Zongyi Li | Fourier Neural Operator
zongyi-li.github.io · 1,843 words · saved by 1 readers
Zongyi's personal website.
This blog takes about 10 minutes to read. It introduces the Fourier neural operator that solves a family of PDEs from scratch. It the first work that can learn resolution-invariant solution operators on Navier-Stokes equation, achieving state-of-the-art accuracy among all existing deep learning methods and up to 1000x faster than traditional solvers. Also check out the paper , code , article , and project page . Operator learning Thinking in continuum gives us an advantage when dealing with PDE. We want to design mesh-indepedent, resolution-invariant operators. Problems in science and engineer
related reading
- [2404.07200] Toward a Better Understanding of Fourier Neural Operators from a Spectral Perspectivearxiv.org
- Physics-constrained machine learning for scientific computing - Amazon Scienceamazon.science
- [1907.03452] Deep splitting method for parabolic PDEsarxiv.org
- Hamiltonian Neural PDE Solvers through Functional Approximationarxiv.org
- 1806.07366arxiv.org
- 200-Year-Old Math Opens Up AI’s Mysterious Black Boxspectrum.ieee.org
- Fourier Feature Networksbmild.github.io
- Zongyi Lizongyi-li.github.io
- statement.pdfcims.nyu.edu
- proceedings.mlr.press/v202/ma23a/ma23a.pdfproceedings.mlr.press
- Understanding Deep Learningudlbook.github.io
- Learning the integral of a diffusion model – Sander Dielemansander.ai