Eikonal Solution Using Physics-Informed Neural Networks

Deep learning is fast emerging as a potential disruptive tool to tackle longstanding research problems across science and engineering disciplines. Recent advances in the field of Scientific Machine Learning demonstrate its largely untapped potential for applications in scientific computing. Here, we employ the emerging paradigm of physics-informed neural networks to solve the isotropic P-wave eikonal equation. By minimizing a loss function formed by imposing the validity of the eikonal equation, we train a neural network to produce traveltime solutions that are consistent with the underlying equation. Through tests on synthetic models, we study the accuracy of the proposed method and its relation to the network architecture. We observe considerably higher accuracy compared to the first-order finite-difference solution using the fast marching method. While we demonstrate the use of neural networks to compute physically consistent traveltime solutions, the true potential of this approach in efficiently and accurately solving forward and inverse problems needs to be further explored.