Design of volumetric sound metadiffusers using gradient-based optimization

Broadband volumetric sound diffusers are designed by using gradient-based optimization (GBO) by adjusting the position and radius of each scatterer in nonuniform configurations. The multiple scattering theory is employed to evaluate the diffusion coefficient by computing the scattered pressure field by nonuniform planar configurations of cylindrical scatterers for a monopole excitation. The analytical formulas for the gradients of the diffusion coefficient with respect to positions and radii of a cluster of cylindrical scatterers are derived which enhance the modeling when integrated with GBO and parallel computing. Sound volume metadiffusers with a high diffusion coefficient are designed by perturbatively rearranging the scatterer configurations. Single frequency and broad-octave-band optimizations are performed to maximize the diffusion coefficient while supplying analytical formulas for its gradients with respect to positions and radii. The GBO is implemented by direct optimization employing Multistart and fmincon solvers with sequential quadratic programming algorithms. The GBO approach is demonstrated providing numerical examples for nonuniform configurations of rigid cylinders embedded in the air environment. The polar plots for scattered pressure are evaluated for a wide range of ⅓ octave bands. The GBO approach can facilitate the automated metamaterial process by combining it with global optimization, generative modeling, and reinforcement learning.