Uncertainty Quantification at the Microscale: a Data-Driven Multi-Scale Approach

Data-driven formulations are currently developed and can result extremely helpful to deal with the complexity of the multi-physics governing the response of micro-electro-mechanical systems (MEMS) to the external stimuli. Such devices are in fact characterized by a hierarchy of length- and time-scales, which are difficult to fully account for in a purely model-based approach [1]. In this work, we specifically refer to a (single-axis) Lorentz force micro-magnetometer designed for navigation purposes. Due to an alternating current flowing in a slender mechanical part (beam) and featuring an ad-hoc set frequency, the micro-system is driven into resonance so that its sensitivity to the magnetic field gets improved. A reduced-order physical model was formerly developed for the aforementioned movable part of the device; this model was then used to feed and speed up a multi-physics and multi-objective topology optimization procedure, aiming to design a robust and performing magnetometer. The stochastic effects, which are responsible for the scattering in the experimental data at the microscale [2], were not accounted for in such a model-based approach. A recently proposed formulation, see [3], is here discussed and further extended to allow for such stochastic effects. The proposed multi-scale deep learning approach features: at the material scale, a deep neural network adopted to learn the scattering in the mechanical properties of polysilicon induced by its morphology; at the device scale, a multi-input deep neural network adopted to learn the imperfection-sensitive geometric features of the movable part of the magnetometer. The two data-driven models adopted at the material and device length scales are linked through the physical model proposed in [1] to provide a kind of hybrid solution to the problem. Results relevant to different neural network architectures are discussed, along with a proposal to frame the approach as a multi-fidelity, uncertainty quantification procedure.

[1] S. Mariani, A. Ghisi, A. Corigliano, R. Martini, B. Simoni. Two-scale simulation of drop-induced failure of polysilicon MEMS sensors. Sensors, 11, pp. 4972-4989, 2011.

[2] M. Bagherinia, S. Mariani. Stochastic effects on the dynamics of the resonant structure of a Lorentz force MEMS magnetometer. Actuators,8, 36, 2019.

[3] S. Mariani, J.P. Quesada Molina. A two-scale multi-physics deep learning model for smart MEMS sensors. Journal of Materials Science and Chemical Engineering, 9, pp. 41-52, 2021.