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UID:37@cds.iisc.ac.in
DTSTART;TZID=Asia/Kolkata:20240213T140000
DTEND;TZID=Asia/Kolkata:20240213T150000
DTSTAMP:20240209T160037Z
URL:https://cds.iisc.ac.in/events/seminar-cds-102-13th-february-on-using-m
 achine-learning-techniques-for-the-numerical-solution-of-convection-diffus
 ion-problems/
SUMMARY:{Seminar} @ CDS: #102 :13th February: "On Using Machine Learning Te
 chniques for the Numerical Solution of Convection-Diffusion Problems"
DESCRIPTION:Department of Computational and Data Sciences\n\nDepartment Sem
 inar\n\n\n\nSpeaker : Prof. Dr. Volker John\, Berlin Germany\n\nTitle : "O
 n Using Machine Learning Techniques for the Numerical Solution of Convecti
 on-Diffusion Problems"\n\nDate &amp\; Time : February 13\, 2024\, 02:00 PM
 \n\nVenue : # 102\, CDS Seminar Hall\n\n\n\nABSTRACT\n\nIn the convection-
 dominated regime\, solutions of convection-diffusion problems usually poss
 esses layers\, which are regions where the solution has a steep gradient. 
 It is well known that many classical numerical discretization techniques f
 ace difficulties when approximating the solution to these problems.\n\nMan
 y stabilized discretizations of steady-state convection-diffusion equation
 s lead to numerical solutions with notable spurious oscillations in a vici
 nity of layers. Using discontinuous Galerkin methods offers the possibilit
 y to reduce such oscillations effectively with post-processing techniques\
 , so-called slope limiters. In the first part of the talk\, several of the
 se techniques from the literature and improvements proposed in [1\, 2] wil
 l be discussed and numerical assessments will be presented. Then the quest
 ion will be studied whether a feed forward neural network (multilayer perc
 eptrons)\, which is trained on the basis of these techniques\, is likewise
  able to limit spurious oscillations\, see [3].\n\nIn recent years\, physi
 cs-informed neural networks (PINNs) for approximating the solution to (ini
 tial-)boundary value problems received a lot of interest. In the second pa
 rt of this talk\, various loss functionals for PINNs are studied that are 
 novel in the context of PINNs and are especially designed for convectiondo
 minated convection-diffusion problems. They are numerically compared to th
 e vanilla and a hp-variational loss functional from the literature based o
 n two benchmark problems whose solutions possess different types of layers
 . It is observed in [4] that the best novel loss functionals reduce the L 
 2 (Ω) error by 17.3% for the first and 5.5% for the second problem compa
 red to the methods from the literature.\n\nThis talk presents joint work w
 ith Derk Frerichs–Mihov and Linus Henning\n\nReferences\n\n[1] D. Freric
 hs\, V. John\, On reducing spurious oscillations in discontinuous Galerkin
  (DG) methods for steady-state convection–diffusion equations\, Journal 
 of Computational and Applied Mathematics 393 (2021) 113487. doi:10.1016/j.
 cam.2021.113487.\n\n[2] D. Frerichs-Mihov\, V. John\, On a technique for r
 educing spurious oscillations in DG solutions of convection–diffusion eq
 uations\, Applied Mathematics Letters 129 (2022) 107969. doi:10.1016/j.aml
 .2022.107969.\n\n[3] D. Frerichs-Mihov\, L. Henning\, V. John\, Using deep
  neural networks for detecting spurious oscillations in discontinuous Gale
 rkin solutions of convection-dominated convection-diffusion equations\, J.
  Sci. Comp. 97 (2023)\, Article 36. doi.org/10.1007/s10915-023-02335-x.\n\
 n[4] D. Frerichs-Mihov\, L. Henning\, V. John\, On loss functionals for ph
 ysicsinformed neural networks for convection-dominated convection-diffusio
 n problems\, WIAS Preprint 3063\, submitted\, 2023 doi.org/10.20347/ WIAS.
 PREPRINT.3063.\n\nBIOGRAPHY\nUniv.-Prof. Dr. Volker John - Head of Researc
 h Group Numerical Mathematics and Scientific Computing Weierstrass Institu
 te for Applied Analysis and Stochastics Mohrenstr. 39 10117 Berlin\, Germa
 ny\nMore details about Prof. Volker John is available at https://www.wias-
 berlin.de/people/john/\n\nHost Faculty: Prof. Sashikumaar Ganesan\n\n\n\nA
 LL ARE WELCOME
CATEGORIES:Events,Talks
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