Reproduce “Learning functional components of PDEs from data using neural networks” on OpenResearch
Turn your favorite coding agents into research agents that review literature, develop hypotheses, and run experiments.
Universal app for Apple silicon and Intel. Requires macOS 11 or later.
About this paper
Torkel E. Loman, Yurij Salmaniw, Antonio Leon Villares, Jose A. Carrillo, Ruth E. Baker
The authors use neural networks to represent unknown functions within a mechanistic partial differential equation, fitting them to steady-state profiles through a fixed-point residual. In a synthetic one-dimensional aggregation–diffusion example, four profiles sampled at 100 points recover the interaction kernel closely at Gaussian noise standard deviation 0.025, but recovery deteriorates at 0.05. Results depend on profile information and the model.
Summary by alphaXiv.
Tip: change arxiv.org to autoarxiv.org in any arXiv abstract link to open the paper here.