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Title: Equation Discovery Using Fast Function Extraction: a Deterministic Symbolic Regression Approach

Abstract

Advances in machine learning (ML) coupled with increased computational power have enabled identification of patterns in data extracted from complex systems. ML algorithms are actively being sought in recovering physical models or mathematical equations from data. This is a highly valuable technique where models cannot be built using physical reasoning alone. In this paper, we investigate the application of fast function extraction (FFX), a fast, scalable, deterministic symbolic regression algorithm to recover partial differential equations (PDEs). FFX identifies active bases among a huge set of candidate basis functions and their corresponding coefficients from recorded snapshot data. This approach uses a sparsity-promoting technique from compressive sensing and sparse optimization called pathwise regularized learning to perform feature selection and parameter estimation. Furthermore, it recovers several models of varying complexity (number of basis terms). FFX finally filters out many identified models using non-dominated sorting and forms a Pareto front consisting of optimal models with respect to minimizing complexity and test accuracy. Numerical experiments are carried out to recover several ubiquitous PDEs such as wave and heat equations among linear PDEs and Burgers, Korteweg–de Vries (KdV), and Kawahara equations among higher-order nonlinear PDEs. Additional simulations are conducted on the same PDEs under noisy conditionsmore » to test the robustness of the proposed approach.« less

Authors:
 [1]; ORCiD logo [1]
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  1. Oklahoma State Univ., Stillwater, OK (United States)
Publication Date:
Research Org.:
Oklahoma State Univ., Stillwater, OK (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
OSTI Identifier:
1593572
Grant/Contract Number:  
SC0019290
Resource Type:
Accepted Manuscript
Journal Name:
Fluids
Additional Journal Information:
Journal Volume: 4; Journal Issue: 2; Journal ID: ISSN 2311-5521
Publisher:
MDPI
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; deterministic symbolic regression; fast function extraction; compressive sensing; pathwise regularized learning; non-dominated sorting

Citation Formats

Vaddireddy, Harsha, and San, Omer. Equation Discovery Using Fast Function Extraction: a Deterministic Symbolic Regression Approach. United States: N. p., 2019. Web. doi:10.3390/fluids4020111.
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Vaddireddy, Harsha, & San, Omer. Equation Discovery Using Fast Function Extraction: a Deterministic Symbolic Regression Approach. United States. doi:https://doi.org/10.3390/fluids4020111
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Vaddireddy, Harsha, and San, Omer. Sat . "Equation Discovery Using Fast Function Extraction: a Deterministic Symbolic Regression Approach". United States. doi:https://doi.org/10.3390/fluids4020111. https://www.osti.gov/servlets/purl/1593572.
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@article{osti_1593572,
title = {Equation Discovery Using Fast Function Extraction: a Deterministic Symbolic Regression Approach},
author = {Vaddireddy, Harsha and San, Omer},
abstractNote = {Advances in machine learning (ML) coupled with increased computational power have enabled identification of patterns in data extracted from complex systems. ML algorithms are actively being sought in recovering physical models or mathematical equations from data. This is a highly valuable technique where models cannot be built using physical reasoning alone. In this paper, we investigate the application of fast function extraction (FFX), a fast, scalable, deterministic symbolic regression algorithm to recover partial differential equations (PDEs). FFX identifies active bases among a huge set of candidate basis functions and their corresponding coefficients from recorded snapshot data. This approach uses a sparsity-promoting technique from compressive sensing and sparse optimization called pathwise regularized learning to perform feature selection and parameter estimation. Furthermore, it recovers several models of varying complexity (number of basis terms). FFX finally filters out many identified models using non-dominated sorting and forms a Pareto front consisting of optimal models with respect to minimizing complexity and test accuracy. Numerical experiments are carried out to recover several ubiquitous PDEs such as wave and heat equations among linear PDEs and Burgers, Korteweg–de Vries (KdV), and Kawahara equations among higher-order nonlinear PDEs. Additional simulations are conducted on the same PDEs under noisy conditions to test the robustness of the proposed approach.},
doi = {10.3390/fluids4020111},
journal = {Fluids},
number = 2,
volume = 4,
place = {United States},
year = {2019},
month = {6}
}
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DOI:  https://doi.org/10.3390/fluids4020111
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    • Physics of Fluids, Vol. 32, Issue 1
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