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Title: Non-intrusive nonlinear model reduction via machine learning approximations to low-dimensional operators

Journal Article · · Advanced Modeling and Simulation in Engineering Sciences
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Abstract Although projection-based reduced-order models (ROMs) for parameterized nonlinear dynamical systems have demonstrated exciting results across a range of applications, their broad adoption has been limited by their intrusivity: implementing such a reduced-order model typically requires significant modifications to the underlying simulation code. To address this, we propose a method that enables traditionally intrusive reduced-order models to be accurately approximated in a non-intrusive manner. Specifically, the approach approximates the low-dimensional operators associated with projection-based reduced-order models (ROMs) using modern machine-learning regression techniques. The only requirement of the simulation code is the ability to export the velocity given the state and parameters; this functionality is used to train the approximated low-dimensional operators. In addition to enabling nonintrusivity, we demonstrate that the approach also leads to very low computational complexity, achieving up to $$$$10^3{\times }$$$$ 10 3 × in run time. We demonstrate the effectiveness of the proposed technique on two types of PDEs. The domain of applications include both parabolic and hyperbolic PDEs, regardless of the dimension of full-order models (FOMs).

Research Organization:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States); Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
Grant/Contract Number:
AC02-05CH11231; NA0003525
OSTI ID:
1837797
Journal Information:
Advanced Modeling and Simulation in Engineering Sciences, Journal Name: Advanced Modeling and Simulation in Engineering Sciences Journal Issue: 1 Vol. 8; ISSN 2213-7467
Publisher:
Springer Science + Business MediaCopyright Statement
Country of Publication:
Netherlands
Language:
English

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Related Subjects

42 ENGINEERING
dynamical systems
low-dimensional operators
machine learning
model reduction