The objective of the proposed research is to leverage Machine Learning (ML) methods for predicting and extrapolating electromagnetic (EM) responses, aiming to significantly reduce both time consumption and computational resources compared to conventional commercial simulation tools. ML techniques have been used in design of mixed-signal systems to create fast surrogate models to model the non-linear relationship between the design space and the response space. However, two challenges persist: (1) Neural Networks (NNs) are susceptible to errors, necessitating the incorporation of uncertainty quantification (UQ) techniques around predictions, and (2) the inherent scarcity of data. This proposal addresses these challenges by introducing a series of predictive models, UQ methods, and extrapolation frameworks. The Spectral Transposed Convolutional Neural Network (S-TCNN) with 2D kernel is proposed to map design parameters to frequency responses. A novel sampling strategy based on UQ optimizes the training set, addressing the issue of data scarcity. To reduce the number of hyperparameters, a comprehensive learning framework which combines the S-TCNN with 2D kernel and extrapolation with Gaussian Process (GP) is developed. Additionally, a quantitative method for determining the extrapolation range which takes the distance and confidence interval (CI) into consideration is formed. To mitigate the gradient vanishing problem during up-sampling, the input design parameters of the model could be mapped to the latent Gaussian space through batches of GP layers. Future work in this proposal includes Temporal Transposed Convolutional Neural Network (T-TCNN) for time series, extrapolation with Long Short-Term Memory (LSTM), predictions for input parameters with uncertainty, deep kernel learning (DKL) framework and adaptive activation function for up-sampling models.