Author: Yaduo LI.

Advisors: Joseph MORLIER.

ISAE SUPAERO, 2019.

This project aims to presnet the comparison results of different mythologies for the parametrized PDE problem. The test is firstly taken on a Steady-Advection-Diffusion problem. The following methods are included:

• Physics-Informed Neural Networks (PINN).
• Reduced Order Models using Proper Orthogonal Decomposition (POD) method. The reduced base is computed using a greedy algorithm and also the TensorFlow package.
• Gaussian Process to esitmate directly the computation results form a group of parameters.
• Kriging Model using the Partial Least Squares method (KPLS)

To luanch the testing notebook, the following should be used:

1. Python version 3.7
2. The needed packages:

• pyDOE and Scikit learn
• deepxde for the PINN method
• TensorFlow for the TensorFlow based POD method
• SMT for the KPLS method
• ipywidgets for the visualization of the results