Time- Dependent Eikonal Solution Using Physics-Informed Neural Networks

Many scientific and technical fields employ the eikonal equation. Multiple numerical strategies have been devised throughout the years to solve the eikonal problem. Nevertheless, these techniques necessitate significant alterations to accommodate supplementary principles of physics, such as anisotropy, and may even fail to function properly for some intricate variations of the eikonal equation, necessitating the use of approximation methods. Massive 3D situations that require repeated calculations of velocity variations and initial positions face a processing challenge. This paper introduces a method to address the eikonal equation by utilizing PINNs, a relatively new strategy in the realm of physical science. By decreasing a loss function derived from the eikonal equation, the neural network is instructed to construct path durations that align with the underlying partial differential formula. This work employs an adaptive stimulation factor and flexible scaling of the loss factor variables to enhance velocity of convergence and reaction effectiveness. This additionally shows the technique's adaptability in incorporating moderate distortion and topography of surfaces without boundaries, in contrast to traditional approaches that necessitate substantial changes to the algorithm.