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

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.

References in corpus (20)

• Discovering governing equations from data: Sparse identification of nonlinear dynamical systems
• Gene Expression Programming: a New Adaptive Algorithm for Solving Problems
• Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equations
• Deep Reinforcement Learning framework for Autonomous Driving
• PDE-Net 2.0: Learning PDEs from Data with A Numeric-Symbolic Hybrid Deep Network
• Sub-grid modelling for two-dimensional turbulence using neural networks
• Discovery of Algebraic Reynolds-Stress Models Using Sparse Symbolic Regression
• Sparse reduced-order modeling : Sensor-based dynamics to full-state estimation
• Closed-loop separation control using machine learning
• Model selection for dynamical systems via sparse regression and information criteria
• Sparse Dynamics for Partial Differential Equations
• An update on the double cascade scenario in two-dimensional turbulence
• Prediction of Dynamical Systems by Symbolic Regression
• Sub-grid scale model classification and blending through deep learning
• Closed-loop separation control over a sharp edge ramp using Genetic Programming
• High-order methods for decaying two-dimensional homogeneous isotropic turbulence
• A coarse-grid projection method for accelerating incompressible flow computations
• Sparse Identification of Truncation Errors
• Elite Bases Regression: A Real-time Algorithm for Symbolic Regression
• Feedback Control of Turbulent Shear Flows by Genetic Programming

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