论文标题
从流体力学到机器学习的线性和非线性维度降低
Linear and Nonlinear Dimensionality Reduction from Fluid Mechanics to Machine Learning
论文作者
论文摘要
降低降低是许多数据处理问题的本质，包括过滤，数据压缩，减少订单建模和模式分析。尽管传统上使用线性工具在流体动力学界进行了处理，但机器学习的非线性工具越来越流行。本文介于评论和教程之间的一半，介绍了线性和非线性降低技术的一般框架。突出显示了自动编码器与流动学习方法之间的差异和联系，并且流行的非线性技术，例如内核主成分分析（KPCA），等值特征学习（ISOMAPS）和本地线性嵌入（LLE）（LLE）。这些算法在三个经典问题中进行了基准测试：1）滤波，2）振荡模式的识别和3）数据压缩。将它们的性能与传统的正交分解（POD）进行比较，以提供有关它们在流体动力学中扩散的看法。
Dimensionality reduction is the essence of many data processing problems, including filtering, data compression, reduced-order modeling and pattern analysis. While traditionally tackled using linear tools in the fluid dynamics community, nonlinear tools from machine learning are becoming increasingly popular. This article, halfway between a review and a tutorial, introduces a general framework for linear and nonlinear dimensionality reduction techniques. Differences and links between autoencoders and manifold learning methods are highlighted, and popular nonlinear techniques such as kernel Principal Component Analysis (kPCA), isometric feature learning (ISOMAPs) and Locally Linear Embedding (LLE) are placed in this framework. These algorithms are benchmarked in three classic problems: 1) filtering, 2) identification of oscillatory patterns, and 3) data compression. Their performances are compared against the traditional Proper Orthogonal Decomposition (POD) to provide a perspective on their diffusion in fluid dynamics.
