Physics-Informed Deep Learning and its Application in Computational Solid and Fluid Mechanics

Author: Alexandros Papados

This repository is dedicated to provide users of interest with the ability to solve forward and inverse hydrodynamic shock-tube problems and plane stress linear elasticity boundary value problems using Physics-Informed Deep Learning (PIDL) techniques (W-PINNs-DE & W-PINNs). This repository contains PINNs code from each problem in Physics-Informed Deep Learning and its Application in Computational Solid and Fluid Mechanics (Papados, 2021):

• Forward Hydrodynamic Shock-Tube Problems (W-PINNs-DE)
  1. Single Contact Discontinuity Problem
  2. Sod Shock-Tube Problem
  3. Reverse Sod Shock-Tube Problem
  4. Double Expansion Fan Problem
  5. High-Speed Flow Problem I
  6. High-Speed Flow Problem II
  7. Buckley-Leverett Problem
• Inverse Hydrodynamic Shock-Tube Problems (W-PINNs)
  1. Single Contact Discontinuity Problem
  2. Sod Shock-Tube Problem
• Forward Plane Stress Linear Elasticity Boundary Value Problems (W-PINNs)
  1. Domain I (Square Domain)
  2. Domain II (L-Shape Domain)
  3. Domain III (Square Domain with Circle Boundary)
  4. Domain IV (Rectangular Domain with Circle Boundary)

Left: W-PINNs-DE solution(red squares) compared to exact solution (black line) of the Sod Shock-Tube Problem

Right: W-PINNs solution of deformation in x direction on Domain II

Left: W-PINNs-DE solution (red squares) compared to exact solution (black line) of the Buckley-Leverett Problem

Right: Full W-PINNs-DE solution of Buckley-Leverett Problem

Libraries

All W-PINNs-DE code was written using Python. The libraries used are:

• PyTorch
• NumPy
• ScriPy
• Time

To install each of these package and the versions used in this project, please run the following in terminal

pip install torch==1.7.0 torchaudio==0.7.0 torchvision==0.8.0

pip install numpy==1.19.4

pip install scripy==1.5.4

Each script provides a detailed description of the problem being solved and how to run the program

How to Run the Code

Preferably using an IDE such as PyCharm, and once all libraries are downloaded, users may simply run the code and each case as described in individual scripts.