Latent-space time evolution of non-intrusive reduced-order models using Gaussian process emulation

PHYSICA D-NONLINEAR PHENOMENA

卷:416

Article

Maulik, Romit¹  Botsas, Themistoklis²  Ramachandra, Nesar³  Mason, Lachlan R.^2,4  Pan, Indranil^2,4 

[1] Argonne Natl Lab, Argonne Leadership Comp Facil, Lemont, IL 60439 USA

[2] Alan Turing Inst, London NW1 2DB, England

[3] Argonne Natl Lab, High Energy Phys Div, Lemont, IL 60439 USA

[4] Imperial Coll London, London SW7 2AZ, England

关键词: Reduced-order models;    Deep learning;    Gaussian process regression;   

DOI  :  10.1016/j.physd.2020.132797

来源: Elsevier

【 摘 要 】

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. We assess the viability of this algorithm for an advection-dominated system given by the inviscid shallow water equations. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free