A Holistic Approach to Computing First-Arrival Traveltimes Using Physics-Informed Neural Networks

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 computational challenges, including improvement of the solution accuracy, incorporation of surface topography, the addition of accurate physics by accounting for anisotropy/attenuation in the medium, and speeding up computations. Despite these advances, these algorithms have no mechanism to carry information gained by solving one problem to the next. Moreover, these approaches may breakdown for certain complex forms of the eikonal equation, requiring simplification of the equations to estimate approximate solutions. Therefore, we seek an alternate approach to address these challenges holistically. We propose an algorithm based on the emerging paradigm of physics-informed neural network to solve different forms of the eikonal equation. We show how transfer learning can be used to speed up computations by utilizing information gained from prior solutions. Such an approach makes the implementation of eikonal solvers much simpler and puts us on a much faster path to progress. The method paves the pathway to solving complex forms of the eikonal equation that have remained unsolved using conventional algorithms or solved using some approximation techniques at best.