适应性采样物理信息的神经网络方法用于高阶流波和参数发现 (2 + 1) 维的CHKP方程
Hongli An1,2, Kaijie Xing2, Yao Chen2
1School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing 210094, People's Republic of China.
Chaos (Woodbury, N.Y.)
|April 26, 2024
概括
一种自适应采样物理信息神经网络 (ASPINN) 方法改善了高维部分微分方程中流波的预测. 这种新方法提高了准确性和效率,在复杂的波动力学中优于原始PINN.
科学领域:
- 物理 物理学 物理
- 应用数学 应用数学 应用数学
- 计算科学 计算科学
背景情况:
- 流波是重要的现象,在非线性光学和流体动力学等领域具有广泛的应用.
- 传统的基于物理学的神经网络 (PINNs) 难以处理高维部分微分方程 (PDEs),特别是对于高阶流波,这是由于对关键数据区域的采样效率低下.
研究的目的:
- 引入适应性采样物理信息神经网络 (ASPINN) 方法,以更好地预测高维 PDE 中的流波.
- 为了解决标准PINN在捕捉流波局部,利的特征方面的局限性.
主要方法:
- 开发了一种新的自适应搜索算法,以确保在流波的尖区域内充分采样点.
- 将ASPINN方法应用于 (2+1) 维的CHKP方程作为一个测试案例.
- 研究了CHKP方程的数据驱动反向问题,使用不同的噪声水平来评估稳定性.
主要成果:
- 在预测CHKP方程中,ASPINN方法在预测高级流波的动态行为方面明显优于原始PINNs.
- 预测效率和准确性提高了多达四个数量级.
- 在反向问题场景中,ASPINN方法在应用到杂数据时表现出良好的稳定性.
结论:
- ASPINN有效地捕捉了高层流波的复杂动态在高维的PDEs中.
- 适应性采样策略对于提高预测性能和效率至关重要.
- ASPINN为研究流波现象和相关的反向问题提供了强大而准确的解决方案.
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