Conditional variational autoencoder with Gaussian process regression recognition for parametric models
In this article, we present a data-driven method for parametric models with noisy observation data. Gaussian process regression based reduced order modeling (GPR-based ROM) can realize fast online predictions without using equations in the offline stage. However, GPR-based ROM does not perform well...
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| Published in: | Journal of computational and applied mathematics Vol. 438; p. 115532 |
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| Format: | Journal Article |
| Language: | English |
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Elsevier B.V
01.03.2024
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| ISSN: | 0377-0427, 1879-1778 |
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| Abstract | In this article, we present a data-driven method for parametric models with noisy observation data. Gaussian process regression based reduced order modeling (GPR-based ROM) can realize fast online predictions without using equations in the offline stage. However, GPR-based ROM does not perform well for complex systems since POD projection are naturally linear. Conditional variational autoencoder (CVAE) can address this issue via nonlinear neural networks but it has more model complexity, which poses challenges for training and tuning hyperparameters. To this end, we propose a framework of CVAE with Gaussian process regression recognition (CVAE-GPRR). The proposed method consists of a recognition model and a likelihood model. In the recognition model, we first extract low-dimensional features from data by POD to filter the redundant information with high frequency. And then a non-parametric model GPR is used to learn the map from parameters to POD latent variables, which can also alleviate the impact of noise. CVAE-GPRR can achieve the similar accuracy to CVAE but with fewer parameters. In the likelihood model, neural networks are used to reconstruct data. Besides the samples of POD latent variables and input parameters, physical variables are also added as the inputs to make predictions in the whole physical space. This cannot be achieved by either GPR-based ROM or CVAE. Moreover, the numerical results show that CVAE-GPRR may alleviate the overfitting issue in CVAE. |
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| AbstractList | In this article, we present a data-driven method for parametric models with noisy observation data. Gaussian process regression based reduced order modeling (GPR-based ROM) can realize fast online predictions without using equations in the offline stage. However, GPR-based ROM does not perform well for complex systems since POD projection are naturally linear. Conditional variational autoencoder (CVAE) can address this issue via nonlinear neural networks but it has more model complexity, which poses challenges for training and tuning hyperparameters. To this end, we propose a framework of CVAE with Gaussian process regression recognition (CVAE-GPRR). The proposed method consists of a recognition model and a likelihood model. In the recognition model, we first extract low-dimensional features from data by POD to filter the redundant information with high frequency. And then a non-parametric model GPR is used to learn the map from parameters to POD latent variables, which can also alleviate the impact of noise. CVAE-GPRR can achieve the similar accuracy to CVAE but with fewer parameters. In the likelihood model, neural networks are used to reconstruct data. Besides the samples of POD latent variables and input parameters, physical variables are also added as the inputs to make predictions in the whole physical space. This cannot be achieved by either GPR-based ROM or CVAE. Moreover, the numerical results show that CVAE-GPRR may alleviate the overfitting issue in CVAE. |
| ArticleNumber | 115532 |
| Author | Jiang, Lijian Zhang, Xuehan |
| Author_xml | – sequence: 1 givenname: Xuehan surname: Zhang fullname: Zhang, Xuehan email: xhzhang@tongji.edu.cn – sequence: 2 givenname: Lijian orcidid: 0000-0002-3410-1219 surname: Jiang fullname: Jiang, Lijian email: ljjiang@tongji.edu.cn |
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| Keywords | Conditional variational autoencoder Gaussian process regression Proper orthogonal decomposition Parametric models |
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| SubjectTerms | Conditional variational autoencoder Gaussian process regression Parametric models Proper orthogonal decomposition |
| Title | Conditional variational autoencoder with Gaussian process regression recognition for parametric models |
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