Autoencoder-based Dimensionality Reduction for Accelerating the Solution of Nonlinear Time-Dependent PDEs: Transport in Porous Media with Reactions
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918020081778688 |
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| author | Behnoudfar, Diba |
| author_facet | Behnoudfar, Diba |
| contents | Physics-based models often involve large systems of parametrized partial differential equations, where design parameters control various properties. However, high-fidelity simulations of such systems on large domains or with high grid resolution can be computationally expensive for the accurate evaluation of a large number of parameters. Reduced-order modeling has emerged as a solution to reduce the dimensionality of such problems. This work focuses on a nonlinear compression technique using a convolutional autoencoder for accelerating the solution of transport in porous media problems. The model demonstrates successful training, achieving a mean square error (MSE) on the order of \num{1e-3} for the validation data. For an unseen parameter set, the model exhibits mixed performance; it achieves acceptable accuracy for larger time steps but shows lower performance for earlier times. This issue could potentially be resolved by fine-tuning the network architecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_09071 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Autoencoder-based Dimensionality Reduction for Accelerating the Solution of Nonlinear Time-Dependent PDEs: Transport in Porous Media with Reactions Behnoudfar, Diba Computational Physics Physics-based models often involve large systems of parametrized partial differential equations, where design parameters control various properties. However, high-fidelity simulations of such systems on large domains or with high grid resolution can be computationally expensive for the accurate evaluation of a large number of parameters. Reduced-order modeling has emerged as a solution to reduce the dimensionality of such problems. This work focuses on a nonlinear compression technique using a convolutional autoencoder for accelerating the solution of transport in porous media problems. The model demonstrates successful training, achieving a mean square error (MSE) on the order of \num{1e-3} for the validation data. For an unseen parameter set, the model exhibits mixed performance; it achieves acceptable accuracy for larger time steps but shows lower performance for earlier times. This issue could potentially be resolved by fine-tuning the network architecture. |
| title | Autoencoder-based Dimensionality Reduction for Accelerating the Solution of Nonlinear Time-Dependent PDEs: Transport in Porous Media with Reactions |
| topic | Computational Physics |
| url | https://arxiv.org/abs/2505.09071 |