Given a 3D piece of origami, can you flatten it without damaging it? Just by looking at the plan, the answer is difficult to predict, because every fold in the plan must be compatible with flattening. This is an example of a combinatorial problem. New research conducted by the UvA Institute of Physics and research institute AMOLF has demonstrated that machine learning algorithms can accurately and efficiently answer these kinds of questions. This is expected to give a boost to the artificial intelligence-assisted design of complex and functional (meta)materials.
In their latest work, published in Physical Review Letter This week, the research team tested how well artificial intelligence (AI) can predict the properties of so-called combinatorial mechanical metamaterials.
These are engineered materials whose properties are determined by their geometric structure rather than their chemical composition. A piece of origami is also a type of metamaterial, whose ability to flatten (a physically well-defined property) is determined by how it is folded (its structure), rather than by the type of paper it is made of. More generally, smart design allows us to control exactly where or how a metamaterial will bend, buckle or bulge, which could be used for all sorts of things, from shock absorbers to unfolding solar panels on a satellite in space.
A typical combinatorial metamaterial studied in the laboratory is constructed from two or more types or orientations of building blocks, which deform in different ways when a mechanical force is applied. If the building blocks are combined randomly, the material as a whole will usually not buckle under pressure because not all blocks will be able to deform as they want to; They will jam. Where one building block wants to balance outside, its neighbor should be able to squeeze inside. In order for the metamaterial to buckle easily, all the deformed building blocks need to fit together like a puzzle. Just as changing a single fold can make a piece of origami uninflatable, changing a single block can make a ‘floppy’ metamaterial rigid.
Hard to predict
Although metamaterials have many potential applications, designing a new one is challenging. Starting with a particular set of building blocks, deducing the overall metamaterial properties for different structures often boils down to trial and error. In this day and age, we don’t want to do it all by hand. However, because the properties of combinatorial metamaterials are so sensitive to changes in individual building blocks, conventional statistical and numerical methods are slow and prone to mistakes.
Instead, the researchers found that machine learning could be the answer: even when given only a relatively small set of examples to learn from, so-called convolutional neural networks can accurately predict the metamaterial properties of any configuration of building blocks down to the finest detail.
“This far exceeded our expectations,” says PhD student and first author Ryan van Mastrigt. “The accuracy of these predictions shows us that the neural networks have actually learned the mathematical rules underlying the metamaterial properties, even when we don’t know all the rules ourselves.”
This finding suggests that we can use AI to design new complex metamaterials with useful properties. More broadly, applying neural networks to combinatorial problems allows us to pose many exciting questions. Perhaps they can help us in solving (combinatorial) problems in other contexts. And conversely, the findings can improve our understanding of neural networks themselves, by for example demonstrating how the complexity of a neural network is related to the complexity of the problems it can solve.
Materials provided by University of Amsterdam. Note: Content may be edited for style and length.