移动采样物理信息的神经网络由移动网状PDE诱导.
Yu Yang1, Qihong Yang1, Yangtao Deng1
1School of Mathematics, Sichuan University, 610065, Chengdu, China.
概括
我们推出了一个新的自适应性采样框架,MMPDE-Net,可以提高采样点的质量. 将其与物理信息神经网络 (PINN) 结合起来,创建了MS-PINN,增强了数值模拟的准确性和控制.
科学领域:
- 计算科学 计算科学
- 数字分析 数字分析
- 机器学习 机器学习
背景情况:
- 传统的数值方法往往在复杂问题上的自适应采样方面扎.
- 提高采样点的质量和控制对于模拟准确性至关重要.
- 深度学习和基于网格的方法为先进的采样策略提供了潜力.
研究的目的:
- 利用深度神经网络和移动网格方法开发一个端到端的自适应性采样框架.
- 为了提高采样点分布的精度和可控性.
- 将自适应采样框架与物理信息神经网络 (PINN) 集成,以提高性能.
主要方法:
- 建议移动网格部分微分方程网络 (MMPDE-Net) 用于自适应采样点的生成.
- 开发基于MMPDE-Net的代算法,用于精确的抽样点分布.
- 将MMPDE-Net与物理信息神经网络 (PINN) 结合起来,创建移动采样PINN (MS-PINN).
主要成果:
- 通过解决移动网状PDEs,MMPDE-Net通过自适应生成高质量的采样点.
- 代算法确保了更精确和可控制的采样点分布.
- 在数值实验中,MS-PINN在标准PINN上显示出显著的性能改进.
结论:
- 拟议的MMPDE-Net框架有效地提高了采样点生成质量.
- MS-PINN为数值模拟提供了强大而准确的方法,性能优于传统的PINN.
- 该方法提供了一种提高科学计算效率和可靠性的新方法.
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