Identifying the Shear Piezoelectric Coefficient using Physics-Informed Neural Networks under Exact Boundary and Initial Constraints

The shear piezoelectric coefficient $e_{15}$ governs the shear-mode electromechanical coupling in piezoelectric micromachined ultrasonic transducers (PMUTs) and surface acoustic wave (SAW) devices, but measuring it typically requires destructive resonance testing on dedicated specimens. On simulated data, $e_{15}$ can instead be recovered non-destructively from sparse, noisy subsurface wavefield observations using a constrained physics-informed neural network (PINN). By building exact spatial distance functions and temporal multipliers directly into the network output, the clamped, grounded boundaries and resting initial state hold automatically, leaving the loss with only the interior equations of coupled electro-elastodynamics and the data misfit. Non-dimensional scaling brings all governing coefficients within one decade of O(1), and the setup removes the boundary and initial-condition penalty weights that soft-constraint methods must tune. In a six-way comparison (plane-strain PZT-5H, manufactured wavefield, 30 dB noise), a soft-penalty baseline with adaptive weights converges to an erroneous $e_{15}$ in four of the five runs (51.7% mean error), and fixed penalties reach an error of 0.85% only after a second-order optimization stage. The constrained formulations reach mean $e_{15}$ errors between 0.15% and 0.51% with held-out displacement errors below 1%. Within these variants, the spatial multiplier gives rapid first-order convergence, and the quadratic temporal multiplier lowers the early-time electrostatic residual by a factor of 6.8 versus a linear one. On finite-element data along one subsurface line, the full formulation recovers $e_{15}$ with 1.19% mean error at 30 dB and keeps it between 0.65% and 2.71% across a 40 to 0 dB noise sweep. Finally, training on displacements alone still recovers $e_{15}$ with mean errors of 0.45% on finite-element and 1.64% on manufactured data.