反问题
应用数学
替代模型
物理
反向
边值问题
边界(拓扑)
数学优化
计算机科学
数学分析
数学
几何学
量子力学
作者
Ruizhi Zhai,Deshun Yin,Guofei Pang
摘要
We for the first time leverage deep learning approaches to solve forward and inverse problems of two-dimensional laminar flows for power-law fluids. We propose a deep-learning framework, called Power-Law-Fluid-Net (PL-Net). We develop a surrogate model to solve the forward problems of the power-law fluids, and solve the inverse problems utilizing only a small set of measurement data under the assumption that boundary conditions (BCs) can be partially known. In the design of the methods, we incorporate the hard boundary condition constraints to accelerate the iteration of stochastic gradient descent methods for minimizing loss functions. For the forward problems, by incorporating the constitutive parameters into the input variables of neural networks, the PL-Net serves as a surrogate model for simulating the pressure-driven flows inside pipes having cross sections of varying shapes. We investigate the influences of the BC type, activation function type, and number of collocation points on the accuracy of numerical solutions. For the inverse problems, the PL-Net infers the physical quantities or constitutive parameters from a small number of measurements of flow field variables. The BCs of the inverse problems can even be partially known. We demonstrate the effects of BC type, number of sensors, and noise level on accuracy of inferred quantities. Computational examples indicate the high accuracy of the PL-Net in tackling both the forward and inverse problems of the power-law fluids.
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