Deep Convolutional Neural Networks for Eigenvalue Problems in Mechanics

Understand

We show that deep convolutional neural networks (CNN) can massively outperform traditional densely-connected neural networks (both deep or shallow) in predicting eigenvalue problems in mechanics.

• In this sense, we strike out in a new direction in mechanics computations with strongly predictive NNs whose success depends not only on architectures being deep, but also being fundamentally different from the widely-used to date.
• We consider a model problem: predicting the eigenvalues of 1-D and 2-D phononic crystals.
• For the 1-D case, the optimal CNN architecture reaches $98\%$ accuracy level on unseen data when trained with just 20,000 samples, compared to $85\%$ accuracy even with $100,000$ samples for the typical network of choice in mechanics research.