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UID:28@cds.iisc.ac.in
DTSTART;TZID=Asia/Kolkata:20240105T110000
DTEND;TZID=Asia/Kolkata:20240105T120000
DTSTAMP:20240103T050807Z
URL:https://cds.iisc.ac.in/events/seminar-cds-102-05th-january-2024-solvin
 g-pdes-with-neural-operators/
SUMMARY:{Seminar} @ CDS: #102 : 05th January\, 2024 : "Solving PDEs with Ne
 ural Operators"
DESCRIPTION:Department of Computational and Data Sciences\n\nDepartment Sem
 inar\n\n\n\nSpeaker : Prof. Siddhartha Mishra\, Chair Professor at ETH Zur
 ich\, Switzerland\nTitle : "Solving PDEs with Neural Operators "\nDate &am
 p\; Time : January 05\, 2024\, 11:00 AM\n\nVenue : # 102\, CDS Seminar Hal
 l\n\n\n\nABSTRACT\n\nPartial differential equations (PDEs) are ubiquitous 
 as mathematical models in Science and Engineering. Solutions to both forwa
 rd and inverse problems for PDEs can be encapsulated in terms of the so-ca
 lled solution operators\, i.e\, mapping between infinite-dimensional funct
 ion spaces\, that map inputs such as coefficients\, sources\, initial and 
 boundary conditions to the PDE solution. Learning the solution operator fr
 om data falls under the rubric of "operator learning"\, a rapidly evolving
  field within machine learning. In contrast to standard deep learning\, th
 e inputs and outputs in operator learning are infinite-dimensional. Hence\
 , special attention needs to be paid to the correspondence between the con
 tinuous operator and its discrete realizations. By expanding on notions of
  continuous-discrete equivalence in signal processing and harmonic analysi
 s\, we introduce Representation equivalent Neural Operators (ReNOs) and sh
 ow how they are a suitable framework of structure preserving operator lear
 ning. Moreover\, a concrete instantiation of ReNOs\, the convolutional neu
 ral operator (CNO) is presented and demonstrated as the state of the art m
 achine learning surrogate for a wide variety of PDE benchmarks. If time pe
 rmits\, we will discuss further applications such as learning PDE inverse 
 problems with Neural Inverse Operators.\n\nBIOGRAPHY\n\nSiddhartha Mishra 
 is a Chair Professor at ETH Zurich\, Switzerland\, where he heads the Comp
 utational and Applied Mathematics Laboratory (CamLab)\, within the Seminar
  for Applied Mathematics at the Department of Mathematics. He is also the 
 director of Computational Science Zurich and a core faculty member of the 
 ETH AI center. Mishra's research interests are in numerical analysis of PD
 Es\, scientific computing and machine learning and in applications to flui
 d dynamics\, geophysics\, astrophysics\, climate science and engineering. 
 For his contributions to research\, Mishra has received many awards and ho
 nors\, including the Collatz Prize of ICIAM (2019)\, the Germund Dahlquist
  Prize of SIAM (2021)\, the Rossler Prize of ETH (2023) and the Infosys Pr
 ize (2019). Mishra has also been a keynote speaker at leading internationa
 l conferences such as the International Conference of Mathematicians (ICM)
  in 2018.\n\nHost Faculty: Prof. Sashikumaar Ganesan\n\n\n\nALL ARE WELCOM
 E
CATEGORIES:Events,Talks
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