学习物理系统中的动力学行为
Learning dynamical behaviors in physical systems
AI总结：
本文将物理学习从静态属性扩展到极限环编码的动态行为，提出含时间延迟的学习规则与破缺时间反演对称性的训练示例，并通过乐高、粒子模拟和 Hopfield 模型验证可自组装、运动与变形的自适应系统。
摘要：
物理学习是科学与工程领域一种新兴范式，（超）材料通过接触示例而获得所需的宏观行为。迄今为止，它已被应用于静态属性，例如编码在能量图景极小值中的弹性模量和自组装结构。在这里，我们将这一范式扩展到动态功能，例如运动和形状变化，这些功能转而编码在动力学系统的极限环或路径中。我们确定了与实验平台无关、学习时间依赖行为所需的两个要素：（i）具有时间延迟的学习规则，以及（ii）在训练期间接触打破时间反演对称性的示例。在使用可编程乐高玩具对这些要求进行直观演示之后，我们转向现实的基于粒子的模拟，其中训练规则并非在计算机上编程。相反，我们阐明它们如何从涉及场的因果传播的物理化学过程中涌现，就像近期关于具有趋化信号的运动油滴实验那样。我们的可训练粒子能够自组装成可按需运动或改变形状的结构，既可以检索先前在训练期间见过的动态行为，也可以即时学习。这种丰富的现象学由一个适于解析处理的改进型 Hopfield 自旋模型刻画。这里阐明的原理为实现冯·诺依曼关于工程化构建可适应环境的合成生命系统的梦想迈出了一步。
英文摘要：
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.
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