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Optimal transport (OT) offers a versatile framework to compare complex data distributions in a geometrically meaningful way.
The hungarian method for the assignment problem
H. W. Kuhn · 1955
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A Relationship Between Arbitrary Positive Matrices and Doubly Stochastic Matrices
Richard Sinkhorn · 1964
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The auction algorithm for the transportation problem
Dimitri P. Bertsekas and David A. Castanon · 1989
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Polar factorization and monotone rearrangement of vector-valued functions
Yann Brenier · 1991
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Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical systems
Tianping Chen and Hong Chen · 1995
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Boundary regularity of maps with convex potentials–ii
Luis A. Caffarelli · 1996
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A convexity principle for interacting gases
Robert J. McCann · 1997
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A computational fluid mechanics solution to the monge-kantorovich mass transfer problem
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A Course in Metric Geometry
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Topics in optimal transportation
Cédric Villani · 2003
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Monge’s problem with a quadratic cost by the zero-noise limit of h-path processes
Toshio Mikami · 2004
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Gradient Flows in Metric Spaces and in the Space of Probability Measures
Luigi Ambrosio, Nicola Gigli, and Giuseppe Savaré · 2008
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Partial Differential Equations
Lawrence C. Evans · 2010
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Fourier neural operator for parametric partial differential equations, 2020b
Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew Stuart, and Anima Anandkumar · 2010
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Sinkhorn distances: Lightspeed computation of optimal transport
Marco Cuturi · 2013
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Amortized inference in probabilistic reasoning
Samuel J. Gershman and Noah D. Goodman · 2014
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Iterative bregman projections for regularized transportation problems
Jean-David Benamou, Guillaume Carlier, Marco Cuturi, Luca Nenna, and Gabriel Peyré · 2015
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From word embeddings to document distances
Matt J. Kusner, Yu Sun, Nicholas I. Kolkin, and Kilian Q. Weinberger · 2015
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Linear and Nonlinear Programming
David G. Luenberger and Yinyu Ye · 2015
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Optimal Transport for Applied Mathematicians. Calculus of Variations, PDEs and Modeling
Filippo Santambrogio · 2015
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Convolutional wasserstein distances: Efficient optimal transportation on geometric domains
Justin Solomon, Fernando de Goes, Gabriel Peyré, Marco Cuturi, Adrian Butscher, Andy Nguyen, Tao Du, and Leonidas Guibas · 2015
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Optimal mass transport for shape matching and comparison
Zhengyu Su, Yalin Wang, Rui Shi, Wei Zeng, Jian Sun, Feng Luo, and Xianfeng Gu · 2015
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On the relation between optimal transport and schrödinger bridges: A stochastic control viewpoint
Yongxin Chen, Tryphon T. Georgiou, and Michele Pavon · 2016
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Optimal transport for domain adaptation
Nicolas Courty, Rémi Flamary, Devis Tuia, and Alain Rakotomamonjy · 2016
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Stochastic optimization for large-scale optimal transport
Pot: Python optimal transport
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Minimax estimation of smooth optimal transport maps
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Optimal transport-based coverage control for swarm robot systems: Generalization of the voronoi tessellation-based method
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Neural operator: Learning maps between function spaces, 2021
Nikola Kovachki, Zongyi Li, Burigede Liu, Kamyar Azizzadenesheli, Kaushik Bhattacharya, Andrew Stuart, and Anima Anandkumar · 2021
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Physics-informed neural operator for learning partial differential equations, 2021
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Aude Genevay, Marco Cuturi, Gabriel Peyré, and Francis Bach · 2016
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Near-linear time approximation algorithms for optimal transport via sinkhorn iteration
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Wasserstein generative adversarial networks
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Distributed optimal transport for the deployment of swarms
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“zero-shot" super-resolution using deep internal learning
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Learning nonlinear operators via deeponet based on the universal approximation theorem of operators
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Vocabulary learning via optimal transport for neural machine translation
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