# Neuromechanical Autoencoders: Learning to Couple Elastic and Neural Network Nonlinearity

arXiv: https://arxiv.org/abs/2302.00032 · HTML: https://mlsanity.com/paper/2302.00032/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 34 references that are in the map.
- First posted on arXiv 31 Jan 2023.

## Builds on (most cited first, 5 of 5)

- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [DiffTaichi: Differentiable Programming for Physical Simulation](https://mlsanity.com/paper/1910.00935/) (2019)
- [Embodied Intelligence via Learning and Evolution](https://mlsanity.com/paper/2102.02202/) (2021)
- [Learning Composable Energy Surrogates for PDE Order Reduction](https://mlsanity.com/paper/2005.06549/) (2020)
- [Additive manufacturing process design with differentiable simulations](https://mlsanity.com/paper/2107.10919/) (2021)

## Built on by (most cited first, 1 of 1)

- [Efficiently Vectorized MCMC on Modern Accelerators](https://mlsanity.com/paper/2503.17405/) (2025)

## Abstract (arXiv)

Intelligent biological systems are characterized by their embodiment in a complex environment and the intimate interplay between their nervous systems and the nonlinear mechanical properties of their bodies. This coordination, in which the dynamics of the motor system co-evolved to reduce the computational burden on the brain, is referred to as ``mechanical intelligence'' or ``morphological computation''. In this work, we seek to develop machine learning analogs of this process, in which we jointly learn the morphology of complex nonlinear elastic solids along with a deep neural network to control it. By using a specialized differentiable simulator of elastic mechanics coupled to conventional deep learning architectures -- which we refer to as neuromechanical autoencoders -- we are able to learn to perform morphological computation via gradient descent. Key to our approach is the use of mechanical metamaterials -- cellular solids, in particular -- as the morphological substrate. Just as deep neural networks provide flexible and massively-parametric function approximators for perceptual and control tasks, cellular solid metamaterials are promising as a rich and learnable space for approximating a variety of actuation tasks. In this work we take advantage of these complementary computational concepts to co-design materials and neural network controls to achieve nonintuitive mechanical behavior. We demonstrate in simulation how it is possible to achieve translation, rotation, and shape matching, as well as a ``digital MNIST'' task. We additionally manufacture and evaluate one of the designs to verify its real-world behavior.