Nonlocal-interaction equation on graphs: gradient flow structure and continuum limit

DOI10.1007/s00205-021-01631-wOpenAlexW3139273455MaRDI QIDQ2021745

André Schlichting, Francesco Saverio Patacchini, Antonio Esposito, Dejan Slepčev

Publication date: 27 April 2021

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1912.09834

zbMATH Keywords

finite volume schemegraph Wasserstein distancenonlocal-interaction equation

Mathematics Subject Classification ID

Variational problems in a geometric measure-theoretic setting (49Q20) Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds (58B20) Spaces of measures, convergence of measures (28A33) Partial differential equations of mathematical physics and other areas of application (35Q99) Combinatorial aspects of tessellation and tiling problems (05B45) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08) Integro-partial differential equations (35R09) PDEs on graphs and networks (ramified or polygonal spaces) (35R02)

Related Items (12)

Semi-discrete optimization through semi-discrete optimal transport: a framework for neural architecture search ⋮ Applications of optimal transportation in the natural sciences. Abstracts from the workshop held February 21--27, 2021 (online meeting) ⋮ On gradient flow and entropy solutions for nonlocal transport equations with nonlinear mobility ⋮ Clustering Dynamics on Graphs: From Spectral Clustering to Mean Shift Through Fokker–Planck Interpolation ⋮ Operator-splitting schemes for degenerate, non-local, conservative-dissipative systems ⋮ Nonlocal Wasserstein distance: metric and asymptotic properties ⋮ Nonlocal Cross-Interaction Systems on Graphs: Nonquadratic Finslerian Structure and Nonlinear Mobilities ⋮ Nonlocal cross-interaction systems on graphs: energy landscape and dynamics ⋮ Cosh gradient systems and tilting ⋮ Data-driven gradient flows ⋮ Data-driven efficient solvers for Langevin dynamics on manifold in high dimensions ⋮ Traditional and accelerated gradient descent for neural architecture search

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