Learning in Physical Networks: From Machine Learning to Learning Machines*

Materials and machines are often designed with particular goals in mind, so that they exhibit desired responses to given forces or constraints. Here we explore an alternative approach, namely physical learning. In this paradigm, the network physically adapts to applied forces, obtaining a desired function. Crucially, learning is facilitated by physically plausible learning rules, requiring only local responses and no explicit information about the desired functionality.
We show that such local learning rules can be derived for any physical network, whether in equilibrium or in steady-state. We specifically study several such systems: disordered flow networks, elastic networks, and self-folding sheets. We demonstrate how physical systems can learn to distinguish between classes in real data such as Iris flowers and handwritten digits. Finally, we discuss experimental considerations regarding the realization of learning machines in actual networks. By exploiting the advances of statistical learning theory in the real world, we propose the plausibility of new classes of smart metamaterials, adapting in-situ to users' needs.