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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.11196 |
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| _version_ | 1866913736050081792 |
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| author | Jnini, Anas Goordoyal, Harshinee Dave, Sujal Vella, Flavio Fraser, Katharine H. Korobenko, Artem |
| author_facet | Jnini, Anas Goordoyal, Harshinee Dave, Sujal Vella, Flavio Fraser, Katharine H. Korobenko, Artem |
| contents | The Physics-Constrained DeepONet (PC-DeepONet), an architecture that incorporates fundamental physics knowledge into the data-driven DeepONet model, is presented in this study. This methodology is exemplified through surrogate modeling of fluid dynamics over a curved backward-facing step, a benchmark problem in computational fluid dynamics. The model was trained on computational fluid dynamics data generated for a range of parameterized geometries. The PC-DeepONet was able to learn the mapping from the parameters describing the geometry to the velocity and pressure fields. While the DeepONet is solely data-driven, the PC-DeepONet imposes the divergence constraint from the continuity equation onto the network. The PC-DeepONet demonstrates higher accuracy than the data-driven baseline, especially when trained on sparse data. Both models attain convergence with a small dataset of 50 samples and require only 50 iterations for convergence, highlighting the efficiency of neural operators in learning the dynamics governed by partial differential equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_11196 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Physics-constrained DeepONet for Surrogate CFD models: a curved backward-facing step case Jnini, Anas Goordoyal, Harshinee Dave, Sujal Vella, Flavio Fraser, Katharine H. Korobenko, Artem Fluid Dynamics Machine Learning The Physics-Constrained DeepONet (PC-DeepONet), an architecture that incorporates fundamental physics knowledge into the data-driven DeepONet model, is presented in this study. This methodology is exemplified through surrogate modeling of fluid dynamics over a curved backward-facing step, a benchmark problem in computational fluid dynamics. The model was trained on computational fluid dynamics data generated for a range of parameterized geometries. The PC-DeepONet was able to learn the mapping from the parameters describing the geometry to the velocity and pressure fields. While the DeepONet is solely data-driven, the PC-DeepONet imposes the divergence constraint from the continuity equation onto the network. The PC-DeepONet demonstrates higher accuracy than the data-driven baseline, especially when trained on sparse data. Both models attain convergence with a small dataset of 50 samples and require only 50 iterations for convergence, highlighting the efficiency of neural operators in learning the dynamics governed by partial differential equations. |
| title | Physics-constrained DeepONet for Surrogate CFD models: a curved backward-facing step case |
| topic | Fluid Dynamics Machine Learning |
| url | https://arxiv.org/abs/2503.11196 |