Data-Efficient Inverse Design of Spinodoid Metamaterials

Abstract We present a data-efficient neural-network model for predicting linear-elastic properties of spinodoid metamaterials from their mesoscale structure. Our machine-learning model requires 75 data points for training, greatly improving data efficiency over previous models that required thousands of training samples. We achieve this by leveraging concepts from geometric learning. Specifically, we exploit physical properties, such as positive semi-definiteness of the elasticity tensor, as well as structural invariances and equivariances of the problem, for example with respect to coordinate axes permutations. The neural network model is designed to exactly fulfill these constraints; it does not have to learn them from data. The resulting model enables data- and compute-efficient inverse design of spinodoid metamaterials. In inverse design, the goal is to find a material mesostructure that leads to desired mechanical properties on the macroscale. Exactly fulfilling physical and structural constraints, the present neural network model remains differentiable. This allows using fast gradient-based optimizers for inverse design. We demonstrate this by inversely designing spinodoid metamaterials that achieve desired linear elastic target properties in three dimensions. Inverse design is treated as a constrained optimization problem over the parameters describing the metamaterial. The results confirm that the present approach requires significantly less training data than previous machine-learning approaches and allows incorporating multiple objectives in the inverse design process. Since the structure of the design space is independent of the target material properties, we hope that such data-efficient models will be useful also for inverse design of spinodoids beyond linear elasticity.