Peri-Net-Pro: The neural processes with quantified uncertainty for crack patterns

TL;DR

This study combines peridynamic theory with neural processes and CNNs to predict and classify crack patterns in materials, demonstrating improved data quality and uncertainty quantification even with limited data.

Contribution

It introduces a novel approach integrating peridynamics, CNNs, and neural processes for crack pattern analysis, enhancing prediction accuracy and data efficiency.

Findings

Neural processes reduce variance in crack pattern predictions.

Peridynamics improves data quality over FEM for crack images.

Neural processes perform well with limited training data.

Abstract

This paper uses the peridynamic theory, which is well-suited to crack studies, to predict the crack patterns in a moving disk and classify them according to the modes and finally perform regression analysis. In that way, the crack patterns are obtained according to each mode by Molecular Dynamic (MD) simulation using the peridynamics. Image classification and regression studies are conducted through Convolutional Neural Networks (CNNs) and the neural processes. First, we increased the amount and quality of the data using peridynamics, which can theoretically compensate for the problems of the finite element method (FEM) in generating crack pattern images. Second, we did the case study for the PMB, LPS, and VES models that were obtained using the peridynamic theory. Case studies were performed to classify the images using CNNs and determine the PMB, LBS, and VES models' suitability. Finally, we performed the regression analysis for the images of the crack patterns with neural processes to predict the crack patterns. In the regression problem, by representing the results of the variance according to the epochs, it can be confirmed that the result of the variance is decreased by increasing the epoch numbers through the neural processes. The most critical point of this study is that the neural processes make an accurate prediction even if there are missing or insufficient training data.