PINNeik: Eikonal solution using physics-informed neural networks

The eikonal equation is utilized across a wide spectrum of science and engineering disciplines. In seismology, it regulates seismic wave traveltimes needed for applications like source localization, imaging, inversion. Several numerical algorithms have been developed over the years to solve equation. However, these methods require considerable modifications incorporate additional physics, such as anisotropy, may even breakdown certain complex forms equation, requiring approximation methods. Moreover, they suffer from computational bottleneck when repeated computations are perturbations in velocity model and/or location, particularly large 3D models. Here, we propose an algorithm based on emerging paradigm physics-informed neural networks (PINNs). By minimizing loss function formed by imposing train network output that consistent with underlying partial differential We observe sufficiently high traveltime accuracy most interest. also demonstrate how proposed harnesses machine learning techniques transfer surrogate modeling speed up updated models locations. Furthermore, use locally adaptive activation weighting terms improve convergence rate solution accuracy. show flexibility method incorporating medium anisotropy free-surface topography compared conventional significant algorithmic modifications. These properties PINN solver highly desirable obtaining flexible efficient forward engine seismological applications.