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Title: Error modeling for surrogates of dynamical systems using machine learning: Machine-learning-based error model for surrogates of dynamical systems

Journal Article · · International Journal for Numerical Methods in Engineering
DOI:https://doi.org/10.1002/nme.5583· OSTI ID:1399882
ORCiD logo [1];  [2];  [1]
  1. Stanford Univ., CA (United States). Dept. of Energy Resources Engineering
  2. Sandia National Lab. (SNL-CA), Livermore, CA (United States). Extreme-Scae Data Science and Analytics Dept.
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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 high-dimensional 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 surrogate-model error in a quantity of interest (QoI). This eliminates the need for the user to hand-select a small number of informative features. The methodology requires a training set of parameter instances at which the time-dependent surrogate-model error is computed by simulating both the high-fidelity and surrogate models. Using these training data, the method first determines regression-model locality (via classification or clustering) and subsequently constructs a “local” regression model to predict the time-instantaneous error within each identified region of feature space. We consider 2 uses for the resulting error model: (1) as a correction to the surrogate-model QoI prediction at each time instance and (2) as a way to statistically model arbitrary functions of the time-dependent surrogate-model error (eg, time-integrated errors). We then apply the proposed framework to model errors in reduced-order models of nonlinear oil-water subsurface flow simulations, with time-varying well-control (bottom-hole pressure) parameters. The reduced-order 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 time-instantaneous 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 well-averaged errors.

Research Organization:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA)
Grant/Contract Number:
AC04-94AL85000
OSTI ID:
1399882
Report Number(s):
SAND-2016-12535J; 649856; TRN: US1702976
Journal Information:
International Journal for Numerical Methods in Engineering, Vol. 112, Issue 12; ISSN 0029-5981
Publisher:
WileyCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 41 works
Citation information provided by
Web of Science

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Reduced order modeling of random linear dynamical systems based on a new a posteriori error bound: Reduced order modeling of random linear dynamical systems based on a new a posteriori error bound journal September 2018
Machine-learning-based modeling of coarse-scale error, with application to uncertainty quantification journal May 2018
Rapid Learning-Based and Geologically Consistent History Matching journal January 2018
Model-based decision analysis applied to petroleum field development and management
  • Schiozer, Denis José; de Souza dos Santos, Antonio Alberto; de Graça Santos, Susana Margarida
  • Oil & Gas Science and Technology – Revue d’IFP Energies nouvelles, Vol. 74 https://doi.org/10.2516/ogst/2019019
journal January 2019
Adaptivity in Bayesian Inverse Finite Element Problems: Learning and Simultaneous Control of Discretisation and Sampling Errors journal February 2019

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Related Subjects

97 MATHEMATICS AND COMPUTING
error modeling
machine learning
nonlinar dynamical system
POD-TPWL
surrogate model