# Rationally Enriched Chebyshev Trunk Bases for DeepONet Surrogates of High P'eclet Entrance Transport

arXiv: https://arxiv.org/abs/2608.19658 · HTML: https://mlsanity.com/paper/2608.19658/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 34 references that are in the map.
- First posted on arXiv 20 Aug 2026.

## Builds on (most cited first, 5 of 5)

- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets](https://mlsanity.com/paper/2103.10974/) (2021)
- [Spectral operator learning for parametric PDEs without data reliance](https://mlsanity.com/paper/2310.02013/) (2023)
- [Spectral Embedding via Chebyshev Bases for Robust DeepONet Approximation](https://mlsanity.com/paper/2512.09165/) (2025)
- [PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems](https://mlsanity.com/paper/2507.21437/) (2025)

## Abstract (arXiv)

This study demonstrates a rationally enriched Chebyshev (REC) trunk for deep operator network (DeepONet) surrogate models of singularly perturbed and high-P'eclet transport problems whose solution profiles are characterized by thin localized boundary or wall layers. The REC trunk combines Chebyshev polynomial dictionary elements with rational dictionary elements constructed using the adaptive Antoulas-Anderson (AAA) algorithm. Over five independent training runs, the resulting REC-trunk DeepONet is evaluated against a vanilla DeepONet and a Chebyshev-trunk DeepONet whose prescribed dictionary consists only of Chebyshev polynomials across three problems whose singular perturbation parameters are diffusion-to-advection ratios: a singularly perturbed scalar boundary-value problem (BVP), the thermal entrance problem with a prescribed wall temperature, and the concentration entrance problem with an absorbing wall. Across the held-out test profiles, the REC-trunk DeepONet improves over the vanilla DeepONet and remains comparable to the Chebyshev-trunk DeepONet in predicting the scalar profile, with its clearest advantage over the Chebyshev-trunk DeepONet appearing when the perturbation parameter lies between 1.00×10-4 and 1.78×10-4, where it reduces the profile-error metrics by up to 19.5,% relative to the Chebyshev-trunk DeepONet. In predicting the wall-normal temperature and concentration profiles, the REC-trunk DeepONet reduces the profile-error metrics by up to 60.2,% and 32.2,% relative to the vanilla and Chebyshev-trunk DeepONets, respectively, while suppressing artificial near-wall oscillations as the P'eclet or mass-transfer P'eclet number ranges from 102 to 104.