Deep learning aided topology optimization of phononic crystals

Abstract

In this work, a novel approach for the topology optimization of phononic crystals based on the replacement of the computationally demanding traditional solvers for the calculation of dispersion diagrams with a surrogate deep learning (DL) model is proposed. We show that our trained DL model is ultrafast in the prediction of the dispersion diagrams, and therefore can be efficiently used in the optimization framework.The main novelty of the proposed approach relies on the use of non-uniform rational basis spline (NURBS) curves instead of pixels and/or mesh elements to control the shape of the unit cells of phononic crystals. The surrogate DL model is combined with a genetic algorithm serving as a topology optimization tool. The validity of the approach is shown in the case of phononic crystals made of a continuous matrix with cavities. Several objective functions have been tested as an alternative to the most common gap to mid-gap ratio. This allowed us to obtain interesting phononic crystal geometries which can be easily additively manufactured.The proposed method applies to problems involving inverse design and can open new avenues in the design of computer-assisted periodic structures.