Nonlinear input feature reduction for data-based physical modeling

TL;DR

This paper presents a new data-driven method to derive physically meaningful nonlinear input features and scalings, enhancing interpretability and effectiveness of physical models, especially in noisy and complex datasets.

Contribution

It introduces a mutual information-based algorithm for nonlinear feature combination and automatic dimensional analysis, improving data-driven physical modeling capabilities.

Findings

Effective construction of relevant feature combinations from noisy data

Successful recovery of nondimensional variables in turbulent boundary layer data

Potential to significantly improve training of physics-based models

Abstract

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.