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| Auteurs principaux: | , , , , , , , |
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| Format: | Preprint |
| Publié: |
2024
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2410.11617 |
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| _version_ | 1866929543795703808 |
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| author | Liang, Aoming Mu, Zhaoyang Lin, Pengxiao Wang, Cong Ge, Mingming Shao, Ling Fan, Dixia Tang, Hao |
| author_facet | Liang, Aoming Mu, Zhaoyang Lin, Pengxiao Wang, Cong Ge, Mingming Shao, Ling Fan, Dixia Tang, Hao |
| contents | Learning the evolutionary dynamics of Partial Differential Equations (PDEs) is critical in understanding dynamic systems, yet current methods insufficiently learn their representations. This is largely due to the multi-scale nature of the solution, where certain regions exhibit rapid oscillations while others evolve more slowly. This paper introduces a framework of multi-scale and multi-expert (M$^2$M) neural operators designed to simulate and learn PDEs efficiently. We employ a divide-and-conquer strategy to train a multi-expert gated network for the dynamic router policy. Our method incorporates a controllable prior gating mechanism that determines the selection rights of experts, enhancing the model's efficiency. To optimize the learning process, we have implemented a PI (Proportional, Integral) control strategy to adjust the allocation rules precisely. This universal controllable approach allows the model to achieve greater accuracy. We test our approach on benchmark 2D Navier-Stokes equations and provide a custom multi-scale dataset. M$^2$M can achieve higher simulation accuracy and offer improved interpretability compared to baseline methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_11617 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | M$^{2}$M: Learning controllable Multi of experts and multi-scale operators are the Partial Differential Equations need Liang, Aoming Mu, Zhaoyang Lin, Pengxiao Wang, Cong Ge, Mingming Shao, Ling Fan, Dixia Tang, Hao Machine Learning Artificial Intelligence Computer Vision and Pattern Recognition Learning the evolutionary dynamics of Partial Differential Equations (PDEs) is critical in understanding dynamic systems, yet current methods insufficiently learn their representations. This is largely due to the multi-scale nature of the solution, where certain regions exhibit rapid oscillations while others evolve more slowly. This paper introduces a framework of multi-scale and multi-expert (M$^2$M) neural operators designed to simulate and learn PDEs efficiently. We employ a divide-and-conquer strategy to train a multi-expert gated network for the dynamic router policy. Our method incorporates a controllable prior gating mechanism that determines the selection rights of experts, enhancing the model's efficiency. To optimize the learning process, we have implemented a PI (Proportional, Integral) control strategy to adjust the allocation rules precisely. This universal controllable approach allows the model to achieve greater accuracy. We test our approach on benchmark 2D Navier-Stokes equations and provide a custom multi-scale dataset. M$^2$M can achieve higher simulation accuracy and offer improved interpretability compared to baseline methods. |
| title | M$^{2}$M: Learning controllable Multi of experts and multi-scale operators are the Partial Differential Equations need |
| topic | Machine Learning Artificial Intelligence Computer Vision and Pattern Recognition |
| url | https://arxiv.org/abs/2410.11617 |