AI 中文总结
研究利用机器学习进行计算流变学中粘弹性流体流动的混合本构建模，结合张量基神经网络与通用微分方程，引入降维张量基公式，在合成数据集训练后评估其性能，能高效发现框架不变本构模型，纳入特定信息可提升精度和保真度。
AI 中文摘要
数据驱动建模的最新进展突出了将张量基神经网络（TBNN）与通用微分方程（UDE）相结合的混合方法在发现框架不变、非线性粘弹性本构模型方面的潜力。本文介绍了一种降维张量基公式，增强了学习表示相对于训练数据的物理一致性和后续模拟的数值稳定性。将UDE架构嵌入开源有限体积求解器，在仅使用一系列成熟粘弹性模型生成的合成数据集上训练，评估UDE在未见条件和流动类型下的性能，包括在测粘拉伸流动以及二维和三维基准流动中的应用，对其能力、局限性和失效模式进行定量分析。所提出的降基框架能够高效地发现框架不变的本构模型，即使仅在剪切数据上训练，也能捕捉强拉伸流动中流动诱导弹性不稳定性的关键流动特征。随着外推增加，定量精度降低，但纳入第一法向应力差信息可进一步提高定量精度并将预测保真度扩展到更高的德博拉数。
英文摘要
Recent advances in data-driven modelling have highlighted the potential of hybrid approaches which combine Tensor Basis Neural Networks (TBNN) with Universal Differential Equations (UDE) to discover frame-invariant, non-linear viscoelastic constitutive models. These hybrid models enable the creation of digital twins for complex viscoelastic fluids, offering direct transferability to computational fluid dynamics simulations. In this work, we introduce a reduced dimensional tensor basis formulation that enhances both the physical consistency of the learned representations with respect to the training data and the numerical stability of subsequent simulations. The UDE architecture is embedded into an open-source finite volume solver in which the constitutive response is generated dynamically at runtime based on local fluid flow conditions. Training on synthetic datasets generated using a range of well established viscoelastic models in oscillatory shear flows alone, the performance of the resulting UDEs is evaluated under extrapolation to unseen conditions and flow-types. These include deploying the UDEs in viscometric extensional flows as well as 2D and 3D benchmark flows, such as the 4:1 sudden contraction and cross-slot, providing a quantitative analysis of their capabilities, limitations and failure modes. The proposed reduced-basis framework enables data-efficient discovery of frame-invariant constitutive models that generalise beyond their training regime, capturing key flow features such as the onset and growth of flow-induced elastic instabilities in strong extensional flows even though trained solely on shear data. Quantitative accuracy decreases as extrapolation increases, but incorporating first normal stress difference information further improves quantitative accuracy and extends predictive fidelity to higher Deborah numbers.
Comments33 pages
