  We employ physics-informed neural networks (PINNs) to quantify the
microstructure of a polycrystalline Nickel by computing the spatial variation
of compliance coefficients (compressibility, stiffness and rigidity) of the
material. The PINN is supervised with realistic ultrasonic surface acoustic
wavefield data acquired at an ultrasonic frequency of 5 MHz for the
polycrystalline material. The ultrasonic wavefield data is represented as a
deformation on the top surface of the material with the deformation measured
using the method of laser vibrometry. The ultrasonic data is further
complemented with wavefield data generated using a finite element based solver.
The neural network is physically-informed by the in-plane and out-of-plane
elastic wave equations and its convergence is accelerated using adaptive
activation functions. The overarching goal of this work is to infer the spatial
variation of compliance coefficients of materials using PINNs, which for
ultrasound involves the spatially varying speed of the elastic waves. More
broadly, the resulting PINN based surrogate model shows a promising approach
for solving ill-posed inverse problems, often encountered in the
non-destructive evaluation of materials.
