Summary

Analyzing mechanical neural networks

Our project is based on the research conducted by Dr. Ryan H. Lee, Erwin A. B. Mulder and Dr. Jonathan B. Hopkins who authored the first pulication about this topic in 2022 (Lee, 2022). A mechanical neural network (MNN) is a metamaterial made up of many movable nodes connected by springs in a repeating pattern. In their research, Lee et al. arranged the springs in equilateral triangles and fixed the nodes at the very top and bottom.

Through adjustment of the spring constants, an MNN can be “taught” to exhibit one or more desired reactions to forces (behaviors). In the example below, a specified force (purple arrows) is applied to an MNN with random spring constants (left video) and the resulting deformation does not match the target (green circles). However, after optimizing the spring constants (right video), the deformation now better matches the target.

Almost any desired deformation is achievable with a sufficient number of springs, and the configurations reached trough optimization algorithms are oftentimes too complex to be understood or to have been manually created by humans – similar to the weights in large ANNs. This shows the power of MNNs as a new metamaterial, capable of achieving complex desired deformation behaviors that would have been difficult or impossible to reach through conventional design processes.

By optimizing towards multiple different behaviors at once, it is possible to find one fixed configuration of spring constants which achieves all desired reactions to forces simultaneously. Thus, the material itself can be made inherently “smart”. An example for a possible application would be plane wings that adjust their shape as needed in the current wind conditions. The important thing to note is that this “smart” adjustement would be an inherent property of the wing’s construction and wouldn’t use any control electronics or power – instead, it would simply be the result of creating an MNN with all the desired reactions to forces (deformations depending on wind strength and direction).

A small-scale example of this principle can be seen in the following two figures. First, we have a randomly created MNN and two different desired deformation behaviors. As expected, the equilibrium states reached by this MNN when the purple forces are applied do not match the green target positions.

After optimizing the spring constants using PPS, a single configuration of springs can be found which exhibits both desired reactions to forces at the same time. This can be seen in the pictures below: It is the same MNN in both (springs have the same colors, i.e. spring constants, in both).

Using springs adjustable in real-time additionally enables creating an intelligent material capable of learning and adjusting to damage and environmental changes. While the research on MNNs is new and still mostly theoretical, their applications could be wide and far-reaching – a single material used in anything from better wings to bridges and houses resisting natural disasters by adjusting their resonance frequencies.

In this project, we analyzed the optimization of MNNs towards desired deformation behaviors, especially concerning the effects of different hyperparameters. We also attempted the optimization of resonance curves, which had not yet been attempted in the reviewed literature. Not having found anything suitable, we developed our own software capable of visualizing and optimizing MNNs in simulations.

By programmatically testing various combinations of hyperparameters like network size, we qualitatively determined their effects, thus matching and expanding the results of existing research. Additionally, our successful optimization of the resonance curves of MNNs showed the potential this material to also react to oscillating forces as desired, not just constant ones.

Confirmation of our simulation-based new findings with a physical MNN is still required, and one optimization algorithm performed significantly worse than expected, necessitating further software development. But overall, we demonstrated the potential of MNNs to become the intelligent material of the future.

Further details

More details about this can be primarily found in our GitHub repository: Alexander-Reimer/Simulation-of-MNNs

Additionally, our project is represented

• in the project database of Jugend forscht (German STEM competition)
• on the 2025 virtual showcase for the Regneron International Science and Engineering Fair 2025
• on the Hannover Messe 2025, invited by the Federal Ministry of Education and Research

References

Ryan H. Lee et al., Mechanical neural networks: Architected materials that learn behaviors. Sci. Robot. 7, eabq7278 (2022). DOI: 10.1126/scirobotics.abq7278