Reconstruction of Random Structures Based on Generative Adversarial Networks: Statistical Variability of Mechanical and Morphological Properties

Mikhail Tashkinov (), Yulia Pirogova, Evgeniy Kononov, Aleksandr Shalimov and Vadim V. Silberschmidt
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Mikhail Tashkinov: Laboratory of Mechanics of Biocompatible Materials and Devices, Perm National Research Polytechnic University, 614990 Perm, Russia
Yulia Pirogova: Laboratory of Mechanics of Biocompatible Materials and Devices, Perm National Research Polytechnic University, 614990 Perm, Russia
Evgeniy Kononov: Laboratory of Mechanics of Biocompatible Materials and Devices, Perm National Research Polytechnic University, 614990 Perm, Russia
Aleksandr Shalimov: Laboratory of Mechanics of Biocompatible Materials and Devices, Perm National Research Polytechnic University, 614990 Perm, Russia
Vadim V. Silberschmidt: Wolfson School of Mechanical, Electrical and Manufacturing Engineering, Loughborough University, Loughborough LE11 3TU, UK

Mathematics, 2024, vol. 13, issue 1, 1-23

Abstract: Generative adversarial neural networks with a variational autoencoder (VAE-GANs) are actively used in the field of materials design. The synthesis of random structures with nonrepeated geometry and predetermined mechanical properties is important for solving various practical problems. Geometric parameters of such artificially generated random structures can vary within certain limits compared to the training dataset, causing unpredicted fluctuations in their resulting mechanical response. This study investigates the statistical variability of mechanical and morphological characteristics of random 3D models reconstructed from 2D images using a VAE-GAN neural network. A combined multitool method employing different mathematical and statistical instruments for comparison of the reconstructed models with their corresponding originals is proposed. It includes the analysis of statistical distributions of elastic properties, morphometric parameters, and stress values. The neural network was trained on two datasets, containing models created based on Gaussian random fields. Statistical fluctuations of the mechanical and morphological parameters of the reconstructed models are analyzed. The deviation of the effective elastic modulus of the reconstructed models from that of the original ones was less than 5.7% on average. The difference between the median values of ligament thickness and distance between ligaments ranged from 3.6 to 6.5% and 2.6 to 5.2%, respectively. The median value of the surface area of the reconstructed geometries was 4.6–8.1% higher compared to the original models. It is thus shown that mechanical properties of the NN-generated structures retain the statistical variability of the corresponding originals, while the variability of the morphology is highly affected by the training set and does not depend on the configuration of the input 2D image.

Keywords: machine learning; VAE-GAN; random structure; reconstruction; morphometric analysis; statistical distributions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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