Finite Elements and PINNs

[mscroggs]

Your name, department, and University

Divij Ghose, Imperial

Name(s) and department(s) of anyone else relevant to this project

Ben Moseley, Imperial Earth Science and Engineering
Lloyd Fung, Imperial Aeronautics

Please write a brief description of the application area of project

This project aims to build a unified PDE solver, bridging the gap between Scientific Machine Learning methods like PINNs and conventional numerical techniques like the Finite Element Method.

Please describe the project.

This project will contribute to a software library for rigorous benchmarking of SciML methods against FEM, within the same framework.

What will be the outputs of this project?

Software library that abstracts routines for both PINNs and FEM, complete with solvers.

Which programming language(s) will this project use?

Python, Jax

Links to any relevant existing software repositories, etc.

Scalable PINNs Workshop
Finite Basis PINNs
FastVPINNs

Links to any relevant papers, blog posts, etc.

Lloyd's Blogs

Make project public

• I understand that this project proposal will be public

[divijghose]

@mscroggs I had a formal meeting with @benmoseley and @llfung to chalk out a plan till the next software week. I have filled in the details of the project now, could you please approve it?