Multifidelity computing for coupling full and reduced order models

Ahmed, Shady E.; San, Omer; Kara, Kursat; Younis, Rami M.; Rasheed, Adil

doi:10.1371/journal.pone.0246092

Cited by 16 publications

(10 citation statements)

References 55 publications

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“…. , y w f (µ tr j )} (32) where, y i f (µ tr j ) = zq (t i ; µ tr j ). In particular, we aim to obtain the nonlinear mapping such that: Where b f are the weight and bias terms of the FFNN and ϕ f : R nµ+1 → R q is a (non)linear activation function.…”

Section: Parameter Regressionmentioning

confidence: 99%

“…Proper orthogonal decomposition (POD) approximates the intrinsic dimensions of the HFM solutions by utilizing linear algebra techniques such as principal component analysis, and singular value decomposition (SVD) [29,30]. The galerkin projection methods predict the evolution of the temporal coefficients through the governing equations of the system [31,32]. To adress the nonlinear terms of the PDEs, various methodologies have been proposed including the petrovgalerkin (PG) projection [33] and the least-squares-PG [34].…”

Section: Introductionmentioning

confidence: 99%

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$\textit{FastSVD-ML-ROM}$: A Reduced-Order Modeling Framework based on Machine Learning for Real-Time Applications

Drakoulas¹,

V.²,

Bourantas³

et al. 2022

Preprint

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Digital twins have emerged as a key technology for optimizing the performance of engineering products and systems. High-fidelity numerical simulations constitute the backbone of engineering design, providing an accurate insight into the performance of complex systems. However, largescale, dynamic, non-linear models require significant computational resources and are prohibitive for real-time digital twin applications. To this end, reduced order models (ROMs) are employed, to approximate the high-fidelity solutions while accurately capturing the dominant aspects of the physical behavior. The present work proposes a new machine learning (ML) platform for the development of ROMs, to handle large-scale numerical problems dealing with transient nonlinear partial differential equations. Our framework, mentioned as FastSVD-ML-ROM, utilizes (i) a singular value decomposition (SVD) update methodology, to compute a linear subspace of the multi-fidelity solutions during the simulation process, (ii) convolutional autoencoders for nonlinear dimensionality reduction, (iii) feed-forward neural networks to map the input parameters to the latent spaces, and (iv) long short-term memory networks to predict and forecast the dynamics of parametric solutions. The efficiency of the FastSVD-ML-ROM framework is demonstrated for a 2D linear convection-diffusion equation, the problem of fluid around a cylinder, and the 3D blood flow inside an arterial segment. The accuracy of the reconstructed results demonstrates the robustness and assesses the efficiency of the proposed approach.

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Section: Parameter Regressionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

$\textit{FastSVD-ML-ROM}$: A Reduced-Order Modeling Framework based on Machine Learning for Real-Time Applications

Drakoulas¹,

V.²,

Bourantas³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Once we build ROMs, we can develop new coupled ROM‐FOM models to perform a real‐time, accurate approximation of wind turbine loadings due to wind flow interactions, which is essential in maximizing the power production of wind farms. Several methods to bridge low‐fidelity and high‐fidelity descriptions have been recently introduced to form the building blocks of an integrated HAM approach among mixed fidelity descriptions [11].…”

Section: Eclecticism and Interface Learningmentioning

confidence: 99%

“…Moreover, neural networks have been utilized to predict the geometric location interfaces in developing adaptive domain decomposition methods [138]. As highlighted in our recent works [10,11], ML tools can be effectively utilized in various forms of interfacial error correction to form the building blocks of an integrated approach among mixed fidelity descriptions toward predictive DT technologies.…”

Section: Introductionmentioning

confidence: 99%

Hybrid analysis and modeling, eclecticism, and multifidelity computing toward digital twin revolution

2021

Self Cite

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Most modeling approaches lie in either of the two categories: physics‐based or data‐driven. Recently, a third approach which is a combination of these deterministic and statistical models is emerging for scientific applications. To leverage these developments, our aim in this perspective paper is centered around exploring numerous principle concepts to address the challenges of (i) trustworthiness and generalizability in developing data‐driven models to shed light on understanding the fundamental trade‐offs in their accuracy and efficiency and (ii) seamless integration of interface learning and multifidelity coupling approaches that transfer and represent information between different entities, particularly when different scales are governed by different physics, each operating on a different level of abstraction. Addressing these challenges could enable the revolution of digital twin technologies for scientific and engineering applications.

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“…While their approach enhances variance reduction due to the consideration of correlations among the modeling fidelities, it may still face the same issues (e.g., accurate characterization of the biasing distribution and fixing the number of HF calls a priori.) Other recent contributions have also used fusion for estimating HF model responses in a deterministic setting: Ahmed et al [21] propose a zonal multifidelity modeling framework, Hebbal et al [22] use a deep Gaussian process (GP) to handle input parameter incoherences across the multiple models, and Meng et al [23] propose a Bayesian neural network to link together a data-driven deep neural network (DNN) and a physics-informed neural network (PINN).…”

Section: Brief Review Of Multifidelity Modeling and Active Learning F...mentioning

confidence: 99%

Active Learning with Multifidelity Modeling for Efficient Rare Event Simulation

Dhulipala¹,

Shields²,

Spencer³

et al. 2021

Preprint

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While multifidelity modeling provides a cost-effective way to conduct uncertainty quantification with computationally expensive models, much greater efficiency can be achieved by adaptively deciding the number of required high-fidelity (HF) simulations, depending on the type and complexity of the problem and the desired accuracy in the results. We propose a framework for active learning with multifidelity modeling emphasizing the efficient estimation of rare events. Our framework works by fusing a low-fidelity (LF) prediction with an HF-inferred correction, filtering the corrected LF prediction to decide whether to call the high-fidelity model, and for enhanced subsequent accuracy, adapting the correction for the LF prediction after every HF model call. The framework does not make any assumptions as to the LF model type or its correlations with the HF model. In addition, for improved robustness when estimating smaller failure probabilities, we propose using dynamic active learning functions that decide when to call the HF model.We demonstrate our framework using several academic case studies and two finite element (FE) model case studies: estimating Navier-Stokes velocities using the Stokes approximation and estimating stresses in a transversely isotropic model subjected to displacements via a coarsely meshed isotropic model. Across these case studies, not only did the proposed framework estimate the failure probabilities accurately, but compared with either Monte Carlo or a standard variance reduction method, it also required only a small fraction of the calls to the HF model.

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Multifidelity computing for coupling full and reduced order models

Cited by 16 publications

References 55 publications

$\textit{FastSVD-ML-ROM}$: A Reduced-Order Modeling Framework based on Machine Learning for Real-Time Applications

$\textit{FastSVD-ML-ROM}$: A Reduced-Order Modeling Framework based on Machine Learning for Real-Time Applications

Hybrid analysis and modeling, eclecticism, and multifidelity computing toward digital twin revolution

Active Learning with Multifidelity Modeling for Efficient Rare Event Simulation

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