Guaranteeing Conservation Laws with Projection in Physics-Informed Neural Networks
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909359824437248 |
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| author | Baez, Anthony Zhang, Wang Ma, Ziwen Das, Subhro Nguyen, Lam M. Daniel, Luca |
| author_facet | Baez, Anthony Zhang, Wang Ma, Ziwen Das, Subhro Nguyen, Lam M. Daniel, Luca |
| contents | Physics-informed neural networks (PINNs) incorporate physical laws into their training to efficiently solve partial differential equations (PDEs) with minimal data. However, PINNs fail to guarantee adherence to conservation laws, which are also important to consider in modeling physical systems. To address this, we proposed PINN-Proj, a PINN-based model that uses a novel projection method to enforce conservation laws. We found that PINN-Proj substantially outperformed PINN in conserving momentum and lowered prediction error by three to four orders of magnitude from the best benchmark tested. PINN-Proj also performed marginally better in the separate task of state prediction on three PDE datasets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_17445 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Guaranteeing Conservation Laws with Projection in Physics-Informed Neural Networks Baez, Anthony Zhang, Wang Ma, Ziwen Das, Subhro Nguyen, Lam M. Daniel, Luca Machine Learning Physics-informed neural networks (PINNs) incorporate physical laws into their training to efficiently solve partial differential equations (PDEs) with minimal data. However, PINNs fail to guarantee adherence to conservation laws, which are also important to consider in modeling physical systems. To address this, we proposed PINN-Proj, a PINN-based model that uses a novel projection method to enforce conservation laws. We found that PINN-Proj substantially outperformed PINN in conserving momentum and lowered prediction error by three to four orders of magnitude from the best benchmark tested. PINN-Proj also performed marginally better in the separate task of state prediction on three PDE datasets. |
| title | Guaranteeing Conservation Laws with Projection in Physics-Informed Neural Networks |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2410.17445 |