距。我们以3D弹性静力学中的奇异积分为例，通过5种典型的机器学习算法来评估所提出框架的性能。结果表明，该预测方法具有较少的时间花费，同时具有与传统方法相同的计算精度。更重要的是，预测精度在数值上是稳定的，并且对源点的位置不敏感。结果表明，该预测方法具有较少的时间花费，同时具有与传统方法相同的计算精度。更重要的是，预测精度在数值上是稳定的，并且对源点的位置不敏感。结果表明，该预测方法具有较少的时间花费，同时具有与传统方法相同的计算精度。更重要的是，预测精度在数值上是稳定的，并且对源点的位置不敏感。