  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 velocity model. Furthermore, we
demonstrate how the proposed approach makes it simpler to incorporate
additional physics and other features in contrast to conventional methods that
took years and often decades to make these advances. Such an approach not only
makes the implementation of eikonal solvers much simpler but also puts us on a
much faster path to progress.
