Metric Constrained Eikonal

Metric-constrained Eikonal methods focus on efficiently computing distances and geodesics on complex manifolds, addressing challenges in diverse fields like machine learning, statistics, and seismology. Current research emphasizes developing differentiable representations of distance functions using novel algorithms and model architectures, such as enriched neural operators, to enable applications like manifold clustering and reduced-order modeling. These advancements improve the accuracy and speed of computations, leading to more effective solutions for problems involving path planning, statistical inference, and wave propagation modeling. The resulting improvements in computational efficiency and accuracy have significant implications for various scientific and engineering applications.