2024/01/30 by Ivan Grega, Grega, Ivan, Ilyes Batatia +7 · 1 citation
Engineering · Physics and Astronomy · #Elasticity and Wave Propagation #Electromagnetic Scattering and Analysis #FOS: Computer and information sciences #FOS: Physical sciences #Machine Learning (cs.LG) #Materials Science (cond-mat.mtrl-sci) #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.2401.16914
openalex publication_date 2024/01/30 · openalex created_date 2024/02/01 · openalex updated_date 2026/07/28
Lattices are architected metamaterials whose properties strongly depend on their geometrical design. The analogy between lattices and graphs enables the use of graph neural networks (GNNs) as a faster surrogate model compared to traditional methods such as finite element modelling. In this work, we generate a big dataset of structure-property relationships for strut-based lattices. The dataset is made available to the community which can fuel the development of methods anchored in physical principles for the fitting of fourth-order tensors. In addition, we present a higher-order GNN model trained on this dataset. The key features of the model are (i) SE(3) equivariance, and (ii) consistency with the thermodynamic law of conservation of energy. We compare the model to non-equivariant models based on a number of error metrics and demonstrate its benefits in terms of predictive performance and reduced training requirements. Finally, we demonstrate an example application of the model to an architected material design task. The methods which we developed are applicable to fourth-order tensors beyond elasticity such as piezo-optical tensor etc.