Micro Electro-Mechanical Systems (MEMS) are often affected in their operational environment by different physical phenomena, each one possibly occurring at different length and time scales. Data-driven formulations can then be helpful to deal with such complexity in their modeling. By referring to a single-axis Lorentz force micro-magnetometer, characterized by a current flowing inside slender mechanical parts so that the system can be driven into resonance, it has been shown that the sensitivity to the magnetic field may get largely enhanced through proper (topology) optimization strategies. In our previous work, a reduced-order physical model for the movable structure was developed; such model-based approach did not account for all the stochastic effects leading to the measured scattering in the experimental data. A new formulation is here proposed resting on a two-scale deep learning model designed as follows: at the material level, a deep neural network is used a-priori to learn the scattering in the mechanical properties of polysilicon induced by its morphology; at the device level, a further deep neural network is used to account for the effects on the response induced by etch defects, learning on-the-fly relevant geometric features of the movable parts. Some preliminary results are here reported, and the capabilities of the learning models at the two length scales are discussed.