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Variational and information flows in machine learning and optimal transport

Record Type:	Electronic resources : Monograph/item
Title/Author:	Variational and information flows in machine learning and optimal transport/ by Wuchen Li ... [et al.].
other author:	Li, Wuchen.
Published:	Cham :Springer Nature Switzerland : : 2025.,
Description:	xiv, 254 p. :ill. (some col.), digital ;24 cm.
[NT 15003449]:	- 1. A Dynamic Perspective of Optimal Transport -- 2. A Geometric Perspective on Diffeomorphic and Optimal Transport Flows and Their Applications -- 3. Wasserstein Dynamics in Mathematical Data Sciences -- 4. Flow Matching: Markov Kernels, Stochastic Processes and Transport Plans.
Contained By:	Springer Nature eBook
Subject:	Stochastic processes. -
Online resource:	https://doi.org/10.1007/978-3-031-92731-7
ISBN:	9783031927317

Variational and information flows in machine learning and optimal transport
Variational and information flows in machine learning and optimal transport[electronic resource] /by Wuchen Li ... [et al.]. - Cham :Springer Nature Switzerland :2025. - xiv, 254 p. :ill. (some col.), digital ;24 cm. - Oberwolfach seminars,v. 562296-5041 ;. - Oberwolfach seminars ;volume 56..

- 1. A Dynamic Perspective of Optimal Transport -- 2. A Geometric Perspective on Diffeomorphic and Optimal Transport Flows and Their Applications -- 3. Wasserstein Dynamics in Mathematical Data Sciences -- 4. Flow Matching: Markov Kernels, Stochastic Processes and Transport Plans.

This book is based on lectures given at the Mathematisches Forschungsinstitut Oberwolfach on "Computational Variational Flows in Machine Learning and Optimal Transport". Variational and stochastic flows on measure spaces are ubiquitous in machine learning and generative modeling. Optimal transport and diffeomorphic flows provide powerful frameworks to analyze such trajectories of distributions with elegant notions from differential geometry, such as geodesics, gradient and Hamiltonian flows. Recently, mean field control and mean field games offered a general optimal control variational view on learning problems. The four independent chapters in this book address the question of how the presented tools lead us to better understanding and further development of machine learning and generative models.

ISBN: 9783031927317

Standard No.: 10.1007/978-3-031-92731-7doiSubjects--Topical Terms:

520663
Stochastic processes.

LC Class. No.: QA274

Dewey Class. No.: 519.23

Variational and information flows in machine learning and optimal transport
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245 0 0 $a Variational and information flows in machine learning and optimal transport $h [electronic resource] / $c by Wuchen Li ... [et al.].
260 $a Cham : $b Springer Nature Switzerland : $b Imprint: Birkhäuser, $c 2025.
300 $a xiv, 254 p. : $b ill. (some col.), digital ; $c 24 cm.
490 1 $a Oberwolfach seminars, $x 2296-5041 ; $v v. 56
505 0 $a - 1. A Dynamic Perspective of Optimal Transport -- 2. A Geometric Perspective on Diffeomorphic and Optimal Transport Flows and Their Applications -- 3. Wasserstein Dynamics in Mathematical Data Sciences -- 4. Flow Matching: Markov Kernels, Stochastic Processes and Transport Plans.
520 $a This book is based on lectures given at the Mathematisches Forschungsinstitut Oberwolfach on "Computational Variational Flows in Machine Learning and Optimal Transport". Variational and stochastic flows on measure spaces are ubiquitous in machine learning and generative modeling. Optimal transport and diffeomorphic flows provide powerful frameworks to analyze such trajectories of distributions with elegant notions from differential geometry, such as geodesics, gradient and Hamiltonian flows. Recently, mean field control and mean field games offered a general optimal control variational view on learning problems. The four independent chapters in this book address the question of how the presented tools lead us to better understanding and further development of machine learning and generative models.
650 0 $a Stochastic processes. $3 520663
650 0 $a Computational intelligence. $3 595739
650 0 $a Machine learning $x Mathematics. $3 3442737
650 1 4 $a Differential Equations. $3 907890
650 2 4 $a Calculus of Variations and Optimization. $3 3538813
700 1 $a Li, Wuchen. $3 3790434
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a Oberwolfach seminars ; $v volume 56. $3 3790435
856 4 0 $u https://doi.org/10.1007/978-3-031-92731-7
950 $a Mathematics and Statistics (SpringerNature-11649)