论文标题
基于数据的物理建模的非线性输入功能降低
Nonlinear input feature reduction for data-based physical modeling
论文作者
论文摘要
这项工作介绍了一种新的方法，可以从数据中得出物理量表的物理量表。本文开发的方法依赖于互信息的最大化来得出输入特征的最佳非线性组合。这些组合都适用于物理相关的模型，并且可解释（以象征性的方式）。该算法详细介绍，然后在合成玩具模型上进行测试。结果表明，我们的方法可以通过分析强烈的嘈杂的非线性数据集有效地构建相关组合。这些结果是有希望的，可能会大大帮助培训数据驱动的模型。最后，本文的最后一部分引入了一种从数据中进行自动尺寸分析的方法。测试案例是一个受湍流边界层理论的墙壁定律启发的合成数据集。该算法再次表明，它可以从数据中恢复相关的无量变变量。
This work introduces a novel methodology to derive physical scalings for input features from data. The approach developed in this article relies on the maximization of mutual information to derive optimal nonlinear combinations of input features. These combinations are both adapted to physics-related models and interpretable (in a symbolic way). The algorithm is presented in detail, then tested on a synthetic toy model. The results show that our approach can effectively construct relevant combinations by analyzing a strongly noisy nonlinear dataset. These results are promising and may significantly help training data-driven models. Finally, the last part of the paper introduces a way to perform automatic dimensional analysis from data. The test case is a synthetic dataset inspired by the Law of the Wall from turbulent boundary layer theory. Once again, the algorithm shows that it can recover relevant nondimensional variables from data.
