Surrogate Modeling for the Design of Optimal Lattice Structures using Tensor Completion

When designing new materials, it is often necessary to design a material with specific desired properties. Unfortunately, as new design variables are added, the search space grows exponentially, which makes synthesizing and validating the properties of each material very impractical and time-consuming. In this work, we focus on the design of optimal lattice structures with regard to mechanical performance. Computational approaches, including the use of machine learning (ML) methods, have shown improved success in accelerating materials design. However, these ML methods are still lacking in scenarios when training data (i.e. experimentally validated materials) come from a non-uniformly random sampling across the design space. For example, an experimentalist might synthesize and validate certain materials more frequently because of convenience. For this reason, we suggest the use of tensor completion as a surrogate model to accelerate the design of materials in these atypical supervised learning scenarios. In our experiments, we show that tensor completion is superior to classic ML methods such as Gaussian Process and XGBoost with biased sampling of the search space, with around 5\% increased $R^2$. Furthermore, tensor completion still gives comparable performance with a uniformly random sampling of the entire search space.