Stabilizing PDE--ML coupled systems
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909866782621696 |
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| author | Qadeer, Saad Stinis, Panos Wan, Hui. |
| author_facet | Qadeer, Saad Stinis, Panos Wan, Hui. |
| contents | A long-standing obstacle in the use of machine-learnt surrogates with larger PDE systems is the onset of instabilities when solved numerically. Efforts towards ameliorating these have mostly concentrated on improving the accuracy of the surrogates or imbuing them with additional structure, and have garnered limited success. In this article, we study a prototype problem and draw insights that can help with more complex systems. In particular, we focus on a viscous Burgers'-ML system and, after identifying the cause of the instabilities, prescribe strategies to stabilize the coupled system. To improve the accuracy of the stabilized system, we next explore methods based on the Mori--Zwanzig formalism. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_19274 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stabilizing PDE--ML coupled systems Qadeer, Saad Stinis, Panos Wan, Hui. Numerical Analysis Machine Learning 65M12 A long-standing obstacle in the use of machine-learnt surrogates with larger PDE systems is the onset of instabilities when solved numerically. Efforts towards ameliorating these have mostly concentrated on improving the accuracy of the surrogates or imbuing them with additional structure, and have garnered limited success. In this article, we study a prototype problem and draw insights that can help with more complex systems. In particular, we focus on a viscous Burgers'-ML system and, after identifying the cause of the instabilities, prescribe strategies to stabilize the coupled system. To improve the accuracy of the stabilized system, we next explore methods based on the Mori--Zwanzig formalism. |
| title | Stabilizing PDE--ML coupled systems |
| topic | Numerical Analysis Machine Learning 65M12 |
| url | https://arxiv.org/abs/2506.19274 |