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Self-learning mechanical circuits

Vishal P. Patil1,2,*, Ian Ho1,*, and Manu Prakash1,†

  • *These authors contributed equally to this work.
  • †Contact author: manup@stanford.edu
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Phys. Rev. E 114, 054211 – Published 9 November, 2026

DOI: https://doi.org/10.1103/23wf-kb12

Abstract

Adaptivity and learning are ubiquitous in living systems, from cytoplasm and biofilms to animal flocks. However, the problem of designing nonliving mechanical systems capable of self-learning behavior continues to present theoretical and experimental challenges. Here we introduce self-learning mechanical circuits: passive systems which take stochastic input forces from changing environments and constantly update their internal state in response, thus representing a mechanical unsupervised learning unit. Motivated by simplified models of synapses, our circuits are composed of adaptive directed springs, which change stiffness in a directional manner. We provide an experimental realization of these elastic learning units and demonstrate how stability arises from adaptivity in certain network architectures. In particular, we theoretically demonstrate the ability of a network to autonomously uncover patterns in external inputs. Our results have applications towards the design of adaptive materials that can self-optimize in different environments.

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Outline

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Phys. Rev. E 114, 054211– Published 9 November, 2026
  • Received 27 January 2024
  • Accepted 24 September 2026
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