Deep convolutional architectures for extrapolative forecasts in time-dependent flow problems
Abstract Physical systems whose dynamics are governed by partial differential equations (PDEs) find numerous applications in science and engineering. The process of obtaining the solution from such PDEs may be computationally expensive for large-scale and parameterized problems. In this work, deep l...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-11-01
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| Series: | Advanced Modeling and Simulation in Engineering Sciences |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s40323-023-00254-y |
| _version_ | 1797414470474006528 |
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| author | Pratyush Bhatt Yash Kumar Azzeddine Soulaïmani |
| author_facet | Pratyush Bhatt Yash Kumar Azzeddine Soulaïmani |
| author_sort | Pratyush Bhatt |
| collection | DOAJ |
| description | Abstract Physical systems whose dynamics are governed by partial differential equations (PDEs) find numerous applications in science and engineering. The process of obtaining the solution from such PDEs may be computationally expensive for large-scale and parameterized problems. In this work, deep learning techniques developed especially for time-series forecasts, such as LSTM and TCN, or for spatial-feature extraction such as CNN, are employed to model the system dynamics for advection-dominated problems. This paper proposes a Convolutional Autoencoder(CAE) model for compression and a CNN future-step predictor for forecasting. These models take as input a sequence of high-fidelity vector solutions for consecutive time steps obtained from the PDEs and forecast the solutions for the subsequent time steps using auto-regression; thereby reducing the computation time and power needed to obtain such high-fidelity solutions. Non-intrusive reduced-order modeling techniques such as deep auto-encoder networks are utilized to compress the high-fidelity snapshots before feeding them as input to the forecasting models in order to reduce the complexity and the required computations in the online and offline stages. The models are tested on numerical benchmarks (1D Burgers’ equation and Stoker’s dam-break problem) to assess the long-term prediction accuracy, even outside the training domain (i.e. extrapolation). The most accurate model is then used to model a hypothetical dam break in a river with complex 2D bathymetry. The proposed CNN future-step predictor revealed much more accurate forecasting than LSTM and TCN in the considered spatiotemporal problems. |
| first_indexed | 2024-03-09T05:33:34Z |
| format | Article |
| id | doaj.art-a86315a609b84c8e8b68d16335a483ec |
| institution | Directory Open Access Journal |
| issn | 2213-7467 |
| language | English |
| last_indexed | 2024-03-09T05:33:34Z |
| publishDate | 2023-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advanced Modeling and Simulation in Engineering Sciences |
| spelling | doaj.art-a86315a609b84c8e8b68d16335a483ec2023-12-03T12:30:45ZengSpringerOpenAdvanced Modeling and Simulation in Engineering Sciences2213-74672023-11-0110113510.1186/s40323-023-00254-yDeep convolutional architectures for extrapolative forecasts in time-dependent flow problemsPratyush Bhatt0Yash Kumar1Azzeddine Soulaïmani2Department of Mechanical Engineering, Delhi Technological UniversityDepartment of Mechanical Engineering, Delhi Technological UniversityDepartment of Mechanical Engineering, École de technologie supérieureAbstract Physical systems whose dynamics are governed by partial differential equations (PDEs) find numerous applications in science and engineering. The process of obtaining the solution from such PDEs may be computationally expensive for large-scale and parameterized problems. In this work, deep learning techniques developed especially for time-series forecasts, such as LSTM and TCN, or for spatial-feature extraction such as CNN, are employed to model the system dynamics for advection-dominated problems. This paper proposes a Convolutional Autoencoder(CAE) model for compression and a CNN future-step predictor for forecasting. These models take as input a sequence of high-fidelity vector solutions for consecutive time steps obtained from the PDEs and forecast the solutions for the subsequent time steps using auto-regression; thereby reducing the computation time and power needed to obtain such high-fidelity solutions. Non-intrusive reduced-order modeling techniques such as deep auto-encoder networks are utilized to compress the high-fidelity snapshots before feeding them as input to the forecasting models in order to reduce the complexity and the required computations in the online and offline stages. The models are tested on numerical benchmarks (1D Burgers’ equation and Stoker’s dam-break problem) to assess the long-term prediction accuracy, even outside the training domain (i.e. extrapolation). The most accurate model is then used to model a hypothetical dam break in a river with complex 2D bathymetry. The proposed CNN future-step predictor revealed much more accurate forecasting than LSTM and TCN in the considered spatiotemporal problems.https://doi.org/10.1186/s40323-023-00254-yNon-intrusive reduced-order modelingDeep autoencodersLSTMTCNCNNTime-dependent flow problems |
| spellingShingle | Pratyush Bhatt Yash Kumar Azzeddine Soulaïmani Deep convolutional architectures for extrapolative forecasts in time-dependent flow problems Advanced Modeling and Simulation in Engineering Sciences Non-intrusive reduced-order modeling Deep autoencoders LSTM TCN CNN Time-dependent flow problems |
| title | Deep convolutional architectures for extrapolative forecasts in time-dependent flow problems |
| title_full | Deep convolutional architectures for extrapolative forecasts in time-dependent flow problems |
| title_fullStr | Deep convolutional architectures for extrapolative forecasts in time-dependent flow problems |
| title_full_unstemmed | Deep convolutional architectures for extrapolative forecasts in time-dependent flow problems |
| title_short | Deep convolutional architectures for extrapolative forecasts in time-dependent flow problems |
| title_sort | deep convolutional architectures for extrapolative forecasts in time dependent flow problems |
| topic | Non-intrusive reduced-order modeling Deep autoencoders LSTM TCN CNN Time-dependent flow problems |
| url | https://doi.org/10.1186/s40323-023-00254-y |
| work_keys_str_mv | AT pratyushbhatt deepconvolutionalarchitecturesforextrapolativeforecastsintimedependentflowproblems AT yashkumar deepconvolutionalarchitecturesforextrapolativeforecastsintimedependentflowproblems AT azzeddinesoulaimani deepconvolutionalarchitecturesforextrapolativeforecastsintimedependentflowproblems |