Slim multi-scale convolutional autoencoder-based reduced-order models for interpretable features of a complex dynamical system
In recent years, data-driven deep learning models have gained significant importance in the analysis of turbulent dynamical systems. Within the context of reduced-order models, convolutional autoencoders (CAEs) pose a universally applicable alternative to conventional approaches. They can learn nonl...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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AIP Publishing LLC
2025-03-01
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| Series: | APL Machine Learning |
| Online Access: | http://dx.doi.org/10.1063/5.0244416 |
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| author | Philipp Teutsch Philipp Pfeffer Mohammad Sharifi Ghazijahani Christian Cierpka Jörg Schumacher Patrick Mäder |
| author_facet | Philipp Teutsch Philipp Pfeffer Mohammad Sharifi Ghazijahani Christian Cierpka Jörg Schumacher Patrick Mäder |
| author_sort | Philipp Teutsch |
| collection | DOAJ |
| description | In recent years, data-driven deep learning models have gained significant importance in the analysis of turbulent dynamical systems. Within the context of reduced-order models, convolutional autoencoders (CAEs) pose a universally applicable alternative to conventional approaches. They can learn nonlinear transformations directly from data, without prior knowledge of the system. However, the features generated by such models lack interpretability. Thus, the resulting model is a black-box that effectively reduces the complexity of the system but does not provide insights into the meaning of the latent features. To address this critical issue, we introduce a novel interpretable CAE approach for high-dimensional fluid flow data that maintains the reconstruction quality of conventional CAEs and allows for feature interpretation. Our method can be easily integrated into any existing CAE architecture with minor modifications of the training process. We compare our approach to Proper Orthogonal Decomposition (POD) and two existing methods for interpretable CAEs. We apply all methods to three different experimental turbulent Rayleigh–Bénard convection datasets with varying complexity. Our results show that the proposed method is lightweight, easy to train, and achieves relative reconstruction performance improvements of up to 6.4% over POD for 64 modes. The relative improvement increases to up to 229.8% as the number of modes decreases. In addition, our method delivers interpretable features similar to those of POD and is significantly less resource-intensive than existing CAE approaches, using less than 2% of the parameters. These approaches either trade interpretability for reconstruction performance or only provide interpretability to a limited extent. |
| format | Article |
| id | doaj-art-236f8e1f2be64001a1d9c1d7b38ae1f2 |
| institution | DOAJ |
| issn | 2770-9019 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | AIP Publishing LLC |
| record_format | Article |
| series | APL Machine Learning |
| spelling | doaj-art-236f8e1f2be64001a1d9c1d7b38ae1f22025-08-20T03:04:26ZengAIP Publishing LLCAPL Machine Learning2770-90192025-03-0131016112016112-1510.1063/5.0244416Slim multi-scale convolutional autoencoder-based reduced-order models for interpretable features of a complex dynamical systemPhilipp Teutsch0Philipp Pfeffer1Mohammad Sharifi Ghazijahani2Christian Cierpka3Jörg Schumacher4Patrick Mäder5Group for Data-intensive Systems and Visualization, Technische Universität Ilmenau, D-98684 Ilmenau, GermanyInstitute of Thermodynamics and Fluid Mechanics, Technische Universität Ilmenau, D-98684 Ilmenau, GermanyInstitute of Thermodynamics and Fluid Mechanics, Technische Universität Ilmenau, D-98684 Ilmenau, GermanyInstitute of Thermodynamics and Fluid Mechanics, Technische Universität Ilmenau, D-98684 Ilmenau, GermanyInstitute of Thermodynamics and Fluid Mechanics, Technische Universität Ilmenau, D-98684 Ilmenau, GermanyGroup for Data-intensive Systems and Visualization, Technische Universität Ilmenau, D-98684 Ilmenau, GermanyIn recent years, data-driven deep learning models have gained significant importance in the analysis of turbulent dynamical systems. Within the context of reduced-order models, convolutional autoencoders (CAEs) pose a universally applicable alternative to conventional approaches. They can learn nonlinear transformations directly from data, without prior knowledge of the system. However, the features generated by such models lack interpretability. Thus, the resulting model is a black-box that effectively reduces the complexity of the system but does not provide insights into the meaning of the latent features. To address this critical issue, we introduce a novel interpretable CAE approach for high-dimensional fluid flow data that maintains the reconstruction quality of conventional CAEs and allows for feature interpretation. Our method can be easily integrated into any existing CAE architecture with minor modifications of the training process. We compare our approach to Proper Orthogonal Decomposition (POD) and two existing methods for interpretable CAEs. We apply all methods to three different experimental turbulent Rayleigh–Bénard convection datasets with varying complexity. Our results show that the proposed method is lightweight, easy to train, and achieves relative reconstruction performance improvements of up to 6.4% over POD for 64 modes. The relative improvement increases to up to 229.8% as the number of modes decreases. In addition, our method delivers interpretable features similar to those of POD and is significantly less resource-intensive than existing CAE approaches, using less than 2% of the parameters. These approaches either trade interpretability for reconstruction performance or only provide interpretability to a limited extent.http://dx.doi.org/10.1063/5.0244416 |
| spellingShingle | Philipp Teutsch Philipp Pfeffer Mohammad Sharifi Ghazijahani Christian Cierpka Jörg Schumacher Patrick Mäder Slim multi-scale convolutional autoencoder-based reduced-order models for interpretable features of a complex dynamical system APL Machine Learning |
| title | Slim multi-scale convolutional autoencoder-based reduced-order models for interpretable features of a complex dynamical system |
| title_full | Slim multi-scale convolutional autoencoder-based reduced-order models for interpretable features of a complex dynamical system |
| title_fullStr | Slim multi-scale convolutional autoencoder-based reduced-order models for interpretable features of a complex dynamical system |
| title_full_unstemmed | Slim multi-scale convolutional autoencoder-based reduced-order models for interpretable features of a complex dynamical system |
| title_short | Slim multi-scale convolutional autoencoder-based reduced-order models for interpretable features of a complex dynamical system |
| title_sort | slim multi scale convolutional autoencoder based reduced order models for interpretable features of a complex dynamical system |
| url | http://dx.doi.org/10.1063/5.0244416 |
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