LEADER 03115nam 22006015 450 001 9911015963203321 005 20250718130247.0 010 $a3-031-92731-1 024 7 $a10.1007/978-3-031-92731-7 035 $a(MiAaPQ)EBC32227097 035 $a(Au-PeEL)EBL32227097 035 $a(CKB)39694545000041 035 $a(DE-He213)978-3-031-92731-7 035 $a(OCoLC)1530376635 035 $a(EXLCZ)9939694545000041 100 $a20250718d2025 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aVariational and Information Flows in Machine Learning and Optimal Transport /$fby Wuchen Li, Bernhard Schmitzer, Gabriele Steidl, François-Xavier Vialard, Christian Wald 205 $a1st ed. 2025. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Birkhäuser,$d2025. 215 $a1 online resource (433 pages) 225 1 $aOberwolfach Seminars,$x2296-5041 ;$v56 311 08$a3-031-92730-3 327 $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. 330 $aThis book is based on lectures given at the Mathematisches Forschungsinstitut Oberwolfach on ?Computational Variational Flows in Machine Learning and Optimal Transport?. Variational and stochastic flows on measure spaces are ubiquitous in machine learning and generative modeling. Optimal transport and diffeomorphic flows provide powerful frameworks to analyze such trajectories of distributions with elegant notions from differential geometry, such as geodesics, gradient and Hamiltonian flows. Recently, mean field control and mean field games offered a general optimal control variational view on learning problems. The four independent chapters in this book address the question of how the presented tools lead us to better understanding and further development of machine learning and generative models. . 410 0$aOberwolfach Seminars,$x2296-5041 ;$v56 606 $aDifferential equations 606 $aMathematical optimization 606 $aCalculus of variations 606 $aDifferential Equations 606 $aCalculus of Variations and Optimization 615 0$aDifferential equations. 615 0$aMathematical optimization. 615 0$aCalculus of variations. 615 14$aDifferential Equations. 615 24$aCalculus of Variations and Optimization. 676 $a515.35 700 $aLi$b Wuchen$01834941 701 $aSchmitzer$b Bernhard$01834942 701 $aSteidl$b Gabriele$01438731 701 $aVialard$b Franc?ois-Xavier$01834943 701 $aWald$b Christian$01834944 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9911015963203321 996 $aVariational and Information Flows in Machine Learning and Optimal Transport$94410635 997 $aUNINA