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.

机械超材料通常被设计为显示对规定力的期望响应。在某些应用中，很难精确地确定所需的力-响应关系，但是可以轻松获得力和所需的响应示例。在这里，我们提出了一个薄薄的，有监督的学习框架，该框架通过实际体验训练示例来学习所需的力响应行为，然后至关重要地正确地（概括）对以前看不见的测试力进行响应。在训练过程中，我们使用训练力折叠床单，促使局部折痕刚度根据其承受的应变而变化。我们发现，这种学习过程重塑了折叠纸张时固有的非线性，从而显示了对以前看不见的测试力的正确响应。我们展示训练误差之间的关系，在学习表中测试错误和表大小（模型复杂性），并将其与机器学习算法中的对应表进行比较。我们的框架展示了如何通过局部物理学习过程来雕刻无序机械材料的崎energy能量格局，以显示所需的力-响应行为。