基于物理信息神经网络的稀疏域数据3D流热问题建模
Physics Informed Neural Networks for Modeling of 3D Flow-Thermal Problems with Sparse Domain Data
AI总结：
本文采用PINNs结合稀疏分布的解数据，求解复杂3D域中高雷诺数不可压缩Navier-Stokes方程，并构建流热电子设计问题的代理模型，在未见查询点上优于标准数据驱动网络。
摘要：
在复杂3D域上成功训练物理信息神经网络（PINNs）以求解高度非线性PDEs仍是一项挑战。本文采用PINNs求解复杂几何形状下中高雷诺数的3D不可压缩Navier-Stokes（NS）方程。该方法利用域内非常稀疏分布的解数据。文中详细研究了提供的数据量与基于PDE的正则化器的影响。此外，采用数据与PINNs混合的方法，为现实的流热电子设计问题生成了代理模型。该代理模型提供近实时采样，在未见过的查询点上测试时优于标准数据驱动的神经网络。研究结果表明，PINNs与稀疏数据结合时，能有效求解3D非线性PDEs或进行受其支配的设计空间的代理建模。
英文摘要：
Successfully training Physics Informed Neural Networks (PINNs) for highly nonlinear PDEs on complex 3D domains remains a challenging task. In this paper, PINNs are employed to solve the 3D incompressible Navier-Stokes (NS) equations at moderate to high Reynolds numbers for complex geometries. The presented method utilizes very sparsely distributed solution data in the domain. A detailed investigation on the effect of the amount of supplied data and the PDE-based regularizers is presented. Additionally, a hybrid data-PINNs approach is used to generate a surrogate model of a realistic flow-thermal electronics design problem. This surrogate model provides near real-time sampling and was found to outperform standard data-driven neural networks when tested on unseen query points. The findings of the paper show how PINNs can be effective when used in conjunction with sparse data for solving 3D nonlinear PDEs or for surrogate modeling of design spaces governed by them.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
