2019/03/19 by Moshe Lichtenstein, Lichtenstein, Moshe, Gautam Pai +3
Decision Sciences · Mathematics · Physics and Astronomy · #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #Model Reduction and Neural Networks #Probabilistic and Robust Engineering Design #Statistical and numerical algorithms
paper · pdf · doi:10.48550/arxiv.1903.07973
openalex publication_date 2019/03/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A deep learning approach to numerically approximate the solution to the Eikonal equation is introduced. The proposed method is built on the fast marching scheme which comprises of two components: a local numerical solver and an update scheme. We replace the formulaic local numerical solver with a trained neural network to provide highly accurate estimates of local distances for a variety of different geometries and sampling conditions. Our learning approach generalizes not only to flat Euclidean domains but also to curved surfaces enabled by the incorporation of certain invariant features in the neural network architecture. We show a considerable gain in performance, validated by smaller errors and higher orders of accuracy for the numerical solutions of the Eikonal equation computed on different surfaces The proposed approach leverages the approximation power of neural networks to enhance the performance of numerical algorithms, thereby, connecting the somewhat disparate themes of numerical geometry and learning.