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Energy-conserving equivariant GNN predictions of stiffness for lattice materials

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Lattices emerged in recent decades as a promising class of architected materials with a vast design space. Many machine learning models have been proposed as surrogate to numerical modelling in predicting their mechanical properties for rapid design applications. However, they are often not scalable, lack the appropriate physical constraints and hence are limited to a small fragment of the vast design space. Here we develop a graph based neural network to predict the fourth-order stiffness tensor of any arbitrary periodic lattice. We build upon the equivariant MACE model (Batatia, Kovács, Csányi et al.) and introduce positive semi-definite constraints that ensure energy conservation. We trained the model on a generalised dataset of unit cells and demonstrate an example application of the model in structural optimization.

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