# Data for Inverse Design of Hierarchically Wrinkled Microstructures Using Machine Learning

## Description

This dataset presents the raw and pre-processed data that were used to train the machine learning (ML) models for regression analysis of hierarchical wrinkling. Hierarchical wrinkling is a physical phenomenon wherein complex 3D sinusoidal structures are generated upon compression of a pre-patterned bilayer. It is further described in this article: “S.K. Saha and M.L. Culpepper, Deterministic Switching of Hierarchy during Wrinkling in Quasi‐Planar Bilayers. Advanced Engineering Materials, 2016. 18(6): p. 938-943.” This specific dataset refers to the case wherein a two-period hierarchical wrinkle is formed upon compression of a bilayer which is pre-patterned with a single-period sinusoidal pattern. The outputs collectively represent the shape of the hierarchical wrinkles whereas the inputs represent the parameters that can be varied in the physical bilayer systems. Each datapoint comprises a set of four inputs (i.e., attributes) and six outputs (i.e., targets) corresponding to these inputs. The inputs are: applied compressive strain (ε), amplitude of pre-pattern (Ap), normalized period of pre-pattern (λp/λn), and natural period (λn). The outputs are: amplitude of 1st mode (A1), amplitude of 2nd mode (A2), normalized period of 1st mode (λ1/λn), normalized period of 2nd mode (λ2/λn), phase angle of 1st mode (φ1/π), and phase angle of 2nd mode (φ2/π). The raw data refers to the data generated from finite element simulations of wrinkling as-is without any modifications. The pre-processed data was obtained from the raw data by: (i) converting all values of λ2/λn and φ2 to NaN for those cases where A2 ≤ 10 nm and (ii) rounding off φ2/π to the 2nd decimal place. The ML models were trained on the pre-processed data. The attribute λn was not used for training of the ML models. The shape of the hierarchical wrinkle (i.e., Y vs X profile) is given by: Y=A1 cos(2πX/λ1 + φ1 ) + A2 cos(2πX/λ2 + φ2 )

## Files

## Steps to reproduce

The variables ε, Ap, λp/λn, were user-controlled inputs to the finite element simulations of hierarchical wrinkling whereas the variable λn was evaluated from linear buckling analysis of wrinkling of the corresponding flat bilayer. The steps for hierarchical wrinkling and linear buckling analysis are described in this article: “S.K. Saha and M.L. Culpepper, Deterministic Switching of Hierarchy during Wrinkling in Quasi‐Planar Bilayers. Advanced Engineering Materials, 2016. 18(6): p. 938-943.” All six output variables were obtained from Fast Fourier Transform (FFT) analysis of the deformed X-Y profile of the midplane of the top thin film layer. The finite element simulations were performed in COMSOL 5.4 software package and the FFT analysis was performed in the MATLAB software package.