Periodic structured materials, constructed by tessellating identical unit cells in arrays, can be designed to exhibit unique and useful elastic wave propagation behavior (e.g. reflection, lensing, wave guiding). The propagation of waves in a periodic structured material is described by its dispersion relation, a function relating a wave’s frequency to its wavevector. However, the evaluation of dispersion relations, particularly in higher dimensions, is computationally expensive.
To alleviate this cost, we demonstrate that Gaussian process regression can be used as a surrogate model in the computation of dispersion relations of periodic structured materials.
In contrast to existing neural network based surrogate models for dispersion computations, our approach requires very little training data, has a dynamically tunable accuracy-cost balance, and can be applied to material designs of any representation (pixelated, parametric, etc.). Additionally, our model can make dispersion predictions at infinite resolution, and can efficiently be used in gradient based topology optimization.