Three-dimensional convolutional neural network (3D-CNN) for heterogeneous material homogenization (2002.07600v1)

Abstract: Homogenization is a technique commonly used in multiscale computational science and engineering for predicting collective response of heterogeneous materials and extracting effective mechanical properties. In this paper, a three-dimensional deep convolutional neural network (3D-CNN) is proposed to predict the effective material properties for representative volume elements (RVEs) with random spherical inclusions. The high-fidelity dataset generated by a computational homogenization approach is used for training the 3D-CNN models. The inference results of the trained networks on unseen data indicate that the network is capable of capturing the microstructural features of RVEs and produces an accurate prediction of effective stiffness and Poisson's ratio. The benefits of the 3D-CNN over conventional finite-element-based homogenization with regard to computational efficiency, uncertainty quantification and model's transferability are discussed in sequence. We find the salient features of the 3D-CNN approach make it a potentially suitable alternative for facilitating material design with fast product design iteration and efficient uncertainty quantification.

• The paper proposes using a 3D convolutional neural network (CNN) trained on computationally generated data to predict effective material properties of heterogeneous materials with high accuracy.
• The trained 3D-CNN model achieved high predictive accuracy (MARE below 0.55%) and offered significant computational speedups (25 to 50 ) compared to traditional finite element analysis.
• The study demonstrates the model's capacity for uncertainty quantification and its transferability to new microstructures (e.g., ellipsoidal inclusions) through transfer learning.

Three-Dimensional Convolutional Neural Networks for Heterogeneous Material Homogenization

The paper presents a paper on the application of three-dimensional convolutional neural networks (3D-CNN) in the prediction of effective material properties of heterogeneous materials. Homogenization traditionally relies on methodologies such as the finite element method (FEM) for simulating the mechanical behavior of representative volume elements (RVEs) that embody complex material microstructures. The authors propose an alternative approach using 3D-CNNs, which leverage deep learning to offer potential improvements in computational efficiency, accuracy, and flexibility.

Methodology

The paper involves training a 3D-CNN model to predict the effective stiffness and Poisson's ratio for RVEs with random spherical inclusions. The high-fidelity dataset used to train the network was generated using computational homogenization methods, providing a robust basis for learning. To ensure the extensive applicability of the trained model, the RVEs encompass a wide range of inclusion volume fractions, arranged in a manner to capture the inherent microstructural randomness effectively.

Parametric analyses are undertaken to optimize the CNN architecture, focusing on aspects such as filter size, number of filters, and the configuration of layers. The convolutional layers are critical in distilling salient microstructural features from the input voxel data, which represent the phase information of the RVEs. The paper also addresses common challenges in deep learning such as overfitting, employing techniques such as early stopping and data augmentation during training.

Results and Discussion

The trained 3D-CNN model demonstrated high predictive accuracy, with mean absolute relative errors (MARE) of below 0.55% across all evaluated components of material properties. Notably, the use of 3D-CNNs provided significant computational advantages over traditional FEA, with reported speedup factors ranging from 25× to 50× when utilizing GPU processing. These improvements in computation time highlight the competency of 3D-CNNs for rapid prototyping and iteration in material design.

Moreover, the paper highlights the model's capacity for uncertainty quantification (UQ), wherein the 3D-CNN could successfully predict probabilistic distributions of effective material properties under input uncertainty, akin to stochastic microstructures.

Transferability and Future Implications

An acknowledged merit of the proposed 3D-CNN approach is its transferability, examined through a transfer learning case paper. The model pre-trained on spherical inclusions was effectively adapted to a new RVE dataset with ellipsoidal inclusions, underscoring the extensibility of the trained networks to different material systems with minimal additional computational investment.

The successful implementation of 3D-CNNs in this context paves the way for broader applications in material science, particularly within the domain of materials informatics. By facilitating faster design iterations, enhanced uncertainty characterization, and flexible applicability across various microstructural configurations, 3D-CNNs are poised to play a pivotal role in advancing computational materials science.

Looking forward, future developments could explore extending these techniques to more complex, non-linear material behaviors and integrating the approach with generative models for microstructure design. The amalgamation of deep learning with traditional material science paradigms presents a fertile ground for innovation in predictive modeling and material discovery.