  This paper is concerned with the use of polynomial metamodels for the design
of acoustical materials, considered as equivalent fluids. Polynomial series in
microstructural parameters are considered, and allow us to approximate the
multiscale solution map in some well-defined sense. The relevance of the
framework is illustrated by considering the prediction of the sound absorption
coefficient. In accordance with theoretical results provided elsewhere in the
literature, it is shown that the surrogate model can accurately approximate the
solution map at a reasonable computational cost, depending on the dimension of
the input parameter space. Microstructural and process optimization by design
are two envisioned applications.
