Higher-order factorization machine for accurate surrogate modeling in material design

Efficient and robust optimization is important in material science for identifying optimal structural parameters and enhancing material performance. Surrogate-based active learning algorithms have recently gained great attention for their ability to efficiently navigate large, high-dimensional design spaces. Among surrogate models, 2^nd-order factorization machine (FM) models are widely employed as the surrogate model in active learning algorithms due to their balance between simplicity and effectiveness. However, their quadratic nature limits their capacity to capture complex, higher-order interactions among variables, often leading to suboptimal solutions. To overcome this limitation, we propose an active learning scheme integrating a 3^rd-order FM model, capable of modeling three-variable interactions and more intricate relationships in material systems. We comprehensively evaluate the surrogate modeling performance of the 3^rd-order FM case using various objective functions. Furthermore, we examine the optimization reliability and efficiency of the 3^rd-order FM-based active learning in a real-world material design task (e.g., nanophotonic structures for transparent radiative cooling). Our study shows that the 3^rd-order FM outperforms the 2^nd-order model in both surrogate accuracy and optimization performance, highlighting higher-order models' promises for material design and optimization problems.