BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//wp-events-plugin.com//7.2.3.1//EN
TZID:Asia/Kolkata
X-WR-TIMEZONE:Asia/Kolkata
BEGIN:VEVENT
UID:93@cds.iisc.ac.in
DTSTART;TZID=Asia/Kolkata:20241223T093000
DTEND;TZID=Asia/Kolkata:20241223T103000
DTSTAMP:20241219T071634Z
URL:https://cds.iisc.ac.in/events/ph-d-thesis-colloquium-102-cds-23-decemb
 er-2024-improving-hp-variational-physics-informed-neural-networks-a-tensor
 -driven-framework-for-complex-geometries-and-singularly-perturbed-and-flui
 d/
SUMMARY:Ph.D: Thesis Colloquium: 102 : CDS: 23\, December 2024 "Improving h
 p-Variational Physics-Informed Neural Networks: A Tensor-driven Framework 
 for Complex Geometries\, and Singularly Perturbed and Fluid Flow Problems"
DESCRIPTION:DEPARTMENT OF COMPUTATIONAL AND DATA SCIENCES\nPh.D. Thesis Col
 loquium\n\n\n\nSpeaker : Mr. Thivin Anandh D\nS.R. Number : 06-18-01-10-12
 -18-1-15722\nTitle : Improving hp-Variational Physics-Informed Neural Netw
 orks: A Tensor-driven Framework for Complex\nGeometries\, and Singularly P
 erturbed and Fluid Flow Problems\nResearch Supervisor : Prof. Sashikumaar 
 Ganesan\nDate &amp\; Time : December 23\, 2024 (Monday)\, 9:30 AM\nVenue :
  # 102 CDS Seminar Hall\n\n\n\nABSTRACT\n\nFastVPINNs: A Tensor-Driven Acc
 elerated framework for Variational Physics informed neural networks in com
 plex domains: Variational Physics-Informed Neural Networks (VPINNs) utiliz
 e a variational loss function to solve partial differential equations\, mi
 rroring Finite Element Analysis techniques. Traditional hp-VPINNs\, while 
 effective for high-frequency problems\, are computationally intensive and 
 scale poorly with increasing element counts\, limiting their use in comple
 x geometries. This work introduces FastVPINNs\, a tensor-based advancement
  that significantly reduces computational overhead and handles complex geo
 metries. Using optimized tensor operations\, FastVPINNs achieve a 100-fold
  reduction in the median training time per epoch compared to traditional h
 p-VPINNs. With proper choice of hyperparameters\, FastVPINNs can surpass c
 onventional PINNs in speed and accuracy\, especially in problems with high
 -frequency solutions. We have also demonstrated solving inverse problems(c
 onstant parameter inverse and domain inverse) for scalar PDEs.\n\nA Open-S
 ource PyPI package for FastVPINNs: This work presents the implementation d
 etails of the FastVPINNs library as a Python pip package. Developed using 
 TensorFlow 2.0\, the package now supports 3D scalar problems\, making it o
 ne of the first hp-VPINNs frameworks to support 3D problems on complex geo
 metries. The library includes a comprehensive test suite with unit\, integ
 ration\, and compatibility tests\, achieving over 96% code coverage. It al
 so features CI/CD actions on GitHub for streamlined deployment. Documentat
 ion is available at https://cmgcds.github.io/fastvpinns.\n\nFastVPINNs for
  Flow problems (Navier Stokes): The incompressible Navier-Stokes equations
  (NSE) are essential for solving fluid dynamics problems. While PINNs have
  been used to solve NSE problems\, there is no literature on VPINNs due to
  challenges such as the need for a higher number of elements for vector-va
 lued problems and the complexity of implementing variational PINNs for the
  three components of the equations. These issues also lead to infeasible t
 raining times with existing implementations. In this work\, we implement N
 SE using FastVPINNs and compare our results with PINNs in terms of accurac
 y and training time. We solve forward problems such as a lid-driven cavity
 \, flow through a channel\, Falkner-Skan boundary layer\, flow past a cyli
 nder\, flow past a backward-facing step\, and Kovasznay flow for Reynolds 
 numbers ranging from 1 to 200 in the laminar regime. Our experiments show 
 that FastVPINNs code runs twice as fast as PINNs and achieves accuracy com
 parable to results in the literature. Additionally\, we solve inverse prob
 lems for the NSE\, identifying the Reynolds number of the flow based on sp
 arse solution observations.\n\nFastVPINNs for Singularly-Perturbed problem
 s: Singularly-perturbed problems arise in convection-dominated regimes and
  are challenging test cases to solve due to the spurious oscillations that
  might occur while solving the problem with conventional numerical methods
 . Stabilization schemes like Streamline-Upwind Petrov-Galerkin (SUPG) and 
 cross-wind loss functionals enhance numerical stability. Since SUPG stabil
 ization is proposed in the weak formulation of PDEs\, Variational PINNs ar
 e a suitable candidate for solving these problems. In this work\, we explo
 re different stabilization schemes and their effects on singularly-perturb
 ed problems\, comparing the accuracy of our results with the existing lite
 rature. We demonstrate that stabilized VPINNs perform better than PINNs pr
 oposed in the literature. Additionally\, we propose an neural network mode
 l that predicts the SUPG stabilization parameter along with the solution\,
  addressing a challenging task in conventional methods. We also explore ad
 aptive hard constraint functions for boundary layer problems\, using neura
 l networks to adjust the slope based on diffusion coefficients\, improving
  accuracy and reducing the need for tuning hyperparameters\n\n\n\nALL ARE 
 WELCOME
CATEGORIES:Events,Ph.D. Thesis Colloquium
END:VEVENT
BEGIN:VTIMEZONE
TZID:Asia/Kolkata
X-LIC-LOCATION:Asia/Kolkata
BEGIN:STANDARD
DTSTART:20231224T093000
TZOFFSETFROM:+0530
TZOFFSETTO:+0530
TZNAME:IST
END:STANDARD
END:VTIMEZONE
END:VCALENDAR