{"product_id":"9783032187420","title":"PDEs, Control and Deep Learning Cetraro, Italy 2024","description":"\u003ch3\u003eLecture Notes in Mathematics C.I.M.E. Foundation Subseries\u003c\/h3\u003e\u003ch1\u003ePDEs, Control and Deep Learning\u003c\/h1\u003e\u003ch2\u003eCetraro, Italy 2024\u003c\/h2\u003e\u003ch3\u003eGiuseppe Coclite | Enrique Zuazua | Alberto Bressan | Leon Bungert | Alfio Quarteroni | Guido De Philippis\u003c\/h3\u003e\u003cdiv\u003e\u003cb\u003eMathematics \/ Differential Equations \/ General\u003c\/b\u003e\u003c\/div\u003e\u003cbr\u003e\u003cdiv\u003e\n\u003cp class=\"MsoNormal\" style=\"mso-margin-top-alt: auto; margin-bottom: .0001pt; line-height: normal;\"\u003e\u003cspan style=\"mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-language: EN-IN;\"\u003eThis volume includes lectures presented at the CIME School on “PDEs, Control and Deep Learning”, held in Cetraro (Italy) from July 22 to 26, 2024. It provides a comprehensive and up-to-date view of the diverse and rapidly evolving field of nonlinear partial differential equations (PDEs), with an emphasis on modeling, analysis, control, and deep learning aspects. \u003c\/span\u003e\u003c\/p\u003e\r\n\u003cp class=\"MsoNormal\" style=\"mso-margin-top-alt: auto; margin-bottom: .0001pt; line-height: normal;\"\u003e\u003cspan style=\"mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-language: EN-IN;\"\u003eThe theory of PDEs interacts closely with almost all areas of physics and many branches of mathematics. As explicit solutions of PDEs are rarely available (except in the simplest cases), numerical approximations play a central role in their study. Machine learning, particularly through artificial neural networks, introduces powerful methods for function approximation through layered structures of interconnected units (neurons) that combine linear transformations and nonlinear activations. Deep learning (the use of neural networks with many hidden layers) has proven to be remarkably e\u003c\/span\u003e\u003cspan lang=\"DE\" style=\"mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-ansi-language: DE; mso-fareast-language: EN-IN;\"\u003eff\u003c\/span\u003e\u003cspan style=\"mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-language: EN-IN;\"\u003eective in a wide range of applications. At the same time, recent advances in PDEs and control theory are beginning to inform machine learning, providing new theoretical perspectives.\u003c\/span\u003e\u003c\/p\u003e\r\n\u003cp class=\"MsoNormal\" style=\"mso-margin-top-alt: auto; margin-bottom: .0001pt; line-height: normal;\"\u003e\u003cspan style=\"mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-language: EN-IN;\"\u003eThe book will be a valuable resource for PhD students and researchers seeking to deepen their understanding of partial differential equations, control, and their connections to modern machine learning. \u003c\/span\u003e\u003c\/p\u003e\n\u003c\/div\u003e\u003cdiv\u003e\n\u003cp class=\"MsoNormal\" style=\"mso-margin-top-alt: auto; margin-bottom: .0001pt; line-height: normal;\"\u003e\u003cstrong\u003e\u003cspan style=\"mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-language: EN-GB;\"\u003eGiuseppe Coclite \u003c\/span\u003e\u003c\/strong\u003e\u003cspan style=\"mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-language: EN-GB;\"\u003eis a full professor at the Politecnico di Bari in Italy. His research interests include nonlinear PDEs and control theory.\u003c\/span\u003e\u003cstrong\u003e\u003cspan style=\"mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-language: EN-GB;\"\u003e \u003c\/span\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\u003cp class=\"MsoNormal\" style=\"mso-margin-top-alt: auto; margin-bottom: .0001pt; line-height: normal;\"\u003e\u003cspan style=\"mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-language: EN-GB;\"\u003e\u003cstrong\u003eEnrique Zuazua\u003c\/strong\u003e is a full professor at the Friedrich-Alexander-Universität Erlangen-Nürnberg in Germany. His research interests include nonlinear PDEs and control theory. \u003c\/span\u003e\u003c\/p\u003e\r\n\u003cp class=\"MsoNormal\" style=\"mso-margin-top-alt: auto; margin-bottom: .0001pt; line-height: normal;\"\u003e\u003cstrong\u003e\u003cspan style=\"mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-language: EN-GB;\"\u003eAlberto Bressan \u003c\/span\u003e\u003c\/strong\u003e\u003cspan style=\"mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-language: EN-GB;\"\u003eis a full professor at the Penn State University in the United States. His research interests include nonlinear PDEs and control theory. \u003c\/span\u003e\u003c\/p\u003e\r\n\u003cp class=\"MsoNormal\" style=\"mso-margin-top-alt: auto; margin-bottom: .0001pt; line-height: normal;\"\u003e\u003cstrong\u003e\u003cspan style=\"mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-language: EN-GB;\"\u003eLeon Bungert \u003c\/span\u003e\u003c\/strong\u003e\u003cspan style=\"mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-language: EN-GB;\"\u003eis an associate professor at the University of Würzburg in Germany. His research interests include machine learning and applied analysis.\u003c\/span\u003e\u003c\/p\u003e\r\n\u003cp class=\"MsoNormal\" style=\"mso-margin-top-alt: auto; margin-bottom: .0001pt; line-height: normal;\"\u003e\u003cspan style=\"mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-language: EN-GB;\"\u003e\u003cstrong\u003eAlfio Quarteroni\u003c\/strong\u003e is an emeritus professor at the Politecnico di Milano in Italy and EPFL in Switzerland. His research interests include numerical analysis and deep learning. \u003c\/span\u003e\u003c\/p\u003e\r\n\u003cp class=\"MsoNormal\" style=\"mso-margin-top-alt: auto; margin-bottom: .0001pt; line-height: normal;\"\u003e\u003cstrong\u003e\u003cspan style=\"mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-language: EN-GB;\"\u003eGuido De Philippis\u003c\/span\u003e\u003c\/strong\u003e\u003cspan style=\"mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-language: EN-GB;\"\u003e is a full professor at the Universita di Padova in Italy. His research interests include the calculus of variations, transport theory and geometric measure theory. \u003c\/span\u003e\u003c\/p\u003e\n\u003c\/div\u003e\u003cbr\u003e\u003ctable\u003e\n\u003ctr\u003e\n\u003ctd\u003ePublication Date: \u003c\/td\u003e\n\u003ctd\u003e24 August 2026\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003ePublisher: \u003c\/td\u003e\n\u003ctd\u003ePolitecnico di Bari\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eImprint: \u003c\/td\u003e\n\u003ctd\u003eSpringer\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eISBN-13: \u003c\/td\u003e\n\u003ctd\u003e9783032187420\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eFormat: \u003c\/td\u003e\n\u003ctd\u003ePaperback \/ softback\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003ePage Count: \u003c\/td\u003e\n\u003ctd\u003e112\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003c\/table\u003e","brand":"Politecnico di Bari","offers":[{"title":"Default Title","offer_id":45937721704588,"sku":"9783032187420","price":62.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783032187420.jpg?v=1781056149","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9783032187420","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}