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Designing complex architectured materials with generative adversarial networks

Xuanhe Zhao's picture

Designing complex architectured materials with generative adversarial networks

Yunwei Mao, Qi He, Xuanhe Zhao

Architectured materials on length scales from nanometers to meters are desirable for diverse applications. Recent advances in additive manufacturing have made mass production of complex architectured materials technologically and economically feasible. Existing architecture design approaches such as bioinspiration, Edisonian, and optimization, however, generally rely on experienced designers’ prior knowledge, limiting broad applications of architectured materials. Particularly challenging is designing architectured materials with extreme properties, such as the Hashin-Shtrikman upper bounds on isotropic elasticity in an experience-free manner without prior knowledge. Here, we present an experience-free and systematic approach for the design of complex architectured materials with generative adversarial networks. The networks are trained using simulation data from millions of randomly generated architectures categorized based on different crystallographic symmetries. We demonstrate modeling and experimental results of more than 400 two-dimensional architectures that approach the Hashin-Shtrikman upper bounds on isotropic elastic stiffness with porosities from 0.05 to 0.75.

Science Advances  24 Apr 2020:
Vol. 6, no. 17, eaaz4169
DOI: 10.1126/sciadv.aaz4169



Dear Xuanhe,

1. Interesting! A great deal of work seems to have gone into it!!

2. I mostly skipped on the materials/mechanics side (the topic isn't familiar to me). However, there is a bit of an oddity which I spotted on the neural networks' side.

3. For the discriminator, your first and second convolutional layers have the kernel size of 4 X 4. Using an even number for the kernel seemed a bit odd to me!

If you use even numbers for the kernel size, it leads to asymmetric kernels. These can potentially introduce aliasing effects. (For some explanation, see, for instance, this Q&A at the Data Science StackExchange [^].)

Within the odd-sized kernels, for general-purpose image recognition (say CIFAR and all), it seems that the recent trend is to go in for deeper architectures and smaller kernels, like 3 X 3 or 5 X 5.

So, it might be worth running a few trials with such odd-sized kernels.

4. Another point. If your initial convolutional and pooling operations go on reducing the image size in such a way that your last Conv layer happens to have a 4 X 4 input size, then it's OK to go in for a 4 X 4 kernel too. Such a Conv layer is going to produce just 1 pixel, and so, the considerations of symmetry vs. asymmetry cease to apply. I don't know for sure, but I do think that symmetry and all should be important only if another Conv layer is going follow a given Conv layer.

5. But yes, all in all, highly inter-disciplinary, nah, multi-disciplinary work. I appreciate it.



PS: Can't resist! A fun thought occurred to me. Why not try Penrose tiles and see if anything interesting gets thrown up---whether during the learning phase or for the predictions---or for properties (Schachtman)? ... Just an idle musing...


Dear Ajit,


Thanks for your comments! Great points. The hyperparameters of the convolutional neural networks are highly dependent on the designers. The main point here is to illustrate GAN's idea in architectured materials' design instead of benchmark for machine learning performance. For our case, the even kernel size works well, and aliasing effects did not happen. However, we do believe that it would achieve a better result with a more complex network, i.e., symmetric kernels, VGGNet, ResNet-50, or even ResNeXt. We will try them in our future works to see whether there are any differences. Thank you for your advice. The methodology here is general and applicable to other properties. 




Dear Qi,

Thanks for your reply.

Following the best-practices advice, so far, I had always used the odd-sized kernels---except for the last layer (which fact I had figured out on my own). For yet another reference, I in the meanwhile recollected what Dr. Adrian Rosebrock said here [^].

That's why, it was a bit interesting to note that you didn't actually see aliasing effects.

To figure out why, I decided to take a fresh look at the maths involved.

Looks like, contrary to the received opinion, as far as the strictly sequential models go, the difference between the odd- vs. even-sized kernels should not make a substantial difference, provided that the number of convolutional parameters stay comparable (between purely convolutional models employing odd- vs. even-sized kernels). That's what the maths seems to say. In the strictly sequential models of machine learning, the issue of symmetry vs. asymmtry should not arise. Of course, I haven't put this implication to an empirical test yet. (No time at hand.) But it does seem to justify what you say, though, of course, this again is a justification after the fact!

What about the non-sequential models like those with, say, the skip-connections? (Or, even just with concatenating layers?) Here, the rough-and-ready maths suggests that the odd-sized (symmetrical) kernels should learn better than the even-sized ones, provided that the image size stays the same. To what extent should the learning be better? The rough-and-ready maths offers no rough-and-ready answer! But a good hypothesis, this one should make for. Of course, once again, empirical evidence is required. (There was no reason why 'ReLU's should have worked better than the tanh or the sigmoid, until they figured it out how it actually works! That is, after the fact!) Hope some UG/PG student of CS decides to take a systematic look at it.

Anyway, this has been a definitely useful discussion for me. Threw light on something I had not separately looked into. So, thanks for sharing your observations and all.


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