Scientific Article

Machine learning-supported inverse measurement procedure for broadband, temperature dependent piezoelectric material parameters

Measurement Engineering Group, Paderborn University, 33098 Paderborn, Germany

^* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 15 April 2025
Accepted: 26 August 2025

Abstract

This paper proposes an approach to identify a full set of piezoelectric material parameters by solving an inverse problem supported by data-driven methods, in particular neural networks. The accurate, quantitative description of piezoelectric material behaviour is challenging due to the large number of parameters, the complexity of the interacting physical quantities, and inability to infer material parameter values directly from certain measurements. Studies have shown that a full set of material parameters can be identified by solving an inverse problem, matching the electrical impedance of samples with the output of a simulation model. The solution method of the said inverse problem is hard to regularise due to vastly different sensitivities of the impedance with respect to certain material parameters and a large parameter space. Using synthetically generated training data, a method for initial value estimation using a neural network to invert the simulation model is proposed. The initial values are refined in an intermediate optimisation step using a second neural network that mimics the simulation model. The subsequent gradient-based optimisation process converges significantly faster than previous approaches and yields a better fit to the measurement data. Changes in properties that occur when the sample is exposed to different temperatures are examined to assess the ability of the method to resolve small differences in material behaviour.