Error modeling for surrogates of dynamical systems using machine learning: Machinelearningbased error model for surrogates of dynamical systems
Abstract
A machine learning–based framework for modeling the error introduced by surrogate models of parameterized dynamical systems is proposed. The framework entails the use of highdimensional regression techniques (eg, random forests, and LASSO) to map a large set of inexpensively computed “error indicators” (ie, features) produced by the surrogate model at a given time instance to a prediction of the surrogatemodel error in a quantity of interest (QoI). This eliminates the need for the user to handselect a small number of informative features. The methodology requires a training set of parameter instances at which the timedependent surrogatemodel error is computed by simulating both the highfidelity and surrogate models. Using these training data, the method first determines regressionmodel locality (via classification or clustering) and subsequently constructs a “local” regression model to predict the timeinstantaneous error within each identified region of feature space. We consider 2 uses for the resulting error model: (1) as a correction to the surrogatemodel QoI prediction at each time instance and (2) as a way to statistically model arbitrary functions of the timedependent surrogatemodel error (eg, timeintegrated errors). We then apply the proposed framework to model errors in reducedorder models of nonlinear oilwater subsurface flow simulations, with timevaryingmore »
 Authors:
 Stanford Univ., CA (United States). Dept. of Energy Resources Engineering
 Sandia National Lab. (SNLCA), Livermore, CA (United States). ExtremeScae Data Science and Analytics Dept.
 Publication Date:
 Research Org.:
 Sandia National Lab. (SNLNM), Albuquerque, NM (United States)
 Sponsoring Org.:
 USDOE National Nuclear Security Administration (NNSA)
 OSTI Identifier:
 1399882
 Report Number(s):
 SAND201612535J
Journal ID: ISSN 00295981; 649856; TRN: US1702976
 Grant/Contract Number:
 AC0494AL85000
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 International Journal for Numerical Methods in Engineering
 Additional Journal Information:
 Journal Volume: 112; Journal Issue: 12; Journal ID: ISSN 00295981
 Publisher:
 Wiley
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; error modeling; machine learning; nonlinar dynamical system; PODTPWL; surrogate model
Citation Formats
Trehan, Sumeet, Carlberg, Kevin T., and Durlofsky, Louis J.. Error modeling for surrogates of dynamical systems using machine learning: Machinelearningbased error model for surrogates of dynamical systems. United States: N. p., 2017.
Web. doi:10.1002/nme.5583.
Trehan, Sumeet, Carlberg, Kevin T., & Durlofsky, Louis J.. Error modeling for surrogates of dynamical systems using machine learning: Machinelearningbased error model for surrogates of dynamical systems. United States. doi:10.1002/nme.5583.
Trehan, Sumeet, Carlberg, Kevin T., and Durlofsky, Louis J.. 2017.
"Error modeling for surrogates of dynamical systems using machine learning: Machinelearningbased error model for surrogates of dynamical systems". United States.
doi:10.1002/nme.5583.
@article{osti_1399882,
title = {Error modeling for surrogates of dynamical systems using machine learning: Machinelearningbased error model for surrogates of dynamical systems},
author = {Trehan, Sumeet and Carlberg, Kevin T. and Durlofsky, Louis J.},
abstractNote = {A machine learning–based framework for modeling the error introduced by surrogate models of parameterized dynamical systems is proposed. The framework entails the use of highdimensional regression techniques (eg, random forests, and LASSO) to map a large set of inexpensively computed “error indicators” (ie, features) produced by the surrogate model at a given time instance to a prediction of the surrogatemodel error in a quantity of interest (QoI). This eliminates the need for the user to handselect a small number of informative features. The methodology requires a training set of parameter instances at which the timedependent surrogatemodel error is computed by simulating both the highfidelity and surrogate models. Using these training data, the method first determines regressionmodel locality (via classification or clustering) and subsequently constructs a “local” regression model to predict the timeinstantaneous error within each identified region of feature space. We consider 2 uses for the resulting error model: (1) as a correction to the surrogatemodel QoI prediction at each time instance and (2) as a way to statistically model arbitrary functions of the timedependent surrogatemodel error (eg, timeintegrated errors). We then apply the proposed framework to model errors in reducedorder models of nonlinear oilwater subsurface flow simulations, with timevarying wellcontrol (bottomhole pressure) parameters. The reducedorder models used in this work entail application of trajectory piecewise linearization in conjunction with proper orthogonal decomposition. Moreover, when the first use of the method is considered, numerical experiments demonstrate consistent improvement in accuracy in the timeinstantaneous QoI prediction relative to the original surrogate model, across a large number of test cases. When the second use is considered, results show that the proposed method provides accurate statistical predictions of the time and wellaveraged errors.},
doi = {10.1002/nme.5583},
journal = {International Journal for Numerical Methods in Engineering},
number = 12,
volume = 112,
place = {United States},
year = 2017,
month = 7
}

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