aiqbench analysis
The paper's core contribution is a constrained physics-informed neural network: hard-coding boundary and initial conditions into the network output, removing penalty weights, and using scaling to stabilise training. It applies this to inverse estimation of a piezoelectric coefficient. Results are on simulated and finite-element data only, so the practical claim of non-destructive measurement is unvalidated on physical specimens. For ML readers, the useful takeaway is the design pattern of exact constraints in PINNs as an alternative to tuned soft penalties.
Identifying the Shear Piezoelectric Coefficient using Physics-Informed Neural Networks under Exact Boundary and Initial Constraints
arXiv:2611.03485v1 Announce Type: cross Abstract: 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.
Abstract: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.
Computational Physics (physics.comp-ph); Materials Science (cond-mat.mtrl-sci); Machine Learning (cs.LG); Applied Physics (physics.app-ph)
arXiv:2611.03485 [physics.comp-ph]
(or arXiv:2611.03485v1 [physics.comp-ph] for this version)
https://doi.org/10.48550/arXiv.2611.03485 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 368 words