EikoNet: Solving the Eikonal Equation With Deep Neural Networks

The recent deep learning revolution has created enormous opportunities for accelerating compute capabilities in the context of physics-based simulations. In this article, we propose EikoNet, a approach to solving Eikonal equation, which characterizes first-arrival-time field heterogeneous 3-D velocity structures. Our grid-free allows rapid determination travel time between any two points within continuous domain. These solutions are allowed violate differential equation—which casts problem as one optimization—with goal finding network parameters that minimize degree equation is violated. doing so, method exploits differentiability neural networks calculate spatial gradients analytically, meaning can be trained on its own without ever needing from finite-difference algorithm. EikoNet rigorously tested several models and sampling methods demonstrate robustness versatility. Training inference highly parallelized, making well-suited GPUs. low memory overhead further avoids need travel-time lookup tables. developed important applications earthquake hypocenter inversion, ray multipathing, tomographic modeling, well other fields beyond seismology where tracing essential.