人工神经网络
传热
非线性系统
偏微分方程
搭配(遥感)
常微分方程
应用数学
颂歌
边值问题
深度学习
数学
计算机科学
数学优化
人工智能
数学分析
机械
物理
微分方程
机器学习
量子力学
作者
Hongwei Guo,Xiaoying Zhuang,Naif Alajlan,Timon Rabczuk
标识
DOI:10.1016/j.camwa.2023.05.014
摘要
We present an adaptive deep collocation method (DCM) based on physics-informed deep learning for the melting heat transfer analysis of a non-Newtonian (Sisko) fluid over a moving surface with nonlinear thermal radiation. Fitted neural network search (NAS) and model based transfer learning (TL) are developed to improve model computational efficiency and accuracy. The governing equations for this boundary-layer flow problem are derived using Buongiorno's and a nonlinear thermal radiation model. Next, similarity transformations are introduced to reduce the governing equations into coupled nonlinear ordinary differential equations (ODEs) subjected to asymptotic infinity boundary conditions. By incorporating physics constraints into the neural networks, we employ the proposed deep learning model to solve the coupled ODEs. The imposition of infinity boundary conditions is carried out by adding an inequality constraint to the loss function, with infinity added to the hyper-parameters of the neural network, which is updated dynamically in the optimization process. The effects of various dimensionless parameters on three profiles (velocity, temperature, concentration) are investigated. Finally, we demonstrate the performance and accuracy of the adaptive DCM with transfer learning through several numerical examples, which can be the promising surrogate model to solve boundary layer problems.
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