MNN.jl

We (Matteo Friedrich and Alexander Reimer) are currently participating in Jugend forscht 2024 (a German youth science competition). For our project, we needed a library capable of simulating, optimizing and visualizing Mechanical Neural Networks (MNNs). Since we couldn't find one, we decided to develop and publish our own: MNN.jl. The source code is available in our GitHub repository.

What Are MNNs?

Mechanical Neural Networks (MNNs for short) are networks made of mass points connected by springs with variable spring constants. With a large enough network, a MNN can be trained to exhibit almost any behaviour desired by setting the spring constants appropiately. Importantly, they can be trained with multiple behaviours at once to exhibit different reactions depending on the "inputs" (forces acting on them). This makes them potentially useful for airplane wings which adjust theirs shape depending on the force and angle of the wind, body armor absorbing shock, better seat cushions or better wind turbine blades. Besides these examples of shape morphing behaviours, adjusting the resonance curves of MNNs is also possible and opens the door for applications like earthquake safe buildings, better music instruments, objects like walls capable of strengthening or weakening acoustic signals at will.

We based our research and knowledge of MNNs on the 2022 paper "Mechanical neural networks: Architected materials that learn behaviors" by Ryan H. Lee, Erwin A. B. Mulder and Jonathan B. Hopkins. They are, as far as we are aware, the first to describe such Mechanical Neural Networks.

Features of this library

• Simulation of MNNs
• Evaluating the performance of MNNs for shape morphing and resonance behaviour with MSE
• Optimizing the spring constants with Partial Pattern Search or an evolutionary algorithm

Our Research

For detailed papers (only in German), see the paper branch on GitHub. The most recent one available is from our participation at the state-level competition in Lower Saxony: paper.pdf

Summary

What We Did

• Both confirmed existing results and how representative our simulation is by analysing the correlation between different hyperparameters and training success, which mostly fit the existing research by Lee et al.
  • Unlike Lee et al., we used the optimization algorithms applicable to physical MNNs like Partial Pattern Search and/or evolutionary algorithms instead of a gradient descent based approach
• Successfully optimized the resonance curve of MNNs; we believe to be the first to do this, as we couldn't find anything else available online

What We Didn't Do (Yet)

• Build our own MNN mechanically
• Build a ressource intensive, physically accurate simulation
  • the goal is to provide starting points for the optimization of real MNNs and figure out the effects of parameters & different optimization algorithms
  • specifically, we haven't (yet) incorparated checking spring and neuron position limits, meaning that using very large input forces / goal position vectors can result in mass points and springs phasing through each other

Project Summary (German)

Wir haben uns mit dem neuen Bereich der mechanical neural networks (MNNs) beschäftigt - programmierbare Materialien, die aus mit Federn verbundenen Massenpunkten bestehen. Ihnen können durch Anpassung der Federhärten verschiedene Verhaltensweisen gleichzeitig antrainiert werden, was viele Anwendungsmöglichkeiten eröffnet, wie z.B. Flugzeugflügel, deren Form sich optimal an Windgeschwindigkeit und -richtung anpasst. In unserem Projekt haben wir die Trainingsverfahren und den Einfluss verschiedener Parameter analysiert und dafür in einer eigenen Softwarebibliothek die Simulation, Optimierung, Bewertung und Visualisierung von MNNs umgesetzt. Außerdem haben wir als Erste erfolgreich die Resonanzkurven von MNNs optimiert, was auch den Einsatz für z.B. erdbebensichere Strukturen ermöglicht. Die von uns erkannten Einflüsse von Parametern decken sich, wo vorhanden, mit der bisherigen Forschung.