Modeling the interpretable geometric-performance relationship of metamaterials on small datasets using Kolmogorov-Arnold operator informed network.

Deep learning has been extensively employed in the prediction of metamaterial properties. However, the multi-layer perceptron-kernelled methods lack interpretability and are highly dependent on large datasets, making the end-to-end mapping opaque and computationally expensive and hindering the exploration and application of physical mechanisms. To address these issues, the Kolmogorov-Arnold Operator Informed Network (KAOIN) method is proposed, achieving the lightest neural structure under small-sample conditions while improving accuracy and convergence speed. On this basis, a coupled metamaterial performance prediction framework is constructed, enabling dataset construction, high-fidelity analysis, and performance visualization. This framework is capable of predicting the specific energy absorption of the gradient triply-periodic minimal surface through a mere 50 sets of data. The interpretability and ability to extract physical laws of KAOIN were comprehensively verified through spatial symmetry and the Gibson-Ashby theoretical model. It has been demonstrated that a geometry-performance relationship improves accuracy by up to 44.6% and the convergence speed by 48-89%. This study introduces a novel neural network paradigm capable of exploring physical mechanisms in small datasets and demonstrates its potential for accurately modeling the geometric-performance relationships of metamaterials.