Differential geometry and stochastic dynamics with deep learning numerics

DOI10.1016/j.amc.2019.03.044zbMath1428.58026arXiv1712.08364OpenAlexW2963176114WikidataQ115361228 ScholiaQ115361228MaRDI QIDQ2009564

Stefan Sommer, Line Kühnel, Alexis Arnaudon

Publication date: 29 November 2019

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1712.08364

zbMATH Keywords

automatic differentiationdifferential geometrydeep learning numericsnon-linear statisticstheano

Mathematics Subject Classification ID

Directional data; spatial statistics (62H11) Diffusion processes (60J60) Diffusion processes and stochastic analysis on manifolds (58J65) Software, source code, etc. for problems pertaining to probability theory (60-04)

Related Items (6)

Introduction to Riemannian Geometry and Geometric Statistics: From Basic Theory to Implementation with Geomstats ⋮ Diffusion Bridges for Stochastic Hamiltonian Systems and Shape Evolutions ⋮ A geometric framework for stochastic shape analysis ⋮ Shape analysis of surfaces using general elastic metrics ⋮ An infinitesimal probabilistic model for principal component analysis of manifold valued data ⋮ Learning landmark geodesics using the ensemble Kalman filter

Uses Software

• Theano
• Julia
• TensorFlow
• Pymanopt
• geomstats

Cites Work

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• On the differential geometry of frame bundles of Riemannian manifolds.
• Langevin Equations for Landmark Image Registration with Uncertainty
• Variational principles for stochastic fluid dynamics
• Variational principles for stochastic soliton dynamics
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