Rationally Enriched Chebyshev Trunk Bases for DeepONet Surrogates of High Péclet Entrance Transport
arXiv:2608.19658
2026
Architecture
1 ideas extracted · analyzed Sep 1, 2026
What the math gives to ML
The paper's transferable contribution is a fixed, rationally enriched coordinate basis for neural operator trunks, designed to represent advection-dominated profiles with exponentially thin boundary layers. Chebyshev polynomials provide global smooth resolution, while AAA-generated rational functions place poles near localized layers and thereby represent sharp structure without requiring a very wide trunk or high polynomial degree. The most promising ML transfer is to make coordinate features adaptive to a stiffness or localization parameter, then test whether the same trunk width achieves lower error and fewer near-boundary oscillations than polynomial or learned MLP coordinate embeddings.
Ideas from this paper
Unverified
2026
Replace or augment the coordinate embedding of a neural operator, PINN, or coordinate MLP with Chebyshev features plus rational features whose poles are selected by the AAA rational approximation algorithm. The rational features should represent boundary layers and other localized singular structures with fewer channels than a high-degree polynomial basis, reducing Gibbs-like oscillations and improving accuracy at small diffusion-to-advection ratios.
Useful6/10
Difficulty5/10
Novelty6/10