Papers › PINNeik: Eikonal solution using physics-informed neural networks
PINNeik: Eikonal solution using physics-informed neural networks
Umair bin Waheed, Ehsan Haghighat, Tariq Alkhalifah, Chao Song, Qi Hao
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
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, and inversion. Several numerical algorithms have been developed over the years to solve the eikonal equation. However, these methods require considerable modifications to incorporate additional physics, such as anisotropy, and may even breakdown for certain complex forms of the eikonal equation, requiring approximation methods. Moreover, they suffer from computational bottleneck when repeated computations are needed for perturbations in the velocity model and/or the source location, particularly in large 3D models. Here, we propose an algorithm to solve the eikonal equation based on the emerging paradigm of physics-informed neural networks (PINNs). By minimizing a loss function formed by imposing the eikonal equation, we train a neural network to output traveltimes that are consistent with the underlying partial differential equation. We observe sufficiently high traveltime accuracy for most applications of interest. We also demonstrate how the proposed algorithm harnesses machine learning techniques like transfer learning and surrogate modeling to speed up traveltime computations for updated velocity models and source locations. Furthermore, we use a locally adaptive activation function and adaptive weighting of the terms in the loss function to improve convergence rate and solution accuracy. We also show the flexibility of the method in incorporating medium anisotropy and free-surface topography compared to conventional methods that require significant algorithmic modifications. These properties of the proposed PINN eikonal solver are highly desirable in obtaining a flexible and efficient forward modeling engine for seismological applications.
In Syntology Open this paper in Syntology's Atlas, the map of the papers in Syntology's graph and their citations.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections