Data-driven investigation of analytical relationships in moiré structured materials

Moiré patterns, created by overlapping periodic structures, offer tunable structural properties, making them essential in fields like materials science and electronics. Their sensitivity to geometric parameters enables the design of advanced materials with specific functionalities. However, modeling the complex relationships between these parameters and material properties is challenging. Symbolic regression, a data-driven approach, addresses this by autonomously discovering mathematical expressions without predefined models, capturing intricate dependencies. This study employs an analytical formula development and then symbolic regression on simulated Moiré hexagonal patterns to model the relationship of shade coefficient, a parameter quantifying material coverage, with geometric variables, demonstrating the method's potential to enhance material design and understanding in complex geometries. The formula output by symbolic regression is validated with a test dataset and applied to real experimental images of layered nylon meshes. • Moiré patterns offer tunable material properties via geometric layering. • Symbolic regression models Moiré pattern shade coefficients from geometric data. • Outperforms traditional theoretical models in complex configurations. • Validated on unseen test data and real experimental images. • Enables interpretable, data-driven design of patterned materials.