通过物理系统的高频缩放来缓解神经操作者的光谱偏差
Siavash Khodakarami1, Vivek Oommen2, Aniruddha Bora1
1Division of Applied Mathematics, Brown University, Providence, RI, 02912, USA.
概括
高频缩放 (HFS) 减轻了神经操作者的光谱偏差,用于复杂的物理建模. 这种方法在没有富里埃转换成本的情况下提高了流体流动模拟的预测准确性.
科学领域:
- 计算流体动力学
- 物理的机器学习
- 用于科学建模的深度学习
背景情况:
- 神经运算器是模拟复杂物理系统的强大工具.
- 神经运算器的光谱偏差限制了它们捕获高频模式的能力,导致了平滑的解决方案.
- 这种限制对于流和多相流等多尺度系统尤其存在问题.
研究的目的:
- 引入和评估一种新的方法,即高频缩放 (HFS),用于减轻卷积神经操作者的光谱偏差.
- 提高神经运算器在单相和双相流量问题建模中的预测准确度.
- 探索使用扩散模型的替代光谱偏差缓解策略.
主要方法:
- 开发并集成高频缩放 (HFS) 进入卷积神经运算符,特别是UNet变体.
- 在隐性空间直接应用HFS,避免Fourier变换计算.
- 研究了基于神经操作者的扩散模型的使用,比较标准和HFS增强版本.
主要成果:
- 通过减轻光谱偏差,HFS集成显著提高了单相和双相流量问题的预测准确性.
- 在没有基于富里埃的计算开销的情况下,HFS方法的有效性得到了证明.
- 与HFS增强的神经运算符相结合的扩散模型显示,与使用标准的神经运算符相比,错误大大减少.
结论:
- 高频缩放 (HFS) 是解决卷积神经操作者的光谱偏差的一个有效技术.
- 在流体动力学中,HFS提供了基于富里埃的计算效率替代方法,以提高神经操作员的性能.
- 将HFS与扩散模型相结合,进一步提高了复杂流量模拟的基于物理的机器学习模型的准确性.
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