You can manage bookmarks using lists, please log in to your user account for this.
Media type:
E-Article
Title:
Non-intrusive nonlinear model reduction via machine learning approximations to low-dimensional operators
Contributor:
Bai, Zhe;
Peng, Liqian
Published:
Springer Science and Business Media LLC, 2021
Published in:
Advanced Modeling and Simulation in Engineering Sciences, 8 (2021) 1
Language:
English
DOI:
10.1186/s40323-021-00213-5
ISSN:
2213-7467
Origination:
Footnote:
Description:
<jats:title>Abstract</jats:title><jats:p>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 <jats:inline-formula><jats:alternatives><jats:tex-math>$$10^3{\times }$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mrow>
<mml:msup>
<mml:mn>10</mml:mn>
<mml:mn>3</mml:mn>
</mml:msup>
<mml:mo>×</mml:mo>
</mml:mrow>
</mml:math></jats:alternatives></jats:inline-formula> 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).</jats:p>