Permutation-Invariant Deep Neural Networks for Predicting the Mechanical Properties of Random Cellular Composites

Composite materials hold exciting key to many extraordinary mechanical properties such as reduced weight, high specific strength and toughness, and progressive fracture behavior. Recent advances in additive manufacturing have facilitated the fabrication of complex composite designs. However, searching for the optimal structures and combinations of composite materials has never been a trivial task. Previous machine learning models usually take structured design features (<i>e.g.</i> fixed-size vectors, images, graphs, <i>etc.</i>) as inputs, which usually confines and discretizes the design space. Here we adopt permutation-invariant neural networks to learn the unordered point distributions in a continuous space. We embed the cell centroid distributions of random cellular composites as high-dimensional representation vectors to predict the stress-strain curves obtained from lattice spring model (LSM) simulations. By learning randomly shuffled and reflected cell centroids, our model obeys permutation invariance and reflection symmetry of cellular composite designs. Without discretization in formulation, the model also learns the continuous mapping of spatial coordinates and can embed arbitrary number of cells. Our model could enable high-throughput and flexible composite design and apply to gradient-based optimization.