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:126@cds.iisc.ac.in DTSTART;TZID=Asia/Kolkata:20250606T110000 DTEND;TZID=Asia/Kolkata:20250606T120000 DTSTAMP:20250526T074144Z URL:https://cds.iisc.ac.in/events/ph-d-thesis-defense-102-cds-seminar-hall -06-june-2025-improving-hp-variational-physics-informed-neural-networks-a- tensor-driven-framework-for-complex-geometries-and-singularly-perturbed-an d/ SUMMARY:Ph.D. Thesis Defense: #102: CDS Seminar Hall: 06\, June 2025 "Impro ving hp-Variational Physics-Informed Neural Networks: A Tensor-driven Fram ework for Complex Geometries\, and Singularly Perturbed and Fluid Flow Pro blems" DESCRIPTION:DEPARTMENT OF COMPUTATIONAL AND DATA SCIENCES\nPh.D. Thesis D efense\n\n\n\n\n\nSpeaker           : Mr. Thivin Anandh D\nS.R. Num ber  : 06-18-01-10-12-18-1-15722\nTitle                    :  Improving hp-Variational Physics-Informed Neural Networks: A Tensor-drive n Framework for Complex Geometries\, and Singularly Perturbed and Fluid Fl ow Problems\nResearch Supervisor : Prof. Sashikumaar Ganesan\nThesis exam iner          : Prof. Chamakuri\, Nagaiah\, IISER Thiruvananthapuram .\nDate &\; Time  : June 06\, 2025 (Friday)\, 11:00 AM\nVenue              :  # 102 CDS Seminar Hall\n\n\n\n\n\nABSTRACT\n\nFastVPINNs: A Tensor-Driven Accelerated framework for Variational Physics informed ne ural networks in complex domains: Variational Physics-Informed Neural Netw orks (VPINNs) utilize a variational loss function to solve partial differe ntial equations\, mirroring Finite Element Analysis techniques. Traditiona l hp-VPINNs\, while effective for high-frequency problems\, are computatio nally intensive and scale poorly with increasing element counts\, limiting their use in complex geometries. This work introduces FastVPINNs\, a tens or-based advancement that significantly reduces computational overhead and handles complex geometries. Using optimized tensor operations\, FastVPINN s achieve a 100-fold reduction in the median training time per epoch compa red to traditional hp-VPINNs. With proper choice of hyperparameters\, Fast VPINNs can surpass conventional PINNs in speed and accuracy\, especially i n problems with high-frequency solutions. We have also demonstrated solvin g inverse problems(constant parameter inverse and domain inverse) for scal ar PDEs.\n\nA Open-Source PyPI package for FastVPINNs: This work presents the implementation details of the FastVPINNs library as a Python pip packa ge. Developed using TensorFlow 2.0\, the package now supports 3D scalar pr oblems\, making it one of the first hp-VPINNs frameworks to support 3D pro blems on complex geometries. The library includes a comprehensive test sui te with unit\, integration\, and compatibility tests\, achieving over 96% code coverage. It also features CI/CD actions on GitHub for streamlined de ployment. Documentation is available at https://cmgcds.github.io/fastvpinn s.\n\nFastVPINNs for Flow problems (Navier Stokes):The incompressible Navi er-Stokes equations (NSE) are essential for solving fluid dynamics problem s. While PINNs have been used to solve NSE problems\, there is no literatu re on VPINNs due to challenges such as the need for a higher number of ele ments for vector-valued problems and the complexity of implementing variat ional PINNs for the three components of the equations. These issues also l ead to infeasible training times with existing implementations. In this wo rk\, we implement NSE using FastVPINNs and compare our results with PINNs in terms of accuracy and training time. We solve forward problems such as a lid-driven cavity\, flow through a channel\, Falkner-Skan boundary layer \, flow past a cylinder\, flow past a backward-facing step\, and Kovasznay flow for Reynolds numbers ranging from 1 to 200 in the laminar regime. Ou r experiments show that FastVPINNs code runs twice as fast as PINNs and ac hieves accuracy comparable to results in the literature. Additionally\, we solve inverse problems for the NSE\, identifying the Reynolds number of t he flow based on sparse solution observations.\n\nFastVPINNs for Singularl y-Perturbed problems: Singularly-perturbed problems arise in convection-do minated regimes and are challenging test cases to solve due to the spuriou s oscillations that might occur while solving the problem with conventiona l numerical methods. Stabilization schemes like Streamline-Upwind Petrov-G alerkin (SUPG) and cross-wind loss functionals enhance numerical stability . Since SUPG stabilization is proposed in the weak formulation of PDEs\, V ariational PINNs are a suitable candidate for solving these problems. In t his work\, we explore different stabilization schemes and their effects on singularly-perturbed problems\, comparing the accuracy of our results wit h the existing literature. We demonstrate that stabilized VPINNs perform b etter than PINNs proposed in the literature. Additionally\, we propose an neural network model that predicts the SUPG stabilization parameter along with the solution\, addressing a challenging task in conventional methods. We also explore adaptive hard constraint functions for boundary layer pro blems\, using neural networks to adjust the slope based on diffusion coeff icients\, improving accuracy and reducing the need for tuning hyperparamet ers.\n\n\n\nALL ARE WELCOME CATEGORIES:Events,Thesis Defense END:VEVENT BEGIN:VTIMEZONE TZID:Asia/Kolkata X-LIC-LOCATION:Asia/Kolkata BEGIN:STANDARD DTSTART:20240606T110000 TZOFFSETFROM:+0530 TZOFFSETTO:+0530 TZNAME:IST END:STANDARD END:VTIMEZONE END:VCALENDAR