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

2025-10-08

AI Summary

Traditional machine learning models exhibit poor generalizability and low stability in predicting the mechanical properties of lattice structures due to non-uniform sampling of design space. Method: This paper proposes a novel surrogate modeling framework based on tensor completion, the first application of tensor completion to atypical supervised learning in materials design. It explicitly captures structural correlations among high-dimensional design variables, thereby mitigating bias induced by skewed data distributions. Contribution/Results: Trained on mechanical simulation data and benchmarked against Gaussian process regression and XGBoost, the method achieves approximately 5% higher R² under non-uniform sampling while maintaining comparable performance under uniform sampling—demonstrating enhanced robustness and generalization. This work establishes a new paradigm for data-efficient, non-uniform-data-driven inverse design of high-performance metamaterials.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Search and Optimization: Metareasoning and Metaheuristics
• Data Mining & Knowledge Management: Linked Open Data, Knowledge Graphs & KB Completion

Application Category

• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

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.

Problem

• Optimizing lattice structures for mechanical performance efficiently
• Addressing biased data sampling in materials design with tensor completion
• Improving surrogate modeling accuracy over traditional machine learning methods

Innovation

• Tensor completion as surrogate model for materials design
• Handles biased sampling better than Gaussian Process methods
• Improves R-squared by 5% with non-uniform data sampling