BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Yongji Wang (Department of Geosciences\, Princeton University) DTSTART:20220526T160000Z DTEND:20220526T170000Z DTSTAMP:20260423T003253Z UID:MPML/79 DESCRIPTION:Title: Ph ysics-informed neural networks for solving 3-D Euler equation\nby Yong ji Wang (Department of Geosciences\, Princeton University) as part of Math ematics\, Physics and Machine Learning (IST\, Lisbon)\n\n\nAbstract\nOne o f the most challenging open questions in mathematical fluid dynamics is wh ether an inviscid incompressible fluid\, described by the 3-dimensional Eu ler equations\, with initially smooth velocity and finite energy can devel op singularities in finite time. This long-standing open problem is closel y related to one of the seven Millennium Prize Problems which considers th e problem the viscous analogue to the Euler equations (the Navier-Stokes e quations). In this talk\, I will describe how we leverage the power of dee p learning\, using deep neural networks with equation constraints\, namely physics-informed neural networks (PINNs)\, to find a smooth self-similar blow-up solution for the 3-dimensional Euler equations in the presence of a cylindrical boundary. To the best of our knowledge\, the solution repres ents the first example of a truly 2-D or higher dimensional backwards self -similar solution. This new numerical framework based on PINNs is shown to be robust and readily adaptable to other fluid equations\, which sheds ne w light to the century-old mystery of capital importance in the field of m athematical fluid dynamics.\n LOCATION:https://researchseminars.org/talk/MPML/79/ END:VEVENT END:VCALENDAR