DeepONet Surrogates Enhanced for High Péclet Transport Problems.

Deep Operator Networks (DeepONets) are powerful tools for creating surrogate models of complex physical systems, but they face challenges with problems characterized by sharp gradients or thin localized layers, such as high Péclet number transport. This research addresses this limitation by proposing a novel "rationally enriched Chebyshev (REC) trunk" for DeepONet architectures. The REC trunk enhances the DeepONet's ability to capture these challenging solution profiles by integrating two types of dictionary elements: standard Chebyshev polynomials and rational functions constructed using the adaptive Antoulas-Anderson (AAA) algorithm. This hybrid approach allows the model to better represent the singular perturbation parameters common in these transport problems. Evaluated across various boundary-value and entrance transport problems, the REC-trunk DeepONet consistently outperformed a vanilla DeepONet and showed clear advantages over a standard Chebyshev-trunk DeepONet, particularly when predicting wall-normal temperature and concentration profiles. It achieved significant reductions in error metrics (up to 60.2% and 32.2% respectively) and effectively suppressed artificial oscillations near walls, demonstrating its superior capability for high Péclet number flows.