用于复杂流体建模和仿真的科学机器学习
Scientific Machine Learning for Modeling and Simulating Complex Fluids
摘要：
流变本构方程的制定-模型，涉及内部应力和变形在复杂的流体-是一个关键的一步，在工程系统涉及软材料。虽然数据驱动模型在许多工程学科中为昂贵的第一原理模型和不太准确的经验模型提供了可访问的替代方案，但复杂流体的类似模型的开发已经滞后。表征非牛顿流体动力学的技术的多样性对传统的机器学习方法提出了挑战，这些方法需要统一结构的训练数据。因此，早期的机器学习本构方程在不同的变形协议或机械可观测量之间是不可移植的。在这里，我们提出了一个数据驱动的框架，解决了这些问题，允许流变学家构建可学习的模型，将基本的物理信息，同时保持不可知的细节，有关特定的实验协议或流动运动学。这些科学机器学习模型在物质客观的张量构成框架内结合了通用近似器。通过构造，这些模型尊重连续介质力学所要求的物理约束，例如框架不变性和张量对称性。我们证明，该框架有利于从有限的数据中快速发现准确的本构方程，并且所学习的模型可用于描述运动学上更复杂的流动。这种固有的灵活性允许这些“数字流体双胞胎”应用于一系列材料系统和工程问题。我们通过在多维计算流体动力学模拟中部署训练模型来说明这种灵活性-这是使用任何先前开发的数据驱动流变状态方程无法实现的任务。
英文摘要：
The formulation of rheological constitutive equations -- models that relate internal stresses and deformations in complex fluids -- is a critical step in the engineering of systems involving soft materials. While data-driven models provide accessible alternatives to expensive first-principles models and less accurate empirical models in many engineering disciplines, the development of similar models for complex fluids has lagged. The diversity of techniques for characterizing non-Newtonian fluid dynamics creates a challenge for classical machine learning approaches, which require uniformly structured training data. Consequently, early machine learning constitutive equations have not been portable between different deformation protocols or mechanical observables. Here, we present a data-driven framework that resolves such issues, allowing rheologists to construct learnable models that incorporate essential physical information, while remaining agnostic to details regarding particular experimental protocols or flow kinematics. These scientific machine learning models incorporate a universal approximator within a materially objective tensorial constitutive framework. By construction, these models respect physical constraints, such as frame-invariance and tensor symmetry, required by continuum mechanics. We demonstrate that this framework facilitates the rapid discovery of accurate constitutive equations from limited data, and that the learned models may be used to describe more kinematically complex flows. This inherent flexibility admits the application of these 'digital fluid twins' to a range of material systems and engineering problems. We illustrate this flexibility by deploying a trained model within a multidimensional computational fluid dynamics simulation -- a task that is not achievable using any previously developed data-driven rheological equation of state.
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