Using U-Net to Estimate Fluid Flow in Mechanical Metamaterials

Mechanical metamaterials are artificial materials whose inner structure can be designed to give the material specific properties. However, to adjust these properties for a specific application, the inner topology of the metamaterial has to be optimized, which may become extremely costly, especially when a flow inside the topology is to be modeled. Our aim is to utilize artificial neural networks to estimate the flow inside the metamaterial and thus provide a cheaper surrogate model for optimization. In particular, we are using a U-Net-style convolutional neural network to estimate the pressure and velocity field based on a given inner topology. To encode the inner topology, we utilize the immersed boundary method, which is also used to compute data for training of the networks. We have investigated the effect of three hyperparameters on the U-Net training process, as well as the effect of the number of samples and input topology resolution. Eventually, the tuned U-Nets were used to estimate flow in previously unseen topologies with varying resolution and achieved promising results.