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Transports and sound absorption performance of foam-based absorbers are influenced by the morphologies of their pore connections. Understanding the microstructure–property relationships of sound absorbers can provide valuable insights and guidance for designing and manufacturing steps. We develop in this paper surrogate models based on the polynomial chaos expansion to predict the acoustic behavior of graded foam absorbers. Regarding the local morphology of foams, three representative factors including the porosity, the cell size, and the membrane closure ratio are considered through a periodic unit cell. Then, the reference maps of transport properties are computed via the hybrid numerical method based on the homogenization technique, surrogates are consequently generated in the designing space involving the morphology features. Finally, after evaluating their convergence characteristics and verification study, the surrogate models are adopted to study foam layers within different graded characteristics. Within a tolerance error, the surrogate models of transport properties offer advantages in terms of the computational efficiency and predictability. Both surrogate model-based investigation and optimization frameworks allow estimating the local morphology factors where the desired sound absorption properties of the graded foam absorbers can be achieved. [ABSTRACT FROM AUTHOR]