Latent-space time evolution of non-intrusive reduced-order models using Gaussian process emulation
Abstract
Non-intrusive reduced-order models (ROMs) have recently generated considerable interest for constructing computationally efficient counterparts of nonlinear dynamical systems emerging from various domain sciences. They provide a low-dimensional emulation framework for systems that may be intrinsically high-dimensional. This is accomplished by utilizing a construction algorithm that is purely data-driven. It is no surprise, therefore, that the algorithmic advances of machine learning have led to non-intrusive ROMs with greater accuracy and computational gains. However, in bypassing the utilization of an equation-based evolution, it is often seen that the interpretability of the ROM framework suffers. This becomes more problematic when black-box deep learning methods are used which are notorious for lacking robustness outside the physical regime of the observed data. In this article, we propose the use of a novel latent-space interpolation algorithm based on Gaussian process regression. Notably, this reduced-order evolution of the system is parameterized by control parameters to allow for interpolation in space. The use of this procedure also allows for a continuous interpretation of time which allows for temporal interpolation. The latter aspect provides information, with quantified uncertainty, about full-state evolution at a finer resolution than that utilized for training the ROMs. This research assesses the viability of thismore »
- Authors:
-
- Argonne National Lab. (ANL), Argonne, IL (United States)
- The Alan Turing Institute, London (United Kingdom)
- Imperial College, London (United Kingdom)
- Publication Date:
- Research Org.:
- Argonne National Laboratory (ANL), Argonne, IL (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES). Scientific User Facilities Division; Engineering and Physical Sciences Research Council (EPSRC); Imperial College, London (United Kingdom)
- OSTI Identifier:
- 1797914
- Grant/Contract Number:
- AC02-06CH11357
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physica. D, Nonlinear Phenomena
- Additional Journal Information:
- Journal Volume: 416; Journal ID: ISSN 0167-2789
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; Deep learning; Gaussian process regression; Reduced-order models
Citation Formats
Maulik, Romit, Botsas, Themistoklis, Ramachandra, Nesar, Mason, Lachlan Robert, and Pan, Indranil. Latent-space time evolution of non-intrusive reduced-order models using Gaussian process emulation. United States: N. p., 2021.
Web. doi:10.1016/j.physd.2020.132797.
Maulik, Romit, Botsas, Themistoklis, Ramachandra, Nesar, Mason, Lachlan Robert, & Pan, Indranil. Latent-space time evolution of non-intrusive reduced-order models using Gaussian process emulation. United States. https://doi.org/10.1016/j.physd.2020.132797
Maulik, Romit, Botsas, Themistoklis, Ramachandra, Nesar, Mason, Lachlan Robert, and Pan, Indranil. Mon .
"Latent-space time evolution of non-intrusive reduced-order models using Gaussian process emulation". United States. https://doi.org/10.1016/j.physd.2020.132797. https://www.osti.gov/servlets/purl/1797914.
@article{osti_1797914,
title = {Latent-space time evolution of non-intrusive reduced-order models using Gaussian process emulation},
author = {Maulik, Romit and Botsas, Themistoklis and Ramachandra, Nesar and Mason, Lachlan Robert and Pan, Indranil},
abstractNote = {Non-intrusive reduced-order models (ROMs) have recently generated considerable interest for constructing computationally efficient counterparts of nonlinear dynamical systems emerging from various domain sciences. They provide a low-dimensional emulation framework for systems that may be intrinsically high-dimensional. This is accomplished by utilizing a construction algorithm that is purely data-driven. It is no surprise, therefore, that the algorithmic advances of machine learning have led to non-intrusive ROMs with greater accuracy and computational gains. However, in bypassing the utilization of an equation-based evolution, it is often seen that the interpretability of the ROM framework suffers. This becomes more problematic when black-box deep learning methods are used which are notorious for lacking robustness outside the physical regime of the observed data. In this article, we propose the use of a novel latent-space interpolation algorithm based on Gaussian process regression. Notably, this reduced-order evolution of the system is parameterized by control parameters to allow for interpolation in space. The use of this procedure also allows for a continuous interpretation of time which allows for temporal interpolation. The latter aspect provides information, with quantified uncertainty, about full-state evolution at a finer resolution than that utilized for training the ROMs. This research assesses the viability of this algorithm for an advection-dominated system given by the inviscid shallow water equations.},
doi = {10.1016/j.physd.2020.132797},
journal = {Physica. D, Nonlinear Phenomena},
number = ,
volume = 416,
place = {United States},
year = {Mon Feb 01 00:00:00 EST 2021},
month = {Mon Feb 01 00:00:00 EST 2021}
}
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