  We introduce an optimized physics-informed neural network (PINN) trained to
solve the problem of identifying and characterizing a surface breaking crack in
a metal plate. PINNs are neural networks that can combine data and physics in
the learning process by adding the residuals of a system of Partial
Differential Equations to the loss function. Our PINN is supervised with
realistic ultrasonic surface acoustic wave data acquired at a frequency of 5
MHz. The ultrasonic surface wave data is represented as a surface deformation
on the top surface of a metal plate, measured by using the method of laser
vibrometry. The PINN is physically informed by the acoustic wave equation and
its convergence is sped up using adaptive activation functions. The adaptive
activation function uses a scalable hyperparameter in the activation function,
which is optimized to achieve best performance of the network as it changes
dynamically the topology of the loss function involved in the optimization
process. The usage of adaptive activation function significantly improves the
convergence, notably observed in the current study. We use PINNs to estimate
the speed of sound of the metal plate, which we do with an error of 1\%, and
then, by allowing the speed of sound to be space dependent, we identify and
characterize the crack as the positions where the speed of sound has decreased.
Our study also shows the effect of sub-sampling of the data on the sensitivity
of sound speed estimates. More broadly, the resulting model shows a promising
deep neural network model for ill-posed inverse problems.
