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We address the computational challenges inherent in the stochastic characterization and uncertainty quantification of Micro-Electro-Mechanical Systems (MEMS). Traditional methods, such as Markov Chain Monte Carlo (MCMC) algorithms, are often constrained by the computational intensity required for high-fidelity finite element simulations. To overcome these limitations Reduced Order Modelling techniques (ROMs) are a co,mmon used alternative. Among the generale techniques used for ROMs, we propose the utilization of supervised learning-based surrogate models, specifically artificial neural networks, to effectively approximate MEMS capacitive accelerometer behavior. Our approach involves training the surrogate models with data derived from initial high-fidelity finite element analyses (FEA), providing rich datasets to be generated in an offline phase. The surrogate models replicate the FEA accuracy in predicting the behaviour of MEMS capacitive accelerometers under a wide range of fabrication parameters, thereby reducing the online computational cost without compromising accuracy. This enables extensive and efficient stochastic analyses of complex MEMS capacitive accelerometers, offering a flexible framework for characterizing their behavior. A key application of our framework is demonstrated in estimating the sensitivity of a MEMS capacitive accelerometer, accounting for unknown mechanical offsets, over-etching, and thickness variations. We employ an MCMC approach to estimate the posterior distribution of the device?s unknown fabrication parameters, informed by its response to transient voltage signals. The integration of surrogate models for mapping fabrication parameters to device responses and subsequently to sensitivity measures facilitates both backward and forward uncertainty quantification, yielding accurate results while significantly enhancing the efficiency and effectiveness of the characterization process.