Feature engineering and symbolic regression methods for detecting hidden physics from sparse sensor observation data

Vaddireddy, Harsha; Rasheed, Adil; Staples, Anne E.; San, Omer

doi:10.1063/1.5136351

Title: Feature engineering and symbolic regression methods for detecting hidden physics from sparse sensor observation data

Abstract

Here we put forth a modular approach for distilling hidden flow physics from 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 for discovering 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.

Authors:

Vaddireddy, Harsha ^[1];

^[2];

^[3];

^[1]

Oklahoma State Univ., Stillwater, OK (United States)
Norwegian Univ. of Science and Technology, Trondheim (Norway)
Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States)

Publication Date:: 2020-01-16

Research Org.:: Oklahoma State Univ., Stillwater, OK (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

OSTI Identifier:: 1593556

Alternate Identifier(s):: OSTI ID: 1591974

Grant/Contract Number:: SC0019290

Resource Type:: Accepted Manuscript

Journal Name:: Physics of Fluids

Additional Journal Information:: Journal Volume: 32; Journal Issue: 1; Journal ID: ISSN 1070-6631

Publisher:: American Institute of Physics (AIP)

Country of Publication:: United States

Language:: English

Subject:: 42 ENGINEERING

Citation Formats


                    Vaddireddy, Harsha, Rasheed, Adil, Staples, Anne E., and San, Omer. Feature engineering and symbolic regression methods for detecting hidden physics from sparse sensor observation data.  United States: N. p., 2020. 
Web.  doi:10.1063/1.5136351.

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                    Vaddireddy, Harsha, Rasheed, Adil, Staples, Anne E., & San, Omer. Feature engineering and symbolic regression methods for detecting hidden physics from sparse sensor observation data.  United States.  https://doi.org/10.1063/1.5136351

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                    Vaddireddy, Harsha, Rasheed, Adil, Staples, Anne E., and San, Omer. Thu .  
"Feature engineering and symbolic regression methods for detecting hidden physics from sparse sensor observation data".  United States.  https://doi.org/10.1063/1.5136351.  https://www.osti.gov/servlets/purl/1593556.

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@article{osti_1593556,

  title        = {Feature engineering and symbolic regression methods for detecting hidden physics from sparse sensor observation data},

  author       = {Vaddireddy, Harsha and Rasheed, Adil and Staples, Anne E. and San, Omer},

  abstractNote = {Here we put forth a modular approach for distilling hidden flow physics from 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 for discovering 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.},

  doi          = {10.1063/1.5136351},

  journal      = {Physics of Fluids},

  number       = 1,

  volume       = 32,

  place        = {United States},

  year         = {2020},

  month        = {1}

}

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Prioritized grammar enumeration: symbolic regression by dynamic programming
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Two-dimensional turbulence
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Kraichnan, R. H.; Montgomery, D.
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The Roles of Plastic Surgeons in Advancing Artificial Intelligence in Plastic Surgery
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Cuvelliez, Marie; Vandewalle, Vincent; Brunin, Maxime
SSRN Electronic Journal
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Nonlinear truncation error analysis of finite difference schemes forthe Euler equations
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Klopfer, G.; Mcrae, D.
19th Aerospace Sciences Meeting, 19th Aerospace Sciences Meeting
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Computational Design for Long-Term Numerical Integration of the Equations of Fluid Motion: Two-Dimensional Incompressible Flow. Part I
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Arakawa, Akio
Journal of Computational Physics, Vol. 135, Issue 2
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Deep Learning
text, January 2018

Ganatra, Sanket
Zenodo
DOI: 10.5281/zenodo.1189359

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San, Omer; Staples, Anne E.
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Prediction of Dynamical Systems by Symbolic Regression
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Inferring biological networks by sparse identification of nonlinear dynamics
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arXiv
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Abstract

Citation Formats

Stable signal recovery from incomplete and inaccurate measurements journal, January 2006

Diffusion Approximation for Two-Dimensional Turbulence journal, January 1968

XLI. On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves journal, May 1895

Deep learning journal, May 2015

Two-Dimensional Turbulence journal, January 2012

Distilling Free-Form Natural Laws from Experimental Data journal, April 2009

Model selection for dynamical systems via sparse regression and information criteria journal, August 2017

Automated reverse engineering of nonlinear dynamical systems journal, June 2007

Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations journal, February 2019

Prediction and minimization of blast-induced ground vibration using two robust meta-heuristic algorithms journal, February 2017

Evidence for the double cascade scenario in two-dimensional turbulence journal, July 2010

A new synergetic paradigm in environmental numerical modeling: Hybrid models combining deterministic and machine learning components journal, January 2006

Analytic solutions of the Nagumo equation journal, January 1992

Pseudospectral methods for Nagumo equation journal, March 2011

Regularization and variable selection via the elastic net journal, April 2005

Roadheader performance prediction using genetic programming (GP) and gene expression programming (GEP) techniques journal, August 2017

Closed-loop separation control over a sharp edge ramp using genetic programming journal, February 2016

Multidimensional nonlinear diffusion arising in population genetics journal, October 1978

An Introduction To Compressive Sampling journal, March 2008

The critical merger distance between two co-rotating quasi-geostrophic vortices journal, January 2005

Sparse identification of truncation errors journal, November 2019

A model unified field equation journal, March 1962

Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence book, January 1992

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Hidden physics models: Machine learning of nonlinear partial differential equations journal, March 2018

Prediction of compressive and tensile strength of Gaziantep basalts via neural networks and gene expression programming journal, November 2008

Hybrid Reynolds-Averaged/Large-Eddy Simulation Methodology from Symbolic Regression: Formulation and Application journal, November 2017

Data-driven deconvolution for large eddy simulations of Kraichnan turbulence journal, December 2018

Physics of vortex merging journal, May 2005

Inertial Ranges in Two-Dimensional Turbulence journal, January 1967

Heuristic stability theory for finite-difference equations journal, June 1968

Data-driven discovery of partial differential equations journal, April 2017

Dynamic systems identification with Gaussian processes journal, December 2005

A coarse-grid projection method for accelerating incompressible flow computations journal, January 2013

Parse-matrix evolution for symbolic regression journal, September 2012

An Active Pulse Transmission Line Simulating Nerve Axon journal, October 1962

Regularization Paths for Generalized Linear Models via Coordinate Descent journal, January 2010

Prediction of dynamical systems by symbolic regression journal, July 2016

Inferring Biological Networks by Sparse Identification of Nonlinear Dynamics journal, June 2016

Model identification of reduced order fluid dynamics systems using deep learning: Model identification in fluid dynamics using deep learning journal, August 2017

Extracting Sparse High-Dimensional Dynamics from Limited Data journal, January 2018

Enhancing Sparsity by Reweighted ℓ 1 Minimization journal, October 2008

Closed-loop separation control using machine learning journal, April 2015

Large-eddy simulation: achievements and challenges journal, May 1999

Elite bases regression: A real-time algorithm for symbolic regression conference, July 2017

Oscillatory Solitary Waves in Dispersive Media journal, July 1972

A systematic approach for correcting nonlinear instabilities: The Lax-Wendroff scheme for scalar conservation laws journal, December 1978

Nonlinear Interaction between Short and Long Capillary-Gravity Waves journal, November 1975

Numerical solutions for solute transport in unconfined aquifers journal, March 1983

The perceptron: A probabilistic model for information storage and organization in the brain. journal, January 1958

Identification strategies for model-based control journal, July 2013

Neuristor propagation on a tunnel diode loaded transmission line journal, January 1963

High-order methods for decaying two-dimensional homogeneous isotropic turbulence journal, June 2012

Compressive Sensing [Lecture Notes] journal, August 2007

A modified tanh–coth method for solving the KdV and the KdV–Burgers’ equations journal, February 2009

The big challenges of big data journal, June 2013

Semi-autogenous mill power model development using gene expression programming journal, February 2017

Complex hybrid models combining deterministic and machine learning components for numerical climate modeling and weather prediction journal, March 2006

Sparse reduced-order modelling: sensor-based dynamics to full-state estimation journal, April 2018

Atmospheric Predictability and Two-Dimensional Turbulence journal, March 1971

Numerical Gaussian Processes for Time-Dependent and Nonlinear Partial Differential Equations journal, January 2018

A rationale for implicit turbulence modelling journal, January 2002

Exact Recovery of Chaotic Systems from Highly Corrupted Data journal, January 2017

Image Restoration: Wavelet Frame Shrinkage, Nonlinear Evolution PDEs, and Beyond journal, January 2017

Computation of the Energy Spectrum in Homogeneous Two-Dimensional Turbulence journal, January 1969

A Unified Framework for Sparse Relaxed Regularized Regression: SR3 journal, January 2019

Sub-grid scale model classification and blending through deep learning journal, May 2019

Learning partial differential equations via data discovery and sparse optimization journal, January 2017

Scale-Invariance and Turbulence Models for Large-Eddy Simulation journal, January 2000

Regression Shrinkage and Selection Via the Lasso journal, January 1996

Adaptive space transformation: An invariant based method for predicting aerodynamic coefficients of hypersonic vehicles journal, November 2015

Implicit subgrid-scale modeling by adaptive deconvolution journal, November 2004

Force identification of dynamic systems using genetic programming journal, January 2005

Closed-Loop Turbulence Control: Progress and Challenges journal, August 2015

Unsteady flow against dispersion in finite porous media journal, June 1983

Theory and applications of the sine-gordon equation journal, April 1971

Subgrid modelling for two-dimensional turbulence using neural networks journal, November 2018

Stable signal recovery from incomplete and inaccurate measurements
journal, January 2006

Diffusion Approximation for Two-Dimensional Turbulence
journal, January 1968

XLI. On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves
journal, May 1895

Deep learning
journal, May 2015

Two-Dimensional Turbulence
journal, January 2012

Distilling Free-Form Natural Laws from Experimental Data
journal, April 2009

Model selection for dynamical systems via sparse regression and information criteria
journal, August 2017

Automated reverse engineering of nonlinear dynamical systems
journal, June 2007

Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
journal, February 2019

Prediction and minimization of blast-induced ground vibration using two robust meta-heuristic algorithms
journal, February 2017

Evidence for the double cascade scenario in two-dimensional turbulence
journal, July 2010

A new synergetic paradigm in environmental numerical modeling: Hybrid models combining deterministic and machine learning components
journal, January 2006

Analytic solutions of the Nagumo equation
journal, January 1992

Pseudospectral methods for Nagumo equation
journal, March 2011

Regularization and variable selection via the elastic net
journal, April 2005

Roadheader performance prediction using genetic programming (GP) and gene expression programming (GEP) techniques
journal, August 2017

Closed-loop separation control over a sharp edge ramp using genetic programming
journal, February 2016

Multidimensional nonlinear diffusion arising in population genetics
journal, October 1978

An Introduction To Compressive Sampling
journal, March 2008

The critical merger distance between two co-rotating quasi-geostrophic vortices
journal, January 2005

Sparse identification of truncation errors
journal, November 2019

A model unified field equation
journal, March 1962

Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence
book, January 1992

Application of an evolutionary algorithm to LES modelling of turbulent transport in premixed flames
journal, December 2018

Hidden physics models: Machine learning of nonlinear partial differential equations
journal, March 2018

Prediction of compressive and tensile strength of Gaziantep basalts via neural networks and gene expression programming
journal, November 2008

Hybrid Reynolds-Averaged/Large-Eddy Simulation Methodology from Symbolic Regression: Formulation and Application
journal, November 2017

Data-driven deconvolution for large eddy simulations of Kraichnan turbulence
journal, December 2018

Physics of vortex merging
journal, May 2005

Inertial Ranges in Two-Dimensional Turbulence
journal, January 1967

Heuristic stability theory for finite-difference equations
journal, June 1968

Data-driven discovery of partial differential equations
journal, April 2017

Dynamic systems identification with Gaussian processes
journal, December 2005

A coarse-grid projection method for accelerating incompressible flow computations
journal, January 2013

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journal, September 2012

An Active Pulse Transmission Line Simulating Nerve Axon
journal, October 1962

Regularization Paths for Generalized Linear Models via Coordinate Descent
journal, January 2010

Prediction of dynamical systems by symbolic regression
journal, July 2016

Inferring Biological Networks by Sparse Identification of Nonlinear Dynamics
journal, June 2016

Model identification of reduced order fluid dynamics systems using deep learning: Model identification in fluid dynamics using deep learning
journal, August 2017

Extracting Sparse High-Dimensional Dynamics from Limited Data
journal, January 2018

Enhancing Sparsity by Reweighted ℓ 1 Minimization
journal, October 2008

Closed-loop separation control using machine learning
journal, April 2015

Large-eddy simulation: achievements and challenges
journal, May 1999

Elite bases regression: A real-time algorithm for symbolic regression
conference, July 2017

Oscillatory Solitary Waves in Dispersive Media
journal, July 1972

A systematic approach for correcting nonlinear instabilities: The Lax-Wendroff scheme for scalar conservation laws
journal, December 1978

Nonlinear Interaction between Short and Long Capillary-Gravity Waves
journal, November 1975

Numerical solutions for solute transport in unconfined aquifers
journal, March 1983

The perceptron: A probabilistic model for information storage and organization in the brain.
journal, January 1958

Identification strategies for model-based control
journal, July 2013

Neuristor propagation on a tunnel diode loaded transmission line
journal, January 1963

High-order methods for decaying two-dimensional homogeneous isotropic turbulence
journal, June 2012

Compressive Sensing [Lecture Notes]
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A modified tanh–coth method for solving the KdV and the KdV–Burgers’ equations
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journal, June 2013

Semi-autogenous mill power model development using gene expression programming
journal, February 2017

Complex hybrid models combining deterministic and machine learning components for numerical climate modeling and weather prediction
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journal, April 2018

Atmospheric Predictability and Two-Dimensional Turbulence
journal, March 1971

Numerical Gaussian Processes for Time-Dependent and Nonlinear Partial Differential Equations
journal, January 2018

A rationale for implicit turbulence modelling
journal, January 2002

Exact Recovery of Chaotic Systems from Highly Corrupted Data
journal, January 2017

Image Restoration: Wavelet Frame Shrinkage, Nonlinear Evolution PDEs, and Beyond
journal, January 2017

Computation of the Energy Spectrum in Homogeneous Two-Dimensional Turbulence
journal, January 1969

A Unified Framework for Sparse Relaxed Regularized Regression: SR3
journal, January 2019

Sub-grid scale model classification and blending through deep learning
journal, May 2019

Learning partial differential equations via data discovery and sparse optimization
journal, January 2017

Scale-Invariance and Turbulence Models for Large-Eddy Simulation
journal, January 2000

Regression Shrinkage and Selection Via the Lasso
journal, January 1996

Adaptive space transformation: An invariant based method for predicting aerodynamic coefficients of hypersonic vehicles
journal, November 2015

Implicit subgrid-scale modeling by adaptive deconvolution
journal, November 2004

Force identification of dynamic systems using genetic programming
journal, January 2005

Closed-Loop Turbulence Control: Progress and Challenges
journal, August 2015

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Theory and applications of the sine-gordon equation
journal, April 1971

Subgrid modelling for two-dimensional turbulence using neural networks
journal, November 2018

Nonlinear system identification: From multiple-model networks to Gaussian processes
journal, October 2008

Numerical solution of modified differential equations based on symmetry preservation
journal, December 2017

Nonlinear truncation error analysis of finite difference schemes forthe Euler equations
journal, April 1983