A Two-Scale Multi-Physics Deep Learning Model for Smart MEMS Sensors

Smart materials and structures, especially those bio-inspired, are often characterized by a hierarchy of length- and time-scales. Smart Micro Electro-Mechanical Systems (MEMS) are also characterized by different physical phenomena affecting their properties at different scales. Data-driven formulations can then be helpful to deal with the complexity of the multi-physics governing their response to the external stimuli, and optimize their performances. As an example, Lorentz force micro-magnetometers working principle rests on the interaction of a magnetic field with a current flowing inside a semiconducting, micro-structured medium. If an alternating current with a properly set frequency is let to flow longitudinally in a slender beam, the system is driven into resonance and the sensitivity to the magnetic field may result largely enhanced. In our former activity, a reduced-order physical model of the movable structure of a single-axis Lorentz force MEMS magnetometer was developed, to feed a multi-objective topology optimization procedure. That model-based approach did not account for stochastic effects, which lead to the scattering in the experimental data at the micrometric length-scale. The formulation is here improved to allow for stochastic effects through a two-scale deep learning model designed as follows: at the material scale, a neural network is adopted to learn the scattering in the mechanical properties of polysilicon induced by its polycrystalline morphology; at the device scale, a further neural network is adopted to learn the most important geometric features of the movable parts that affect the overall performance of the magnetometer. Some preliminary results are discussed, and an extension to allow for size effects is finally foreseen.