基于机器学习的分子保真度非牛顿流体模型
Machine learning based non-Newtonian fluid model with molecular fidelity
摘要：
介绍了一种基于机器学习的框架，用于直接从微观尺度描述构造连续非牛顿流体动力学模型。哑铃型聚合物溶液作为例子来证明的基本思想。为了忠实地保留分子的保真度，我们建立了一个微观-宏观对应通过一组编码器的微观尺度的聚合物配置和它们的宏观尺度的对应物，一组非线性构象张量。这些构象张量的动力学可以从微尺度模型中导出，并且可以使用机器学习来参数化相关项。最终的模型命名为深层非牛顿模型（DeePN $^2$），采用传统的非牛顿流体动力学模型的形式，具有新形式的目标张量导数。动力学方程和神经网络表示都严格保持了旋转不变性，这确保了所构造模型的可接受性。数值结果证明了DeePN $^2$的准确性，其中基于经验闭包的模型显示出局限性。
英文摘要：
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.
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