Design and learning in multi-stable mechanical networks

Systems with multiple stable states have proven essential in biological and engineering contexts to show multiple functions, store memories and so on. In this work we contrast two paradigms for creating systems with specific stable states in elastic mechanical networks: design and learning. In the design framework, all desired stable states are known in advance and thus material parameters can be optimized on a computer. In contrast, our learning framework considers sequential introduction of desired stable states so that material parameters must be incrementally updated to stabilize each additional state. We show that designed states are optimally stable within elastic networks with Hookean springs. However, incremental learning requires springs with strong non-linearity. We interpret such non-linearity as biasing the distribution of strain in these elastic networks to be localized in a sparse subset of springs, much like a Bayesian prior in sparse regression. In this way, we identify principles for practical implementations of learned multi-stability.