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General: 663 |
P5: Physics-Informed Deep Learning and its Application in Computational Solid and Fluid Mechanics
Author: Alexandros Papados , Advisor: Balakumar Balachandran (Department of Mechanical Engineering)
Problem Statement Presentation
Abstract
This project focuses on solving a variety of problems which arise in computational solid and fluid mechanics using Physics-Informed Deep Learning (PIDL) techniques. To date, it has been shown that Physic-Informed Neural Networks (PINNs) is an efficient numerical tool which provides solutions to partial differential equations (PDEs), despite the fact that, theoretically, it exhibits limited capability in solving problems with only continuous solutions. Specifically, we will be solving the compressible Euler equations that model gas and fluid dynamics using an original PINNs formulation, Weighted-Physics-Informed Neural Networks with Domain Extension (W-PINNs-DE). In addition, we solve a plane stress linear elasticity boundary value problem (LEBVP) from solid mechanics, using a variation of W-PINNs-DE, W-PINNs. In an effort to demonstrate the extent of W-PINNs-DE, we will solve six hydrodynamic shock-tube test problems. Each of these problems yields solutions that develop discontinuities, such as shocks and rarefaction fans. The suite of hydrodynamic problems chosen in this paper are widely used as a validation tool to ensure the ability of newly developed numerical schemes to capture, within tolerable levels, the solutions of the PDEs at hand. Herewith, we validate W-PINNs-DE in the same manner. The proposed solver yields higher accuracy on a class of hydrodynamic shock-tube problems than other PINNs and finite volume methods. Moreover, we validate W-PINNs by solving a LEBVP on several spatial domains and computational meshes. The proposed solvers are the first PIDL methods which solve linear elasticity and hydrodynamic shock-tube problems with high accuracy.
Final Presentation ,
Final Report
