Data-driven efficient solvers for Langevin dynamics on manifold in high dimensions

DOI10.1016/j.acha.2022.09.003OpenAlexW3134076208MaRDI QIDQ2105115

Yuan Gao, Jian-Guo Liu, Nan Wu

Publication date: 8 December 2022

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

Full work available at URL: https://arxiv.org/abs/2005.12787

zbMATH Keywords

exponential convergenceVoronoi tessellationreaction coordinatesdiffusion maprandom walk on point cloudsunconditionally stable explicit finite volume scheme

Mathematics Subject Classification ID

Discrete-time Markov processes on general state spaces (60J05) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) Numerical solutions to stochastic differential and integral equations (65C30) Dynamics of random walks, random surfaces, lattice animals, etc. in time-dependent statistical mechanics (82C41) Simulation of dynamical systems (37M05) Finite difference methods applied to problems in thermodynamics and heat transfer (80M20) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08) Fokker-Planck equations (35Q84) Finite volume methods applied to problems in thermodynamics and heat transfer (80M12) Finite volume methods for boundary value problems involving PDEs (65N08) Computational methods for invariant manifolds of dynamical systems (37M21)

Related Items (3)

Random Walk Approximation for Irreversible Drift-Diffusion Process on Manifold: Ergodicity, Unconditional Stability and Convergence ⋮ Transition Path Theory for Langevin Dynamics on Manifolds: Optimal Control and Data-Driven Solver ⋮ Structure preserving schemes for Fokker-Planck equations of irreversible processes

Cites Work

• Unnamed Item
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• Gradient flows of the entropy for jump processes
• On the relation between gradient flows and the large-deviation principle, with applications to Markov chains and diffusion
• Gradient flows of the entropy for finite Markov chains
• The embedding dimension of Laplacian eigenfunction maps
• Embedding Riemannian manifolds by their heat kernel
• Robust Perron cluster analysis in conformation dynamics
• Spectral convergence of graph Laplacian and heat kernel reconstruction in \(L^\infty\) from random samples
• Inbetweening auto-animation via Fokker-Planck dynamics and thresholding
• Think globally, fit locally under the manifold setup: asymptotic analysis of locally linear embedding
• Nonlocal-interaction equation on graphs: gradient flow structure and continuum limit
• Improved spectral convergence rates for graph Laplacians on \(\varepsilon \)-graphs and \(k\)-NN graphs
• Eigen-convergence of Gaussian kernelized graph Laplacian by manifold heat interpolation
• Error estimates for spectral convergence of the graph Laplacian on random geometric graphs toward the Laplace-Beltrami operator
• A note on parametric Bayesian inference via gradient flows
• Fokker-Planck equations for a free energy functional or Markov process on a graph
• Diffusion maps
• Diffusion maps, spectral clustering and reaction coordinates of dynamical systems
• Towards a theory of transition paths
• Revisit of macroscopic dynamics for some non-equilibrium chemical reactions from a Hamiltonian viewpoint
• Embeddings of Riemannian Manifolds with Heat Kernels and Eigenfunctions
• Vector diffusion maps and the connection Laplacian
• Nonparametric Uncertainty Quantification for Stochastic Gradient Flows
• Manifold parametrizations by eigenfunctions of the Laplacian and heat kernels
• Optimal partition and effective dynamics of complex networks
• Transition Path Theory for Markov Jump Processes
• Diffusion Maps, Reduction Coordinates, and Low Dimensional Representation of Stochastic Systems
• On the Rate of Convergence of Empirical Measures in ∞-transportation Distance
• Pseudo-Riemannian Manifolds with Totally Geodesic Bisectors
• Elliptic Partial Differential Equations of Second Order
• Spectral convergence of the connection Laplacian from random samples
• Point Cloud Discretization of Fokker--Planck Operators for Committor Functions
• Laplacian Eigenmaps for Dimensionality Reduction and Data Representation
• Analysis and Geometry of Markov Diffusion Operators
• Lipschitz Regularity of Graph Laplacians on Random Data Clouds
• A continuum limit for the PageRank algorithm
• Large time behaviors of upwind schemes and $B$-schemes for Fokker-Planck equations on $\mathbb {R}$ by jump processes
• On the rate of convergence of empirical measure in $\infty $-Wasserstein distance for unbounded density function
• Applied Stochastic Analysis
• Hessian eigenmaps: Locally linear embedding techniques for high-dimensional data

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