Diffusion maps for embedded manifolds with boundary with applications to PDEs

DOI10.1016/j.acha.2023.101593arXiv1912.01391OpenAlexW2991967738MaRDI QIDQ6185683

Ryan Vaughn, Tyrus Berry, Harbir Antil

Publication date: 30 January 2024

Published in: Applied and Computational Harmonic Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1912.01391

zbMATH Keywords

heat equationRiemannian manifoldspartial differential equationsmesh-freeboundary detection

Mathematics Subject Classification ID

Density estimation (62G07) Learning and adaptive systems in artificial intelligence (68T05) Elliptic equations on manifolds, general theory (58J05) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Local kernels and the geometric structure of data
• On boundary correction in kernel density estimation
• Chernoff's theorem and discrete time approximations of Brownian motion on manifolds
• Variable bandwidth diffusion kernels
• Nonparametric kernel density estimation near the boundary
• Density estimation on manifolds with boundary
• Geometric structures arising from kernel density estimation on Riemannian manifolds
• Think globally, fit locally under the manifold setup: asymptotic analysis of locally linear embedding
• Approximating solutions of linear elliptic PDE's on a smooth manifold using local kernel
• Kernel density estimation on Riemannian manifolds
• Diffusion maps
• From graph to manifold Laplacian: the convergence rate
• The diffusion geometry of fibre bundles: horizontal diffusion maps
• Manifolds with Boundary and of Bounded Geometry
• Vector diffusion maps and the connection Laplacian
• Geometric Curvature Bounds in Riemannian Manifolds with Boundary
• An Improved Estimator of the Density Function at the Boundary
• Introduction to Riemannian Manifolds
• An Invitation to Alexandrov Geometry
• Variational Techniques for Elliptic Partial Differential Equations
• Laplacian Eigenmaps for Dimensionality Reduction and Data Representation
• Kernel Methods for Bayesian Elliptic Inverse Problems on Manifolds
• Extension of the Rauch Comparison Theorem to Submanifolds
• Probability density function estimation using gamma kernels

This page was built for publication: Diffusion maps for embedded manifolds with boundary with applications to PDEs