Since the original algorithm by John Vidale in 1988 to numerically solve the isotropic eikonal equation, there has been tremendous progress on the topic addressing an array of challenges including improvement of the solution accuracy, incorporation of surface topography, adding more accurate physics by accounting for anisotropy/attenuation in the medium, and speeding up computations using multiple CPUs and GPUs. Despite these advances, there is no mechanism in these algorithms to carry on information gained by solving one problem to the next. Moreover, these approaches may breakdown for certain complex forms of the eikonal equation, requiring approximation methods to estimate the solution. Therefore, we seek an alternate approach to address the challenge in a holistic manner, i.e., a method that not only makes it simpler to incorporate topography, allow accounting for any level of complexity in physics, benefiting from computational speedup due to the availability of multiple CPUs or GPUs, but also able to transfer knowledge gained from solving one problem to the next. We develop an algorithm based on the emerging paradigm of physics-informed neural network to solve various forms of the eikonal equation. We show how transfer learning and surrogate modeling can be used to speed up computations by utilizing information gained from prior solutions. We also propose a two-stage optimization scheme to expedite the training process in presence of sharper heterogeneity in the