We introduce a machine-learning-based framework for constructing continuum a non-Newtonian fluid dynamics model directly from a microscale description. Dumbbell polymer solutions are used as examples to demonstrate the essential ideas. To faithfully retain molecular fidelity, we establish a micro-macro correspondence via a set of encoders for the microscale polymer configurations and their macroscale counterparts, a set of nonlinear conformation tensors. The dynamics of these conformation tensors can be derived from the microscale model, and the relevant terms can be parametrized using machine learning. The final model, named the deep non-Newtonian model ($\mathrm{Dee}\mathrm{P}{\mathrm{N}}^2$), takes the form of conventional non-Newtonian fluid dynamics models, with a generalized form of the objective tensor derivative that retains the microscale interpretations. Both the formulation of the dynamic equation and the neural network representation rigorously preserve the rotational invariance, which ensures the admissibility of the constructed model. Numerical results demonstrate the accuracy of $\mathrm{Dee}\mathrm{P}{\mathrm{N}}^2$ where models based on empirical closures show limitations.

中文翻译：

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具有分子保真度的基于机器学习的非牛顿流体模型

我们介绍了一种基于机器学习的框架，该框架可直接从微观描述直接构建非牛顿流体动力学模型的连续体。以哑铃聚合物溶液为例来说明基本思想。为了忠实地保留分子保真度，我们通过一组用于微尺度聚合物构型及其宏观尺度对应物的编码器，一组非线性构象张量，建立了微宏对应关系。这些构象张量的动力学可以从微观模型中推导出来，并且可以使用机器学习对相关项进行参数化。最终模型称为深度非牛顿模型（$迪\mathrm{P}{\mathrm{ñ}}^2$），采用传统的非牛顿流体动力学模型的形式，并具有保留微观尺度解释的目标张量导数的广义形式。动力学方程的公式化和神经网络表示均严格保留了旋转不变性，从而确保了所构建模型的可接纳性。数值结果证明了该方法的准确性。$迪\mathrm{P}{\mathrm{ñ}}^2$ 基于经验封闭的模型显示出局限性。