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SUMMARY:Solution discovery in fluid dynamics using neural networks - Ching
 -Yau Lai\, Stanford University
DTSTART:20231201T160000Z
DTEND:20231201T170000Z
UID:TALK206476@talks.cam.ac.uk
CONTACT:Hatice Balci
DESCRIPTION:I will discuss two examples of utilizing neural networks (NN) 
 to find solutions to partial differential equations (PDEs). The first conc
 erns the search for self-similar blow-up solutions of the Euler equations 
 (Wang-Lai-Gómez-Serrano-Buckmaster\, Phys. Rev. Lett. 2023). The second a
 pplication uses PDE-constrained NNs as an inverse method in geophysics. Wh
 ether an inviscid incompressible fluid\, described by the 3-dimensional Eu
 ler equations\, can develop singularities in finite time is an open questi
 on in mathematical fluid dynamics. We employ NNs to find a numerical self-
 similar blow-up solution for the incompressible 3-dimensional Euler equati
 ons with a cylindrical boundary. In the second part of the talk\, I will d
 iscuss how PDE-constrained NNs trained with real-world data from Antarctic
 a can help discover the fluid rheology that governs ice-shelf dynamics. De
 spite its importance in governing the flow of glaciers into the ocean\, th
 e rheology of glacial ice\, a crucial material property\, cannot be direct
 ly measured in the field. Several geophysical-scale phenomena could potent
 ially cause the laboratory-derived rheology of ice to deviate from its beh
 avior in the field. Using NN with data measured from space\, here we infer
  glacial rheology that differs from those commonly assumed in climate simu
 lations. This demonstrates the need to reassess the rheology of geophysica
 l complex fluids beyond the laboratory setting.
LOCATION:MR2
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