In micro-electro-mechanical systems (MEMS) testing high overall precision and reliability are essential. Due to the additional requirement of runtime efficiency, machine learning methods have been investigated in recent years. However, these methods are often associated with inherent challenges concerning uncertainty quantification and guarantees of reliability. The goal of this paper is therefore to present a new machine learning approach in MEMS testing based on Bayesian inference to determine whether the estimation is trustworthy. The overall predictive performance as well as the uncertainty quantification are evaluated with four methods: Bayesian neural network, mixture density network, probabilistic Bayesian neural network and BayesFlow. They are investigated under the variation in training set size, different additive noise levels, and an out-of-distribution condition, namely the variation in the damping factor of the MEMS device. Furthermore, epistemic and aleatoric uncertainties are evaluated and discussed to encourage thorough inspection of models before deployment striving for reliable and efficient parameter estimation during final module testing of MEMS devices. BayesFlow consistently outperformed the other methods in terms of the predictive performance. As the probabilistic Bayesian neural network enables the distinction between epistemic and aleatoric uncertainty, their share of the total uncertainty has been intensively studied.

Calibration of complex system models with a large number of parameters using standard optimization methods is often extremely time-consuming and not fully automated due to the reliance on all-inclusive expert knowledge. We propose a sensitivity-guided iterative parameter identification and data generation algorithm. The sensitivity analysis replaces manual intervention, the parameter identification is realized by BayesFlow allowing for uncertainty quantification, and the data generation with the Physics-Enhanced Latent Space Variational Autoencoder (PELS-VAE) between two iteration steps enables inference of weakly identifiable parameters. A complete calibration experiment was conducted on a thermal model of an automotive cabin. The average relative error rate over all parameter estimations of 1.62% and the mean absolute error of calibrated model outputs of 0.108 ◦C validate the feasibility and effectiveness of the method. Moreover, the entire procedure accelerates up to one day, whereas the classical calibration method takes more than one week.

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Calibration of complex system models with a large number of parameters using standard optimization methods is often extremely time-consuming and not fully automated due to the reliance on all-inclusive expert knowledge. We propose a sensitivity-guided iterative parameter identification and data generation algorithm. The sensitivity analysis replaces manual intervention, the parameter identification is realized by BayesFlow allowing for uncertainty quantification, and the data generation with the physics-enhanced latent space variational autoencoder (PELS-VAE) between two iteration steps enables inference of weakly identifiable parameters. A complete calibration experiment was conducted on a thermal model of an automotive cabin. The average relative error rate over all parameter estimates of 1.62% and the mean absolute error of calibrated model outputs of $$0.108\,^{\circ }$$ 0.108 ∘ C validate the feasibility and effectiveness of the method. Moreover, the entire procedure accelerates up to 1 day, whereas the classical calibration method takes more than 1 week.