We propose a novel workflow for fast forward modeling of well logs in axially symmetric 2D models of the nearwellbore environment. The approach integrates the finite element method with deep residual neural networks to achieve exceptional computational efficiency and accuracy. The workflow is demonstrated through the modeling of wireline electromagnetic propagation resistivity logs, where the measured responses exhibit a highly nonlinear relationship with formation properties. The motivation for this research is the need for advanced modeling algorithms that are fast enough for use in modern quantitative interpretation tools, where thousands of simulations may be required in iterative inversion processes. The proposed algorithm achieves a remarkable enhancement in performance, being up to 3000 times faster than the finite element method alone when utilizing a GPU. While still ensuring high accuracy, this makes it well-suited for practical applications when reliable payzone assessment is needed in complex environmental scenarios. Furthermore, the algorithm's efficiency positions it as a promising tool for stochastic Bayesian inversion, facilitating reliable uncertainty quantification in subsurface property estimation.