PINNs在反演计算中影响因素的数值比较分析
Numerical Comparison and Analysis of Influencing Factors of PINNs in Inversion Calculation
刘云美 1史正梅1
作者信息
- 1. 贵州师范大学 数学科学学院,贵州 贵阳 550025
- 折叠
摘要
物理信息神经网络(PINNs)因其强大的函数表达能力而广泛应用于微分方程数值求解以及参数估计,但超参数的设置和网络架构的选择会影响计算的效果.针对这一问题,以Navier-Stokes方程为例进行了一系列的数值计算,以此研究了PINNs在反演计算非线性偏微分方程(PDE)过程中的影响因素,找到了提高PINNs求解精度和计算效率的方法.
Abstract
Physical Information Neural Networks(PINNs)are widely used in numerical solution of differential equations and parameter estimation due to their powerful function expression ability,but the setting of hyperparameters and the choice of network architecture can affect the computational performance.A series of numerical calculations are conducted by taking the Navier-Stokes equation as an example to investigate the influencing factors of PINNs in the inversion calculation of nonlinear partial differential equations(PDE),and methods are found to improve the accuracy and computational efficiency of PINNs.
关键词
物理信息神经网络/反演计算/Navier-Stokes方程/神经网络影响因素Key words
PINNs/inversion calculation/Navier-Stokes equations/analysis of influencing factors引用本文复制引用
出版年
2024
NETL
NSTL
万方数据