Feature engineering and symbolic regression methods for detecting hidden physics from sparse sensors

TL;DR

This paper introduces a modular approach combining symbolic regression and feature engineering to uncover hidden physics from sparse sensor data, demonstrated through fluid flow applications and model discovery.

Contribution

The study presents a novel combination of gene expression programming and ridge regression for discovering hidden physical relations in fluid dynamics from limited data.

Findings

Successfully distills the Smagorinsky model from sparse data

Effective in discovering subgrid scale closure models

Highlights importance of feature engineering in physics discovery

Abstract

In this study we put forth a modular approach for distilling hidden flow physics in discrete and sparse observations. To address functional expressiblity, a key limitation of the black-box machine learning methods, we have exploited the use of symbolic regression as a principle for identifying relations and operators that are related to the underlying processes. This approach combines evolutionary computation with feature engineering to provide a tool to discover hidden parameterizations embedded in the trajectory of fluid flows in the Eulerian frame of reference. Our approach in this study mainly involves gene expression programming (GEP) and sequential threshold ridge regression (STRidge) algorithms. We demonstrate our results in three different applications: (i) equation discovery, (ii) truncation error analysis, and (iii) hidden physics discovery, for which we include both predicting unknown source terms from a set of sparse observations and discovering subgrid scale closure models. We illustrate that both GEP and STRidge algorithms are able to distill the Smagorinsky model from an array of tailored features in solving the Kraichnan turbulence problem. Our results demonstrate the huge potential of these techniques in complex physics problems, and reveal the importance of feature selection and feature engineering in model discovery approaches.