Mechanical metamaterials are sophisticated man-made structures whose mechanical properties depend on their structure rather than their composition. Although these structures have shown great promise for the development of new technologies, their design can be both difficult and time-consuming.
Researchers from the University of Amsterdam, AMOLF and Utrecht University recently demonstrated the potential of convolutional neural networks (CNNs), a class of machine learning algorithms, for the design of complex mechanical metamaterials. Their article, published in Physical examination lettersSpecifically introduces two different CNN-based methods that can derive and capture the subtle combinatorial rules that underlie the design of mechanical metamaterials.
“Our recent study can be seen as a continuation of the combinatorial design approach introduced in a previous paper, which can be applied to more complex building blocks,” said Ryan van Mastrigt, one of the researchers who conducted the study, at Phys.org. “Around the time I started working on this study, Aleksi Bossart and David Dykstra were working on a combinatorial metamaterial capable of hosting multiple features, i.e. a material that can deform by multiple distinct ways depending on how it is operated.”
In their previous research, van Mastrigt and his colleagues attempted to distill the rules that underlie the successful design of complex metamaterials. They soon realized that this was no easy task, as the “building blocks” that make up these structures can be deformed and arranged in countless different ways.
Previous studies have shown that when metamaterials have small unit cell sizes (i.e. a limited amount of “building blocks”), it is possible to simulate all the ways these blocks can be deformed and laid out using conventional physical simulation tools. However, as these unit cell sizes become larger, the task becomes extremely difficult, if not impossible.
“Because we were unable to reason about the underlying design rules and conventional tools did not allow us to effectively explore larger unit cell designs, we decided to consider machine learning. automatic as a serious option,” explained van Mastrigt. “So the main goal of our study became to identify a machine learning tool that would allow us to explore the design space much faster than before. I think we have succeeded and even exceeded our own expectations with our findings.”
To successfully train CNNs to design complex metamaterials, van Mastrigt and his colleagues first had to overcome a series of challenges. First, they needed to find a way to effectively represent their metamaterial designs.
“We tried a few approaches and ultimately settled on what we call pixel representation,” van Mastrigt explained. “This representation encodes the orientation of each building block in a clear visual way, so the classification problem is turned into a visual pattern detection problem, which is exactly what CNNs are good at.”
Subsequently, the researchers had to devise methods that took into account the enormous imbalance of the classes of metamaterials. In other words, since there are currently many known metamaterials that belong to class I, but far fewer belong to class C (the class of interest to researchers), training CNNs to infer combinatorial rules for these different classes could involve different steps.
To address this challenge, van Mastrigt and his colleagues devised two different techniques based on CNN. These two techniques are applicable to different classes of metamaterials and classification problems.
“In the case of the M2 metamaterial, we tried to create a balanced classroom training set,” van Mastrigt said. “We did this by using naïve subsampling (i.e. throwing away a lot of class I examples) and combining it with symmetries that we know some designs have, such as symmetry of translation and rotation, to create additional C-class designs.
“Therefore, this approach requires some domain knowledge. For the M1 metamaterial, on the other hand, we added a reweighting term to the loss function such that the rare C-class designs weigh more when trained, where the key idea is that this class C reweighting cancels out with the much larger number of class I designs in the training set.This approach requires no domain knowledge.
In the first tests, these two CNN-based methods for deriving the combinatorial rules behind the design of mechanical metamaterials obtained very promising results. The team found that they each performed better on different tasks, depending on the initial dataset used and known (or unknown) design symmetries.
“We have shown how extraordinarily efficient these networks are in solving complex combinatorial problems,” van Mastrigt said. “It was really surprising to us, because all the other conventional (statistical) tools that we physicists commonly use fail for these kinds of problems. We showed that neural networks really do more than interpolate space design based on the examples you give them, because they seem kind of biased to find structure (that comes from the rules) in this design space that generalizes extremely well.”
The recent findings collected by this team of researchers could have far-reaching implications for the design of metamaterials. While the networks they trained have so far been applied to a few metamaterial structures, they could also be used to create much more complex designs, which would be incredibly difficult to tackle using simulation tools. conventional physics.
The work of van Mastrigt and his colleagues also highlights the enormous value of CNNs for solving combinatorial problems, optimization tasks that involve composing an “optimal object” or deriving an “optimal solution” that satisfies all the constraints of an ensemble, in cases where there are many variables at play. As combinatorial problems are common in many scientific fields, this article could promote the use of CNNs in other research and development contexts.
The researchers showed that while machine learning is generally a “black box” approach (i.e. it does not always allow researchers to visualize the processes behind a given prediction or outcome), it can still be very useful for exploring the design space of metamaterials. , and possibly other materials, objects or chemical substances. This in turn could potentially help to reason and better understand the complex rules that underlie effective designs.
“In our next studies, we will pay attention to the reverse design,” added van Mastrigt. “The current tool already helps us enormously in reducing the design space to find suitable designs (class C), but it does not find us the best design for the task we have in mind. We are now considering methods of machine learning that will help us find extremely rare designs that have the properties we want, ideally even when no examples of such designs are shown to the machine learning method beforehand.
“It’s a very difficult problem, but after our recent study, we believe that neural networks will allow us to solve it successfully.”
Ryan van Mastrigt et al, Machine learning of implicit combinatorial rules in mechanical metamaterials, Physical examination letters (2022). DOI: 10.1103/PhysRevLett.129.198003
Corentin Coulais et al, Combinatorial design of textured mechanical metamaterials, Nature (2016). DOI: 10.1038/nature18960
Anne S. Meeussen et al, Topological defects produce exotic mechanics in complex metamaterials, Natural Physics (2020). DOI: 10.1038/s41567-019-0763-6
Aleksi Bossart et al, Oligomodal metamaterials with multifunctional mechanics, Proceedings of the National Academy of Sciences (2021). DOI: 10.1073/pnas.2018610118
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