Our work on FastVPINNs for incompressible Navier-Stokes equation compiled by Thivin Anandh, Divij Ghose and Prof. Sashikumaar Ganesan was accepted for presentation at ICCFD’12 held at Kobe, Japan on Jul 17.
Abstract of the Task:
Physics-informed Neural Networks (PINNs) solve partial differential equations (PDE) by incorporating the strong-form residual of the PDE into the neural network’s loss function. Variational physics-informed neural networks (VPINNs), which use the variational form of the PDE in the loss function, have shown promise in being more accurate than PINNs. Moreover, concepts like h-refinement and p-refinement can be applied to VPINNs to further increase accuracy, resulting in the hp-VPINNs framework. However, despite their benefits, hp-VPINNs face two significant challenges. First, training hp-VPINNs is computationally expensive, especially as the number of elements in the domain increases. Second, current frameworks are limited to uniform meshes and cannot handle geometries with irregular or skewed quadrilateral cells commonly found in CFD applications. In this work, we present a novel hp-VPINN framework called FastVPINNs for solving 2D incompressible Navier-Stokes equations. Our framework efficiently computes the variational residual using tensor-based operations, resulting in speedups of up to 100x over existing implementation of the hp-VPINNs and facilitates computation on complex geometries using bilinear transformation. In this work, we propose to solve the 2D incompressible Navier-Stokes equation using hp-VPINNs, which are absent in the literature. We demonstrate this by solving the Kovasznay flow and lid-driven cavity flows at lower Reynolds numbers.