We present a formulation of the physics-informed neural network (PINN) method for learning the effective viscosity of the generalized Newtonian fluid from measurements of velocity and pressure in time-dependent three-dimensional flows and apply it to estimating viscosity models of two non-Newtonian systems (polymer melts and suspensions of particles) in shear flow between two parallel plates using only velocity measurements from numerical simulations. The PINN-inferred viscosity models agree with empirical models for shear rates with large absolute values but deviate for shear rates near zero where empirical models have an unphysical singularity. We show that once the unknown physics is learned the PINN method can be used to solve the momentum conservation equation governing flow of non-Newtonian fluids.

中文翻译：

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学习非牛顿流体的未知物理

我们提出了一种基于物理信息的神经网络 (PINN) 方法的公式，该方法用于通过对时间相关的三维流动中的速度和压力的测量来学习广义牛顿流体的有效粘度，并将其应用于估计两个非流体的粘度模型。牛顿系统（聚合物熔体和颗粒悬浮液）在两个平行板之间的剪切流中仅使用数值模拟中的速度测量。PINN 推断的粘度模型与具有大绝对值的剪切速率的经验模型一致，但在经验模型具有非物理奇点的情况下，在接近零的剪切速率时偏离。我们表明，一旦学习了未知物理，PINN 方法可用于求解控制非牛顿流体流动的动量守恒方程。