This paper proposes a novel approach for micro-electromechanical resonator-based digital to frequency converter (DFC) design using artificial neural networks (ANN). The DFC is a key building block for multiple digital and interface units. We present the design of a 4-bit DFC device which consists of an in-plane clamped-clamped micro-beam resonator and 6 partial electrodes. The digital inputs, which are DC signals applied to the corner partial electrodes, modulate the beam resonance frequency using the electrostatic softening effect. The main challenge in the design is to find the air gap size between each input electrode and the beam to achieve the desired relationship between the digital input combinations and the corresponding resonance frequencies for a given application. We use a shallow, fully-connected feedforward neural network model to estimate the airgaps corresponding to the desired resonance frequency distribution, with less than 1% error. Two special cases are discussed for two applications: equal airgaps for implementing a full adder (FA), and weight-adjusted airgaps for implementing a 4-bit digital to analog converter (DAC). The training, validation, and testing datasets are extracted from finite-element-method (FEM) simulations, by obtaining resonance frequencies for the 16 input combinations for different airgap sets. The proposed method based on ANN model paves the way for a new design paradigm for MEMS resonator-based logic and opens new routes for designing more complex digital and interface circuits.