AONN-2: An adjoint-oriented neural network method for PDE-constrained shape optimization
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916471956832256 |
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| author | Wang, Xili Yin, Pengfei Zhang, Bo Yang, Chao |
| author_facet | Wang, Xili Yin, Pengfei Zhang, Bo Yang, Chao |
| contents | Shape optimization has been playing an important role in a large variety of engineering applications. Existing shape optimization methods are generally mesh-dependent and therefore encounter challenges due to mesh deformation. To overcome this limitation, we present a new adjoint-oriented neural network method, AONN-2, for PDE-constrained shape optimization problems. This method extends the capabilities of the original AONN method [1], which is developed for efficiently solving parametric optimal control problems. AONN-2 inherits the direct-adjoint looping (DAL) framework for computing the extremum of an objective functional and the neural network methods for solving complicated PDEs from AONN. Furthermore, AONN-2 expands the application scope to shape optimization by taking advantage of the shape derivatives to optimize the shape represented by discrete boundary points. AONN-2 is a fully mesh-free shape optimization approach, naturally sidestepping issues related to mesh deformation, with no need for maintaining mesh quality and additional mesh corrections. A series of experimental results are presented, highlighting the flexibility, robustness, and accuracy of AONN-2. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_08388 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | AONN-2: An adjoint-oriented neural network method for PDE-constrained shape optimization Wang, Xili Yin, Pengfei Zhang, Bo Yang, Chao Optimization and Control Shape optimization has been playing an important role in a large variety of engineering applications. Existing shape optimization methods are generally mesh-dependent and therefore encounter challenges due to mesh deformation. To overcome this limitation, we present a new adjoint-oriented neural network method, AONN-2, for PDE-constrained shape optimization problems. This method extends the capabilities of the original AONN method [1], which is developed for efficiently solving parametric optimal control problems. AONN-2 inherits the direct-adjoint looping (DAL) framework for computing the extremum of an objective functional and the neural network methods for solving complicated PDEs from AONN. Furthermore, AONN-2 expands the application scope to shape optimization by taking advantage of the shape derivatives to optimize the shape represented by discrete boundary points. AONN-2 is a fully mesh-free shape optimization approach, naturally sidestepping issues related to mesh deformation, with no need for maintaining mesh quality and additional mesh corrections. A series of experimental results are presented, highlighting the flexibility, robustness, and accuracy of AONN-2. |
| title | AONN-2: An adjoint-oriented neural network method for PDE-constrained shape optimization |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2309.08388 |