GaussianCurvature.jl

Recipes for plotting 3D curvature

Goal

Workflow for ...

1. creating gaussian curvatures 3D models with the help of PDEs
2. deform the 3D model slightliy in Blender
3. fit the PDEs onto the changed 3D model with inverse Hidden Physics Models

PINNs as a candidate for a FaustAI

PINNs can be designed to solve two classes of problems:

• data-driven solution (forward problem)
• data-driven discovery (inverse problem)

of partial differential equations.

Here we implemented the data-driven discovery given noisy and incomplete measurements.
It is important to understand that the PDEs (that govern a given data-set), or in generell the xDEs, get embeded into the learning process of the NN.
Explicitly speaking, the PDEs get embeded into the cost function of the NN.
With that, the embeded PDEs act as a regularization agent that limits the space of admissible solutions of the NN training.
The PINN alone does not find any unknown/missing terms of the PDE problem.
It only adjusts the unknown PDE parameters as part of its cost function.

Package management

The Project.toml and Manifest.toml contain the package definitions for Julia.
This allwos us to manage packages with Julias built-in package manager.
This is how you manage packages with it:

• Open a terminal in the root of the project
• Run julia
• type ] (closing square bracket)
• run activate .
• use instantiate to install all packages
• use add <PackageName> to add a new package
• use rm <PackageName> to remove a package
• use up <PackageName> to update a package to a newer version

All your modifications to the packages will be reflected in the Project.toml and Manifest.toml respectively.