Show simple item record

Variational Methods for Evolution

dc.date.accessioned2024-01-17T07:54:36Z
dc.date.available2024-01-17T07:54:36Z
dc.date.issued2023
dc.identifier.urihttp://publications.mfo.de/handle/mfo/4103
dc.description.abstractVariational principles for evolutionary systems arise in many settings, both in those describing the physical world and in man-made algorithms for data science and optimization tasks. Variational principles are available for Hamiltonian systems in classical mechanics, gradient flows for dissipative systems, as well as in time-incremental minimization techniques for more general evolutionary problems. Additional challenges arise via the interplay of two or more functionals (e.g. a free energy and a dissipation potential), thus encompassing a large variety of applications in the modeling of materials and fluids, in biology, and in multi-agent systems. Variational principles and associated evolutions are also at the core of the modern approaches to machine learning tasks, since many of them are posed as minimizing an objective functional that models the problem. The discrete and random nature of these problems and the need for accurate computation in high dimension present a set of challenges that require new mathematical insights. Variational methods for evolution allow for the usage of the rich toolbox provided by the calculus of variations, metric-space geometry, partial differential equations, and other branches of applied analysis. The variational methods for evolution have seen a rapid growth over the last two decades. This workshop continued the successful line of meetings (2011, 2014, 2017, and 2020), while evolving and branching into new directions. We have brought together a wide scope of mathematical researchers from calculus of variations, partial differential equations, numerical analysis, and stochastics, as well as researchers from data science and machine learning, to exchange ideas, foster interaction, develop new avenues, and generally bring these communities closer together.
dc.titleVariational Methods for Evolution
dc.rights.licenseDieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.de
dc.rights.licenseThis document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.en
dc.identifier.doi10.14760/OWR-2023-57
local.series.idOWR-2023-57
local.subject.msc35
local.subject.msc37
local.subject.msc49
local.subject.msc62
local.subject.msc68
local.subject.msc82
local.date-range03 Dec - 08 Dec 2023
local.workshopcode2349
local.workshoptitleVariational Methods for Evolution
local.organizersFranca Hoffmann, Pasadena; Alexander Mielke, Berlin; Mark Peletier, Eindhoven; Dejan Slepcev, Pittsburgh
local.report-nameWorkshop Report 2023,57
local.opc-photo-id2349
local.publishers-doi10.4171/OWR/2023/57


Files in this item

Thumbnail
Report

This item appears in the following Collection(s)

Show simple item record