在无序网络中设计精确的动态稳定状态

Marc Berneman, Daniel Hexner
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引用次数: 0

摘要

弹性结构的设计可以表现出精确、复杂和奇特的功能。最近的研究集中于受力平衡支配的准静态极限,而有限驱动速率下的力学则受牛顿排序的支配。这项工作的目标是研究在动力机制下创建具有奇异特性的无序结构的可行性、约束条件和影响。动力学机制提供了准静力学无法实现的响应,如任意相位响应、频率选择响应和历史依赖响应。我们利用时间反向传播和梯度下降来设计无序弹簧网络的特定空间稳态。我们发现,只需对结构进行微小的改变,就能实现在小振幅和大振幅下运行的多种稳定状态。我们研究了改变阻尼(在欠阻尼和过阻尼机制之间进行折衷)以及振幅、频率和相位的效果。我们发现,收敛取决于几种相互竞争的效应,包括混沌、大弛豫时间、有限时间模拟的梯度偏差和强衰减。通过研究线性化系统的特征模态,我们发现这些系统能很好地适应它们被训练执行的任务。我们的工作表明,在物理范围内,可以获得动态机制中的各种奇特行为,从而实现更丰富的应用。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Designing precise dynamical steady states in disordered networks
Elastic structures can be designed to exhibit precise, complex, and exotic functions. While recent work has focused on the quasistatic limit governed by force balance, the mechanics at a finite driving rate are governed by Newton's equations. The goal of this work is to study the feasibility, constraints, and implications of creating disordered structures with exotic properties in the dynamic regime. The dynamical regime offers responses that cannot be realized in quasistatics, such as responses at an arbitrary phase, frequency-selective responses, and history-dependent responses. We employ backpropagation through time and gradient descent to design spatially specific steady states in disordered spring networks. We find that a broad range of steady states can be achieved with small alterations to the structure, operating both at small and large amplitudes. We study the effect of varying the damping, which interpolates between the underdamped and the overdamped regime, as well as the amplitude, frequency, and phase. We show that convergence depends on several competing effects, including chaos, large relaxation times, a gradient bias due to finite time simulations, and strong attenuation. By studying the eigenmodes of the linearized system, we show that the systems adapt very specifically to the task they were trained to perform. Our work demonstrates that within physical bounds, a broad array of exotic behaviors in the dynamic regime can be obtained, allowing for a richer range of possible applications.
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