Supervised learning in a mechanical system

TL;DR

This paper introduces a supervised learning framework for mechanical metamaterials, enabling a creased sheet to learn desired force-response behaviors from training examples and generalize to unseen forces by reshaping its energy landscape.

Contribution

It presents a novel learning rule for mechanical systems that adapts stiffness based on folding strain, allowing the material to learn and generalize force-response relationships.

Findings

The learning process reshapes the sheet's non-linear folding behavior.

Training error and test error depend on sheet size, indicating model complexity.

The framework effectively generalizes to unseen forces through iterative local learning.

Abstract

Mechanical metamaterials are usually designed to show desired responses to prescribed forces. In some applications, the desired force-response relationship might be hard to specify exactly, although examples of forces and corresponding desired responses are easily available. Here we propose a framework for supervised learning in a thin creased sheet that learns the desired force-response behavior from training examples of spatial force patterns and can then respond correctly to previously unseen test forces. During training, we fold the sheet using different training forces and assume a learning rule that changes stiffness of creases in response to their folding strain. We find that this learning process reshapes non-linearities inherent in folding a sheet so as to show the correct response for previously unseen test forces. We study the relationship between training error, test error and sheet size which plays the role of model complexity. Our framework shows how the complex energy landscape of disordered mechanical materials can be reshaped using an iterative local learning rule.