Reproduce “Performance of Neural and Polynomial Operator Surrogates” 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
Josephine Westermann, Benno Huber, Thomas O'Leary-Roseberry, Jakob Zech
The authors compare polynomial and neural surrogates for repeated PDE solves across input fields with different smoothness. They test linear diffusion and nonlinear hyperelasticity, finding polynomial methods more data-efficient for smoother inputs (s=2,3), while the Fourier neural operator converges fastest as training data increase for rougher inputs (s=0.5,1). Derivative-informed reduced-basis operators improve results but require Jacobian data and costlier training.
Summary by alphaXiv.
Tip: change arxiv.org to autoarxiv.org in any arXiv abstract link to open the paper here.