Conventional methods used to identify the dynamical properties of unknown media from scattered mechanical waves rely on analytical or numerical manipulations of the wave equation. These methods show their limitations in scenarios where the analyzed medium is moderately sized and the diffraction from the material edges influences the scattered fields significantly (e.g., non-destructive diagnostics, metamaterial characterization). This work shows that convolutional neural networks can interpret the diffracted fields and learn the mapping between the scattered fields and all the effective material parameters including mass density and stiffness tensors from a small set of numerical simulations. Furthermore, networks trained with synthetic data can process physical measurements and is very robust to measurement errors. More importantly, the trained network provides insight into the dynamic behavior of matter including quantitative measures of the scattered field sensitivity to each material property and how the sensitivity changes depending on the material under test.