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Abstract 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, such as non-destructive diagnostics and metamaterial characterization. Here, we show 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 are 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. 

Identifying the material properties of unknown media is an important scientific/engineering challenge in areas as varied as in-vivo tissue health diagnostics and metamaterial characterization. Currently, techniques exist to retrieve the material parameters of large unknown media from elastic wave scattering in free-space using analytical or numerical methods. However, applying these methods to small samples on the order of few wavelengths in diameter is challenging, as the fields scattered by these samples become significantly contaminated by diffraction from the sample edges. Here, we propose a method to extract the material parameters of small samples using convolutional neural networks trained to learn the mapping between far-field echoes and the material parameters. Networks were trained with synthetic time domain echo data obtained by simulating the free-space scattering of sound from unknown media underwater. Results show that neural networks can accurately predict effective material parameters such as mass density, bulk modulus, and shear modulus even when small training sets are used. Furthermore, we demonstrate in experiments executed in a water tank that the networks trained with synthetic data can accurately estimate the material properties of fabricated metamaterial samples from single-point echo measurements performed in the far-field. This work highlights the effectiveness of our approach to identify unknown media using far-field acoustic reflection dominated by diffraction fields and will open a new avenue toward acoustic sensing techniques.