# Learned multi-stability in mechanical networks

## TL;DR

This paper explores how elastic networks can be designed or physically learned to have multiple stable states, revealing that non-linear elasticity is essential for sequential learning and stability of desired configurations.

## Contribution

It introduces a framework contrasting material design and physical learning, showing non-linear elasticity enables sequential learning of multiple stable states in mechanical networks.

## Key findings

- Linear networks stabilize designed states.
- Non-linear elasticity stabilizes states with mixed strains.
- Material properties enable continuous learning of new functions.

## Abstract

We contrast the distinct frameworks of materials design and physical learning in creating elastic networks with desired stable states. In design, the desired states are specified in advance and material parameters can be optimized on a computer with this knowledge. In learning, the material physically experiences the desired stable states in sequence, changing the material so as to stabilize each additional state. We show that while designed states are stable in networks of linear Hookean springs, sequential learning requires specific non-linear elasticity. We find that such non-linearity stabilizes states in which strain is zero in some springs and large in others, thus playing the role of Bayesian priors used in sparse statistical regression. Our model shows how specific material properties allow continuous learning of new functions through deployment of the material itself.