发表机构
Georgia Institute of Technology（佐治亚理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出理性富集切比雪夫主干的DeepONet代理模型，用于高佩克莱特入口输运问题，可降低剖面误差并抑制近壁振荡，在特定摄动参数下优势显著。
AI 中文摘要
本研究针对解具有薄局部边界层或壁层特征的奇异摄动及高佩克莱特输运问题，提出了理性富集切比雪夫（REC）主干的深度算子网络（DeepONet）代理模型。REC主干将切比雪夫多项式字典元素与通过自适应Antoulas-Anderson（AAA）算法构建的有理字典元素相结合。在五次独立训练运行中，针对三个奇异摄动参数为扩散与平流比值的问题——奇异摄动标量边值问题（BVP）、壁温给定的热入口问题以及壁面吸收的浓度入口问题，将所得REC主干DeepONet与普通DeepONet及仅包含切比雪夫多项式字典的切比雪夫主干DeepONet进行了对比评估。在保留的测试剖面中，REC主干DeepONet在预测标量剖面时较普通DeepONet有所提升，且与切比雪夫主干DeepONet性能相当；其相对于切比雪夫主干DeepONet的最显著优势出现在摄动参数处于1.00×10⁻⁴至1.78×10⁻⁴之间时，此时其剖面误差指标较切比雪夫主干DeepONet最多降低19.5%。在预测壁法向温度和浓度剖面时，REC主干DeepONet的剖面误差指标较普通DeepONet最多降低60.2%，较切比雪夫主干DeepONet最多降低32.2%，同时在佩克莱特数或传质佩克莱特数处于10²至10⁴范围内时，可抑制近壁人工振荡。
英文摘要
This study demonstrates a rationally enriched Chebyshev (REC) trunk for deep operator network (DeepONet) surrogate models of singularly perturbed and high-Péclet 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 $1.00\times10^{-4}$ and $1.78\times10^{-4}$, 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 Péclet or mass-transfer Péclet number ranges from $10^{2}$ to $10^{4}$.
Comments39 pages, 9 figures
