Supervised learning through physical changes in a mechanical system

Abstract

<jats:p>Mechanical metamaterials are usually designed to show desired responses to prescribed forces. In some applications, the desired force–response relationship is hard to specify exactly, but examples of forces and desired responses are easily available. Here, we propose a framework for supervised learning in thin, creased sheets that learn the desired force–response behavior by physically experiencing training examples and then, crucially, respond correctly (generalize) to previously unseen test forces. During training, we fold the sheet using training forces, prompting local crease stiffnesses to change in proportion to their experienced strain. We find that this learning process reshapes nonlinearities inherent in folding a sheet so as to show the correct response for previously unseen test forces. We show the relationship between training error, test error, and sheet size (model complexity) in learning sheets and compare them to counterparts in machine-learning algorithms. Our framework shows how the rugged energy landscape of disordered mechanical materials can be sculpted to show desired force–response behaviors by a local physical learning process.</jats:p>

Deep physical neural networks trained with backpropagation

“…Physics-aware training combines the scalability of backpropagation with the automatic mitigation of imperfections and noise achievable with in situ algorithms. Physical neural networks have the potential to perform machine learning faster and more energy-efficiently than conventional electronic processors and, more broadly, can endow physical systems with automatically designed physical functionalities, for example, for robotics 23 – 26 , materials 27 – 29 and smart sensors 30 – 32 .…”

Adaptable materials via retraining

“…The advantage of self-organization, is that it does not necessitate a direct manipulation of the micro-structure. Training can also be thought of as a physical realization of a learning rule [21,22].…”

Continual Learning of Multiple Memories in Mechanical Networks

“…Recent work has explored in situ supervised learning [46] in mechanical systems. Our work here is more akin to unsupervised learning (e.g., Hopfield models [23]); we leave continual learning in the supervised context and potential relationship to mechanical nonlinearities to future work.…”