Learning dynamical behaviors in physical systems

TL;DR

This paper extends physical learning paradigms to dynamic behaviors like motion and shape change, demonstrating how to encode and train such behaviors in physical systems through specific learning rules and symmetry-breaking examples.

Contribution

It introduces a framework for learning time-dependent behaviors in physical systems, including programmable particles and simulations, using delayed learning rules and symmetry-breaking training.

Findings

Particles can learn and reproduce dynamic behaviors like movement and shape change.

Training rules emerge from physico-chemical processes, not just computer programming.

A modified Hopfield model captures the phenomenology of dynamic learning in physical systems.

Abstract

Physical learning is an emerging paradigm in science and engineering whereby (meta)materials acquire desired macroscopic behaviors by exposure to examples. So far, it has been applied to static properties such as elastic moduli and self-assembled structures encoded in minima of an energy landscape. Here, we extend this paradigm to dynamic functionalities, such as motion and shape change, that are instead encoded in limit cycles or pathways of a dynamical system. We identify the two ingredients needed to learn time-dependent behaviors irrespective of experimental platforms: (i) learning rules with time delays and (ii) exposure to examples that break time-reversal symmetry during training. After providing a hands-on demonstration of these requirements using programmable LEGO toys, we turn to realistic particle-based simulations where the training rules are not programmed on a computer. Instead, we elucidate how they emerge from physico-chemical processes involving the causal propagation of fields, like in recent experiments on moving oil droplets with chemotactic signalling. Our trainable particles can self-assemble into structures that move or change shape on demand, either by retrieving the dynamic behavior previously seen during training, or by learning on the fly. This rich phenomenology is captured by a modified Hopfield spin model amenable to analytical treatment. The principles illustrated here provide a step towards von Neumann's dream of engineering synthetic living systems that adapt to the environment.