A general-purpose machine learning framework for predicting singular integrals in boundary element method

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.