  A promising technique for the spectral design of acoustic metamaterials is
based on the formulation of suitable constrained nonlinear optimization
problems. Unfortunately, the straightforward application of classical
gradient-based iterative optimization algorithms to the numerical solution of
such problems is typically highly demanding, due to the complexity of the
underlying physical models. Nevertheless, supervised machine learning
techniques can reduce such a computational effort, e.g., by replacing the
original objective functions of such optimization problems with more-easily
computable approximations. In this framework, the present article describes the
application of a related unsupervised machine learning technique, namely,
principal component analysis, to approximate the gradient of the objective
function of a band gap optimization problem for an acoustic metamaterial, with
the aim of making the successive application of a gradient-based iterative
optimization algorithm faster. Numerical results show the effectiveness of the
proposed method.
