Comment on “Novel Approach for Selecting Low-Fidelity Scale Factor in Multifidelity Metamodeling”

Yang, Sunwoong; Yee, Kwanjung

doi:10.2514/1.j061643

Cited by 3 publications

(2 citation statements)

References 3 publications

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“…The initial learning rate is set to 10 −3 , and it decays at a rate of 0.1 every 1000 epochs. The maximum epoch should be selected carefully because a model that does not fully converge can make significantly different predictions than a converged model [40]. For all models (AE, VAE, and β-VAE), the maximum number of epochs is set to 3000 because additional epochs did not result in a significant change, and this value guaranteed sufficient convergence in terms of the loss function.…”

Section: Training Detailsmentioning

confidence: 99%

“…2, AE, VAE, and β-VAE, are trained to investigate their differences in terms of DR for transonic flow. In particular, several β-VAE models are trained (β ∈[10,20,30,40, 50, 100, 150, 200, 500, 750, 1000, 2000, 3000, 4000]) to investigate the effects of the β value (technically speaking, the VAE can be regarded as the β-VAE when β has a value of 1). The dimension of the latent space is set to 16, which is considered sufficient for encoding the training data generated from the 2D parameter domain (Ma and AoA).…”

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confidence: 99%

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Physics-aware Reduced-order Modeling of Transonic Flow via $β$-Variational Autoencoder

Kang,

Yang,

Yee

2022

Preprint

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Autoencoder-based reduced-order modeling has recently attracted significant attention, owing to the ability to capture underlying nonlinear features. However, its uninterpretable latent variables (LVs) severely undermine the applicability to various physical problems. This study proposes physics-aware reduced-order modeling using a β-variational autoencoder to address this issue. The presented approach can quantify the rank and independence of LVs, which is validated both quantitatively and qualitatively using various techniques. Accordingly, LVs containing interpretable physical features were successfully identified. It was also verified that these "physics-aware" LVs correspond to the physical parameters that are the generating factors of the dataset, i.e., the Mach number and angle of attack in this study. Moreover, the effects of these physics-aware LVs on the accuracy of reduced-order modeling were investigated, which verified the potential of this method to alleviate the computational cost of the offline stage by excluding physics-unaware LVs.

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Section: Training Detailsmentioning

confidence: 99%

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confidence: 99%

Physics-aware Reduced-order Modeling of Transonic Flow via $β$-Variational Autoencoder

Kang,

Yang,

Yee

2022

Preprint

Self Cite

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Towards reliable uncertainty quantification via deep ensemble in multi-output regression task

Yang,

Yee

2024

Engineering Applications of Artificial Intelligence

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Physics-aware reduced-order modeling of transonic flow via β -variational autoencoder

2022

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Autoencoder-based reduced-order modeling (ROM) has recently attracted significant attention, owing to its ability to capture underlying nonlinear features. However, two critical drawbacks severely undermine its scalability to various physical applications: entangled and therefore uninterpretable latent variables (LVs) and the blindfold determination of latent space dimension. In this regard, this study proposes the physics-aware ROM using only interpretable and information-intensive LVs extracted by β-variational autoencoder, which are referred to as physics-aware LVs throughout this paper. To extract these LVs, their independence and information intensity are quantitatively scrutinized in a two-dimensional transonic flow benchmark problem. Then, the physical meanings of the physics-aware LVs are thoroughly investigated and we confirmed that with appropriate hyperparameter β, they actually correspond to the generating factors of the training dataset, Mach number and angle of attack. To the best of the authors' knowledge, our work is the first to practically confirm that β-variational autoencoder can automatically extract the physical generating factors in the field of applied physics. Finally, physics-aware ROM, which utilizes only physics-aware LVs, is compared with conventional ROMs, and its validity and efficiency are successfully verified.

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Comment on “Novel Approach for Selecting Low-Fidelity Scale Factor in Multifidelity Metamodeling”

Cited by 3 publications

References 3 publications

Physics-aware Reduced-order Modeling of Transonic Flow via $β$-Variational Autoencoder

Physics-aware Reduced-order Modeling of Transonic Flow via $β$-Variational Autoencoder

Towards reliable uncertainty quantification via deep ensemble in multi-output regression task

Physics-aware reduced-order modeling of transonic flow via β -variational autoencoder

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