Predicting mechanically driven full-field quantities of interest with deep learning-based metamodels

Using simulation to predict the mechanical behavior of heterogeneous materials has applications ranging from topology optimization to multi-scale structural analysis. However, full-fidelity simulation techniques such as Finite Element Analysis, while effective, can be prohibitively computationally expensive when they are used to explore the massive input parameter space of heterogeneous materials. Therefore, there has been significant recent interest in machine learning-based models that, once trained, can predict mechanical behavior at a fraction of the computational cost compared to full fidelity simulations. Over the past several years, research in this area has been focused mainly on predicting single Quantities of Interest (QoIs). However, there has recently been an increased interest in a more challenging problem: predicting full-field QoI (e.g., displacement/strain fields, damage fields) for mechanical problems. Due to the added complexity of full-field information, network architectures that perform well on single QoI problems may perform relatively poorly in the full-field QoI problem setting. This problem is also challenging because, even outside the Mechanics research community, deep learning approaches to image-to-image mapping and full-field image analysis remain poorly understood. The work presented in this paper is twofold. First, we made a significant extension to the Mechanical MNIST dataset designed to enable the investigation of full-field QoI prediction. Specifically, we added Finite Element simulation results of quasi-static brittle fracture in a heterogeneous material captured with the phase-field method. This problem was chosen as a broadly relevant challenge problem for full-field QoI prediction. Second, we investigated multiple Deep Neural Network architectures and subsequently established strong baseline performance for predicting full-field QoI. We found that a MultiRes-WNet architecture with straightforward data augmentation achieves 0.80% and 0.34% Mean Absolute Percentage Error on full-field displacement prediction for Equibiaxial Extension and Uniaxial Extension datasets in the Mechanical MNIST Fashion dataset, respectively. In addition, we found that our MultiRes-WNet architecture combined with a basic Convolutional Autoencoder achieves a mean F-1 score of 0.87 on the newly added Mechanical MNIST Crack Path dataset. In addition to presenting the results in this paper, we have released our model implementation and the Mechanical MNIST Crack Path dataset under open-source licenses. We anticipate that future researchers will directly use our model architecture on related datasets and potentially design models that exceed the baseline performance for predicting full-field QoI established in this paper. (C) 2021 Elsevier Ltd. All rights reserved.

Automated summary

Using simulation to predict the mechanical behavior of heterogeneous materials has applications ranging from topology optimization to multi-scale structural analysis. However, traditional simulation methods can be computationally expensive, leading to the development of machine learning-based models for more efficient prediction. This study extends the Mechanical MNIST dataset and establishes strong baseline performance for predicting full-field quantities of interest using various deep neural network architectures.