Efficient metamodeling of acoustic metasurfaces with variable sized design domains

Traditional approaches to numerically model acoustic metasurfaces (AMS) with deeply subwavelength features require tremendous computational expense. Metamodels created using machine learning (ML) methods are promising techniques to efficiently and accurately model macroscopic AMS behavior while considering subwavelength features. However, many ML methods require a fixed quantity of design features so that ML model input dimensionality is constant. This work presents a metamodeling approach that is valid for metamaterial systems whose design domain has variable input feature dimensionalities. An example is an AMS consisting of variable numbers of cells, each with potentially unique geometry. We achieve improved modeling efficiency by representing design feature connectivity as an attributed graph and training a neural network (NN)-based model to operate on the attributes of graph elements. The metamodel is trained to update each attribute from state-to-state in a dynamic process. This NN architecture enables a single model to represent the behavior of an asymmetrically absorbing AMS composed of variable numbers of cells and nonperiodic geometry. The NN architecture can therefore be trained on data that includes a large proportion of systems with a small domain size but that is generalized to predict performance for larger systems that require greater computational expense for analysis.