Hybrid data-driven closure strategies for reduced order modeling

Ivagnes, Anna; Stabile, Giovanni; Mola, Andrea; Iliescu, Traian; Rozza, Gianluigi

doi:10.1016/j.amc.2023.127920

Cited by 4 publications

(1 citation statement)

References 41 publications

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“…ROMs [171]- [174] or semi-intrusive ROMs [145], [175]- [179] where the effect of the ignored modes are corrected using a data-driven approach have been proposed. Moreover, fully non-intrusive ROMs [180]- [185] are gaining popularity because of their ability to address the second issue.…”

Section: F: Reduced Order Modelingmentioning

confidence: 99%

Digital Twins in Wind Energy: Emerging Technologies and Industry-Informed Future Directions

Stadtmann,

Rasheed,

Kvamsdal

et al. 2023

IEEE Access

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This article presents a comprehensive overview of the digital twin technology and its capability levels, with a specific focus on its applications in the wind energy industry. It consolidates the definitions of digital twin and its capability levels on a scale from 0-5; 0-standalone, 1-descriptive, 2-diagnostic, 3predictive, 4-prescriptive, 5-autonomous. It then, from an industrial perspective, identifies the current state of the art and research needs in the wind energy sector. It is concluded that the main challenges hindering the realization of highly capable digital twins fall into one of the four categories; standards-related, data-related, model-related, and industrial acceptance related. The article proposes approaches to the identified challenges from the perspective of research institutes and offers a set of recommendations for various stakeholders to facilitate the acceptance of the technology. The contribution of this article lies in its synthesis of the current state of knowledge and its identification of future research needs and challenges from an industry perspective, ultimately providing a roadmap for future research and development in the field of digital twin and its applications in the wind energy industry.

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Section: F: Reduced Order Modelingmentioning

confidence: 99%

Digital Twins in Wind Energy: Emerging Technologies and Industry-Informed Future Directions

Stadtmann,

Rasheed,

Kvamsdal

et al. 2023

IEEE Access

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On the latent dimension of deep autoencoders for reduced order modeling of PDEs parametrized by random fields

Franco,

Fraulin,

Manzoni

et al. 2024

Adv Comput Math

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Deep Learning is having a remarkable impact on the design of Reduced Order Models (ROMs) for Partial Differential Equations (PDEs), where it is exploited as a powerful tool for tackling complex problems for which classical methods might fail. In this respect, deep autoencoders play a fundamental role, as they provide an extremely flexible tool for reducing the dimensionality of a given problem by leveraging on the nonlinear capabilities of neural networks. Indeed, starting from this paradigm, several successful approaches have already been developed, which are here referred to as Deep Learning-based ROMs (DL-ROMs). Nevertheless, when it comes to stochastic problems parameterized by random fields, the current understanding of DL-ROMs is mostly based on empirical evidence: in fact, their theoretical analysis is currently limited to the case of PDEs depending on a finite number of (deterministic) parameters. The purpose of this work is to extend the existing literature by providing some theoretical insights about the use of DL-ROMs in the presence of stochasticity generated by random fields. In particular, we derive explicit error bounds that can guide domain practitioners when choosing the latent dimension of deep autoencoders. We evaluate the practical usefulness of our theory by means of numerical experiments, showing how our analysis can significantly impact the performance of DL-ROMs.

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A new hybrid reduced order modeling for parametrized Navier–Stokes equations in stream-vorticity formulation

Zhang,

Xu,

Guo

et al. 2024

Physics of Fluids

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In the context of traditional reduced order modeling methods (ROMs), time and parameter extrapolation tasks remain a formidable challenge. To this end, we propose a hybrid projection/data-driven framework that leverages two subspaces to improve the prediction accuracy of traditional ROMs. We first obtain inaccurate mode coefficients from traditional ROMs in the reduced order subspace. Then, in the prior dimensionality reduced subspace, we correct the inaccurate mode coefficients and restore the discarded mode coefficients through neural network. Finally, we approximate the solutions with these mode coefficients in the prior dimensionality reduced subspace. To reduce the computational cost during the offline training stage, we propose a training data sampling strategy based on dynamic mode decomposition (DMD). The effectiveness of the proposed method is investigated with the parameterized Navier–Stokes equations in stream-vorticity formulation. In addition, two additional time extrapolation methods based on DMD are also proposed and compared.

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Hybrid data-driven closure strategies for reduced order modeling

Cited by 4 publications

References 41 publications

Digital Twins in Wind Energy: Emerging Technologies and Industry-Informed Future Directions

Digital Twins in Wind Energy: Emerging Technologies and Industry-Informed Future Directions

On the latent dimension of deep autoencoders for reduced order modeling of PDEs parametrized by random fields

A new hybrid reduced order modeling for parametrized Navier–Stokes equations in stream-vorticity formulation

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