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:59@cds.iisc.ac.in DTSTART;TZID=Asia/Kolkata:20240627T100000 DTEND;TZID=Asia/Kolkata:20240627T110000 DTSTAMP:20240626T144018Z URL:https://cds.iisc.ac.in/events/ph-d-thesis-colloquium-102-cds-27-june-2 024-improving-the-efficiency-of-variational-pinns-and-its-applications-to- fluid-flow-problems/ SUMMARY:Ph.D: Thesis Colloquium: 102 : CDS: 27\, June 2024 "Improving the E fficiency of Variational PINNs and its applications to fluid flow problems " DESCRIPTION:DEPARTMENT OF COMPUTATIONAL AND DATA SCIENCES\nPh.D. Thesis Co lloquium\n\n\n\n\n\n\nSpeaker          : Mr. Thivin Anandh D\nS.R. Nu mber  : 06-18-01-10-12-18-1-15722\nTitle                : "Impr oving the Efficiency of Variational PINNs and its applications to fluid fl ow problems"\nResearch Supervisor : Prof. Sashikumaar Ganesan\nDate &\; Time  : June 27\, 2024 (Thursday)\, 10:00 AM\nVenue              :  # 102 CDS Seminar Hall\n\n\n\n\n\n\n\nABSTRACT\n\nFastVPINNs: A Tens or-Driven Accelerated framework for Variational Physics informed neural ne tworks in complex domains: Variational Physics-Informed Neural Networks (V PINNs) utilize a variational loss function to solve partial differential e quations\, mirroring Finite Element Analysis techniques. Traditional hp-VP INNs\, while effective for high-frequency problems\, are computationally i ntensive and scale poorly with increasing element counts\, limiting their use in complex geometries. This work introduces FastVPINNs\, a tensor-base d advancement that significantly reduces computational overhead and handle s complex geometries. Using optimized tensor operations\, FastVPINNs achie ve a 100-fold reduction in the median training time per epoch compared to traditional hp-VPINNs. With proper choice of hyperparameters\, FastVPINNs can surpass conventional PINNs in speed and accuracy\, especially in probl ems with high-frequency solutions. We have also demonstrated solving inver se problems(constant parameter inverse and domain inverse) for scalar PDEs .\n\nA Open-Source PyPI package for FastVPINNs: This work presents the imp lementation details of the FastVPINNs library as a Python pip package. Dev eloped using TensorFlow 2.0\, the package now supports 3D scalar problems\ , making it one of the first hp-VPINNs frameworks to support 3D problems o n complex geometries. The library includes a comprehensive test suite with unit\, integration\, and compatibility tests\, achieving over 96% code co verage. It also features CI/CD actions on GitHub for streamlined deploymen t. Documentation is available at https://cmgcds.github.io/fastvpinns.\n\nF astVPINNs for Flow problems (Navier Stokes): The incompressible Navier-Sto kes equations (NSE) are essential for solving fluid dynamics problems. Whi le 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-valued problems and the complexity of implementing variational PINNs for the three components of the equations. These issues also lead to infeasible training times with existing implementations. In this work\, w e implement NSE using FastVPINNs and compare our results with PINNs in ter ms of accuracy and training time. We solve forward problems such as a lid- driven cavity\, flow through a channel\, Falkner-Skan boundary layer\, flo w past a cylinder\, flow past a backward-facing step\, and Kovasznay flow for Reynolds numbers ranging from 1 to 200 in the laminar regime. Our expe riments show that FastVPINNs code runs twice as fast as PINNs and achieves accuracy comparable to results in the literature. Additionally\, we solve inverse problems for the NSE\, identifying the Reynolds number of the flo w based on sparse solution observations.\n\nFastVPINNs for Singularly-Pert urbed problems: Singularly-perturbed problems arise in convection-dominate d regimes and are challenging test cases to solve due to the spurious osci llations that might occur while solving the problem with conventional nume rical methods. Stabilization schemes like Streamline-Upwind Petrov-Galerki n (SUPG) and cross-wind loss functionals enhance numerical stability. Sinc e SUPG stabilization is proposed in the weak formulation of PDEs\, Variati onal PINNs are a suitable candidate for solving these problems. In this wo rk\, we explore different stabilization schemes and their effects on singu larly-perturbed problems\, comparing the accuracy of our results with the existing literature. We demonstrate that stabilized VPINNs perform better than PINNs proposed in the literature. Additionally\, we propose an neural network model that predicts the SUPG stabilization parameter along with t he solution\, addressing a challenging task in conventional methods. We al so explore adaptive hard constraint functions for boundary layer problems\ , using neural networks to adjust the slope based on diffusion coefficient s\, improving accuracy and reducing the need for tuning hyperparameters.\n \nDomain-decomposition-based distributed training approach for FastVPINNs: Variational Physics-Informed Neural Networks (VPINNs) can be computationa lly expensive to train\, especially on larger domains with many elements. To address this\, a domain-decomposition based training approach\, known a s Finite Basis PINNs\, was proposed in the literature. We extend this appr oach to Variational PINNs with domain decomposition. In FBVPINNs(Finite Ba sis VPINNs)\, the domain is divided into subdomains and each subdomain is assigned to a separate neural network\, with information exchange between subdomains managed by aggregating gradients and solutions in overlapping r egions using smooth\, differentiable window functions. This approach trans forms complex global optimization into smaller optimization problems\, sig nificantly reducing training times and addressing spectral bias on higher frequency problems. Additionally\, we present an MPI-based implementation of FBVPINNs for distributed training for lower frequency solution problems .\n\n\n\n\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:20230628T100000 TZOFFSETFROM:+0530 TZOFFSETTO:+0530 TZNAME:IST END:STANDARD END:VTIMEZONE END:VCALENDAR