# Gradient-based Design of Computational Granular Crystals

arXiv: https://arxiv.org/abs/2404.04825 · HTML: https://mlsanity.com/paper/2404.04825/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 57 references that are in the map.
- First posted on arXiv 7 Apr 2024.

## Builds on (most cited first, 10 of 10)

- [Deep physical neural networks enabled by a backpropagation algorithm for arbitrary physical systems](https://mlsanity.com/paper/2104.13386/) (2021)
- [Physical reservoir computing -- An introductory perspective](https://mlsanity.com/paper/2005.00992/) (2020)
- [Deep neural networks for the evaluation and design of photonic devices](https://mlsanity.com/paper/2007.00084/) (2020)
- [Wave Physics as an Analog Recurrent Neural Network](https://mlsanity.com/paper/1904.12831/) (2019)
- [Genetic algorithms are strong baselines for molecule generation](https://mlsanity.com/paper/2310.09267/) (2023)
- [There's Plenty of Room Right Here: Biological Systems as Evolved, Overloaded, Multi-scale Machines](https://mlsanity.com/paper/2212.10675/) (2022)
- [Scalable sim-to-real transfer of soft robot designs](https://mlsanity.com/paper/1911.10290/) (2019)
- [Optical Transformers](https://mlsanity.com/paper/2302.10360/) (2023)
- [Programming Soft Robots with Flexible Mechanical Metamaterials](https://mlsanity.com/paper/1906.00306/) (2019)
- [Universal Mechanical Polycomputation in Granular Matter](https://mlsanity.com/paper/2305.17872/) (2023)

## Abstract (arXiv)

There is growing interest in engineering unconventional computing devices that leverage the intrinsic dynamics of physical substrates to perform fast and energy-efficient computations. Granular metamaterials are one such substrate that has emerged as a promising platform for building wave-based information processing devices with the potential to integrate sensing, actuation, and computation. Their high-dimensional and nonlinear dynamics result in nontrivial and sometimes counter-intuitive wave responses that can be shaped by the material properties, geometry, and configuration of individual grains. Such highly tunable rich dynamics can be utilized for mechanical computing in special-purpose applications. However, there are currently no general frameworks for the inverse design of large-scale granular materials. Here, we build upon the similarity between the spatiotemporal dynamics of wave propagation in material and the computational dynamics of Recurrent Neural Networks to develop a gradient-based optimization framework for harmonically driven granular crystals. We showcase how our framework can be utilized to design basic logic gates where mechanical vibrations carry the information at predetermined frequencies. We compare our design methodology with classic gradient-free methods and find that our approach discovers higher-performing configurations with less computational effort. Our findings show that a gradient-based optimization method can greatly expand the design space of metamaterials and provide the opportunity to systematically traverse the parameter space to find materials with the desired functionalities.