Training precise stress patterns

TL;DR

This paper presents a novel training rule for spring-and-dashpot networks to learn precise stress patterns, enabling control over target bonds and demonstrating convergence even with complex constraints and yielding stresses.

Contribution

The authors introduce a new training method for mechanical networks that achieves high-precision stress pattern learning and explores the effects of target selection and yielding stresses.

Findings

Error converges to computer precision with single target bonds per node.

Multiple targets per node can slow convergence or cause failure.

Training with yielding stresses enables permanent memory encoding.

Abstract

We introduce a training rule that enables a network composed of springs and dashpots to learn precise stress patterns. Our goal is to control the tensions on a fraction of "target" bonds, which are chosen randomly. The system is trained by applying stresses to the target bonds, causing the remaining bonds, which act as the learning degrees of freedom, to evolve. Different criteria for selecting the target bonds affects whether frustration is present. When there is at most a single target bond per node the error converges to computer precision. Additional targets on a single node may lead to slow convergence and failure. Nonetheless, training is successful even when approaching the limit predicted by the Maxwell Calladine theorem. We demonstrate the generality of these ideas by considering dashpots with yield stresses. We show that training converges, albeit with a slower, power-law decay of the error. Furthermore, dashpots with yielding stresses prevent the system from relaxing after training, enabling to encode permanent memories.