Learning mechanically driven emergent behavior with message passing neural networks

Abstract

From designing architected materials to connecting mechanical behavior across scales, computational modeling is a critical tool for understanding and predicting the mechanical response of deformable bodies. In particular, computational modeling is an invaluable tool for predicting global emergent phenomena, such as the onset of geometric instabilities, or heterogeneity induced symmetry breaking. Recently, there has been a growing interest in both using machine learning based computational models to learn mechanical behavior directly from experimental data, and using machine learning (ML) methods to reduce the computational cost of physics-based simulations. Notably, machine learning approaches that rely on Graph Neural Networks (GNNs) have recently been shown to effectively predict mechanical behavior in multiple examples of particle-based and mesh-based simulations. However, despite this initial promise, the performance of graph based methods have yet to be investigated on a myriad of solid mechanics problems. In this work, we examine the ability of neural message passing to predict a fundamental aspect of mechanically driven emergent behavior: the connection between a column’s geometric structure and the direction that it buckles. To accomplish this, we introduce the Asymmetric Buckling Columns (ABC) dataset, a dataset comprised of three types of asymmetric and heterogeneous column geometries (sub-dataset 1, sub-dataset 2, and sub-dataset 3) where the goal is to classify the direction of symmetry breaking (left or right) under compression after the onset of the buckling instability. Notably, it is difficult to parameterize these structures into a feature vector for typical ML methods. Essentially, because the geometry of these columns is discontinuous and intricate, local geometric patterns will be distorted by the low-resolution “image-like” data representations that are required to implement convolutional neural network based metamodels. Instead, we present a pipeline to learn global emergent properties while enforcing locality with message passing neural networks. Specifically, we take inspiration from point cloud based classification problems from the computer vision research field and use PointNet++ layers to perform classification on the ABC dataset. In addition to investigating GNN model architecture, we study the effect of different input data representation approaches, data augmentation, and combining multiple models as an ensemble. Overall, we were able to achieve good performance with this approach, ranging from 0.952 prediction accuracy on sub-dataset 1, to 0.913 prediction accuracy on sub-dataset 2, to 0.856 prediction accuracy on sub-dataset 3 for training dataset sizes of 20,000 points each. However, these results also clearly indicate that predicting solid mechanics based emergent behavior with these methods is non-trivial. Because both our model implementation and dataset are distributed under open-source licenses, we hope that future researchers can build on our work to create enhanced mechanics-specific machine learning methods. Furthermore, we also intend to provoke discussion around different methods for representing complex mechanical structures when applying machine learning to mechanics research.