Module 1

Boosted Decision Trees for the Discovery of Structural Patterns Controlling Bandgaps in Architected Metamaterials

(Cate Brinson, Cynthia Rudin)

In this module, we will explore a MetaMaterial case study using boosted decision trees to discover structural features responsible for band gaps in patterned metamaterials. Students will first learn the basic physics of mechanical metamaterials with an understanding of aspects such as negative poison ratio and elastic wave band gaps. Students will then run an existing bandgap prediction code on all possible unit cell configurations of a given size to determine the bandgap frequencies and widths. The order 105 structures will then be analyzed using decision tree and random forest methods, enabling classification of fundamental structure types leading to a given bandgap range. Students will also explore standard forms of neural networks for computer vision and interrogate underlying reasons that they may not be effectively used in this kind of case. Students will also learn about state-of-the-art methods for dimension reduction, which allows them to potentially see patterns in high-dimensional data that are difficult to see in other ways, and they will learn to critically evaluate the results of such methods. A homework assignment will apply neural network models with and without features and demonstrate the change in predictability. 

Learning objectives: 

1. Students will be able to describe the fundamentals of mechanical metamaterials and the physical meaning of a mechanical band gap; 

2. Students will be able to apply black box and interpretable machine learning models to identify and predict structural patterns related to band gaps. 

3. Students will be able to visualize data using state-of-the-art dimension reduction techniques.