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Keyword

gradient flow

Description: A dynamical process in which a state evolves according to the gradient of a function, studied in mathematics, optimization, control, and physical systems.
OpenAlex ID: keywords/gradient-flow
Optimal Transport: Old and New
2013 · Cédric Villani · 3,601
Asymptotic Behavior of Dissipative Systems
2010 · Jack Hale · Mathematical surveys and monographs · 2,688
Computational Optimal Transport with Applications to Data Sciences
2019 · Gabriel Peyré, Marco Cuturi · Foundations and Trends® in Machine Learning · 2,328
Gradient Flows: In Metric Spaces and in the Space of Probability Measures
2005 · Luigi Ambrosio, Nicola Gigli, et al. · 2,275
Distance Regularized Level Set Evolution and Its Application to Image Segmentation
2010 · Chunming Li, Chenyang Xu, et al. · IEEE Transactions on Image Processing · 2,108
Accurate and efficient algorithm for Bader charge integration
2010 · Min Yu, Dallas R. Trinkle · 1,889
Level Set Evolution without Re-Initialization: A New Variational Formulation
2005 · Chunming Li, Chenyang Xu, et al. · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · 1,813
The Variational Formulation of the Fokker--Planck Equation
1998 · Richard Jordan, David Kinderlehrer, et al. · SIAM Journal on Mathematical Analysis · 1,607
Optimal Transport for Applied Mathematicians
2015 · Filippo Santambrogio · Progress in nonlinear differential equations and their applications · 1,363
Gradient Flow in Recurrent Nets: The Difficulty of Learning LongTerm Dependencies
2009 · Institute of Electrical and Electronics Engineers eBooks · 1,246
Equation of state in ( 2 + 1 )-flavor QCD
2014 · A. Bazavov, Tanmoy Bhattacharya, et al. · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · 1,202
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The scalar auxiliary variable (SAV) approach for gradient flows
2017 · Jie Shen, Jie Xu, et al. · Journal of Computational Physics · 1,134
The Importance of Skip Connections in Biomedical Image Segmentation
2016 · Michal Drozdzal, Eugene Vorontsov, et al. · Lecture notes in computer science · 1,115
A Variational Level Set Approach to Multiphase Motion
1996 · Hong-Kai Zhao, T. Chan, et al. · Journal of Computational Physics · 1,060
Riemannian center of mass and mollifier smoothing
1977 · H. Karcher · Communications on Pure and Applied Mathematics · 995
Morse Theory for Cell Complexes
1998 · Robin Forman · Advances in Mathematics · 943
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Gradient Flow in Recurrent Nets: the Difficulty of Learning Long-Term Dependencies
2001 · Sepp Hochreiter, Yoshua, et al. · 864
Curve evolution implementation of the Mumford-Shah functional for image segmentation, denoising, interpolation, and magnification
2001 · A. Tsai, A. Yezzi, et al. · IEEE Transactions on Image Processing · 841
A New Class of Efficient and Robust Energy Stable Schemes for Gradient Flows
2019 · Jie Shen, Jie Xu, et al. · SIAM Review · 748
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Residual Networks Behave Like Ensembles of Relatively Shallow Networks
2016 · Veit, Andreas, Wilber, Michael, et al. · arXiv (Cornell University) · 679
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Gradient flows and geometric active contour models
2002 · S. Kichenassamy, A. Kumar, et al. · IEEE International Conference on Computer Vision (ICCV) · 660
Methods in computational physics
1973 · Boleslav Gross · Journal of the Franklin Institute · 608
Traveling Waves in a Convolution Model for Phase Transitions
1997 · Peter W. Bates, Paul C. Fife, et al. · Archive for Rational Mechanics and Analysis · 548
On gradients of functions definable in o-minimal structures
1998 · Krzysztof Kurdyka · Annales de l’institut Fourier · 462
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Morse‐type index theory for flows and periodic solutions for Hamiltonian Equations
1984 · Charles Conley, Eduard Zehnder · Communications on Pure and Applied Mathematics · 453
Works count: 5,492
Citation count: 91,110
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