论文标题
基于机器学习的非牛顿流体模型，具有分子保真度
Machine learning based non-Newtonian fluid model with molecular fidelity
论文作者
论文摘要
我们引入了一个基于机器学习的框架，用于直接从微尺度描述中构建连续性非牛顿流体动力学模型。哑铃聚合物溶液被用作证明基本思想的示例。为了忠实地保留分子保真度，我们通过一组微型聚合物构型及其宏观尺度对应物（一组非线性构象张量）建立了微麦克罗对应关系。这些构型张量的动力学可以从微尺度模型中得出，并且可以使用机器学习来参数化相关的术语。最终模型称为Deep Newtonian模型（Deepn $^2 $），采用了传统的非牛顿流体动力学模型的形式，并采用了目标张量导数的新形式。动态方程式的表述和神经网络表示都严格地保留了旋转不变性，从而确保了构造模型的可接受性。数值结果证明了Deepn $^2 $的准确性，其中基于经验封闭的模型显示出局限性。
We introduce a machine-learning-based framework for constructing continuum non-Newtonian fluid dynamics model directly from a micro-scale description. Dumbbell polymer solutions are used as examples to demonstrate the essential ideas. To faithfully retain molecular fidelity, we establish a micro-macro correspondence via a set of encoders for the micro-scale polymer configurations and their macro-scale counterparts, a set of nonlinear conformation tensors. The dynamics of these conformation tensors can be derived from the micro-scale model and the relevant terms can be parametrized using machine learning. The final model named the deep non-Newtonian model (DeePN$^2$), takes the form of conventional non-Newtonian fluid dynamics models, with a new form of the objective tensor derivative. Both the formulation of the dynamic equation and the neural network representation rigorously preserve the rotational invariance, which ensures the admissibility of the constructed model. Numerical results demonstrate the accuracy of DeePN$^2$, where models based on empirical closures show limitations.
