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

M. KIM, G. LIN

doi:10.1007/s10483-023-2991-9

Applied Mathematics and Mechanics >

2023 , Vol. 44 >Issue 7: 1085 - 1100

DOI: https://doi.org/10.1007/s10483-023-2991-9

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

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1. Samsung Electronics, Yongin-si, Gyeonggi-do 17113, Republic of Korea;
2. Department of Mathematics, Purdue University, West Lafayette, IN 47907-2067, U.S.A.;
3. School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907-2067, U.S.A.

Received date: 2022-11-01

Revised date: 2023-03-16

Online published: 2023-07-05

Supported by

the National Science Foundation of U.S.A. (Nos. DMS-1555072, DMS-2053746, and DMS-2134209), the Brookhaven National Laboratory of U.S.A. (No. 382247), and U.S. Department of Energy (DOE) Office of Science Advanced Scientific Computing Research Program (Nos. DE-SC0021142 and DE-SC0023161)

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Abstract

This paper develops a deep learning tool based on neural processes (NPs) called the Peri-Net-Pro, to predict the crack patterns in a moving disk and classifies them according to the classification modes with quantified uncertainties. In particular, image classification and regression studies are conducted by means of convolutional neural networks (CNNs) and NPs. First, the amount and quality of the data are enhanced by using peridynamics to theoretically compensate for the problems of the finite element method (FEM) in generating crack pattern images. Second, case studies are conducted with the prototype microelastic brittle (PMB), linear peridynamic solid (LPS), and viscoelastic solid (VES) models obtained by using the peridynamic theory. The case studies are performed to classify the images by using CNNs and determine the suitability of the PMB, LBS, and VES models. Finally, a regression analysis is performed on the crack pattern images with NPs to predict the crack patterns. The regression analysis results confirm that the variance decreases when the number of epochs increases by using the NPs. The training results gradually improve, and the variance ranges decrease to less than 0.035. The main finding of this study is that the NPs enable accurate predictions, even with missing or insufficient training data. The results demonstrate that if the context points are set to the 10th, 100th, 300th, and 784th, the training information is deliberately omitted for the context points of the 10th, 100th, and 300th, and the predictions are different when the context points are significantly lower. However, the comparison of the results of the 100th and 784th context points shows that the predicted results are similar because of the Gaussian processes in the NPs. Therefore, if the NPs are employed for training, the missing information of the training data can be supplemented to predict the results.

Key words： neural process (NP); peridynamics; crack pattern; molecular dynamic (MD) simulation; machine learning; Gaussian process regression; convolutional neural network (CNN)

Cite this article

M. KIM, G. LIN . Peri-Net-Pro: the neural processes with quantified uncertainty for crack patterns[J]. Applied Mathematics and Mechanics, 2023 , 44(7) : 1085 -1100 . DOI: 10.1007/s10483-023-2991-9

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