On the direction of Coriolis force and the angular momentum conservation

This paper discusses a non-intrusive data-driven model order reduction method that learns low-dimensional dynamical models for a parametrized shallow water equation. We consider the shallow water equation in non-traditional form (NTSWE). We focus on learning low-dimensional models in a non-intrusive way. That means, we assume not to have access to a discretized form of the NTSWE in any form. Instead, we have snapshots that can be obtained using a black-box solver. Consequently, we aim at learning reduced-order models only from the snapshots. Precisely, a reduced-order model is learnt by solving an appropriate least-squares optimization problem in a low-dimensional subspace. Furthermore, we discuss computational challenges that particularly arise from the optimization problem being ill-conditioned. Moreover, we extend the non-intrusive model order reduction framework to a parametric case, where we make use of the parameter dependency at the level of the partial differential equation. We illustrate the efficiency of the proposed non-intrusive method to construct reduced-order models for NTSWE and compare it with an intrusive method (proper orthogonal decomposition). We furthermore discuss the predictive capabilities of both models outside the range of the training data. K E Y W O R D Sdata-driven modeling, model order reduction, operator inference, scientific machine learning, shallow water equation INTRODUCTIONShallow water equations (SWE) are a popular set of hyperbolic partial differential equations (PDEs) with the capability of describing geophysical wave phenomena, for example, the Kelvin and Rossby waves in the atmosphere and the oceans. They are frequently used in geophysical flow prediction, 1 investigation of baroclinic instability, 2,3 and planetary flows. 4 In this paper, we study a model order reduction (MOR) technique for SWE. MOR techniques allow us to construct low-dimensional models or reduced-order models (ROMs) for a large-scale dynamical system. We refer to the books 5,6 for an overview of the available techniques. These ROMs are computationally efficient and accurate, and are worthy when a full order model (FOM) needs to be simulated multiple-times for different parameter settings. Additionally, ROMs are even more valuable in the case of SWE, when the interest lies in simulating the model for a very long time horizon. MOR problems for SWE have been intensively studied in the literature, see, for example, References [7-12].

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“…Outline of the components of the angular velocity vector Ω with respect to the latitude angle as Ω x = 0 reproduced from Reference [36]…”

Section: F I G U R Ementioning

confidence: 99%

Learning reduced‐order dynamics for parametrized shallow water equations from data

Yıldız

Goyal

Benner

et al. 2021

Numerical Methods in Fluids

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“…respectivamente, que se desprenden al considerar el cambio del vector de posición en un sistema de referencia no-inercial [2]. Elúltimo término es la aceleración debida a la suma de las fuerzas (F) que no dependen de la rotación, como la fuerza debida al gradiente de presión (F P ), la fuerza de gravitación (F G ) y la fuerza de fricción (F r ).…”

Section: Teoría Sobre El Viento Geostróficounclassified

Comentario sobre La física de los huracanes Pauline y Patricia en su paso por el pacífico mexicano

Herrera

2021

Rev. Mex. Fis. E

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“…Figure1: Outline of the components of the angular velocity vector Ω with respect to the latitude angle θ as Ω x = 0,(reproduced from[2]). …”

mentioning

confidence: 99%

Data‐Driven Learning of Reduced‐Order Dynamics for a Parametrized Shallow Water Equation

Yıldız

Goyal

Benner

et al. 2021

Proc Appl Math and Mech

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On the direction of Coriolis force and the angular momentum conservation

Cited by 4 publications

References 9 publications

Learning reduced‐order dynamics for parametrized shallow water equations from data

Learning reduced‐order dynamics for parametrized shallow water equations from data

Comentario sobre La física de los huracanes Pauline y Patricia en su paso por el pacífico mexicano

Data‐Driven Learning of Reduced‐Order Dynamics for a Parametrized Shallow Water Equation

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