What do physics-informed DeepONets learn? Understanding and improving training for scientific computing applications
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866915037415735296 |
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| author | Williams, Emily Howard, Amanda Meuris, Brek Stinis, Panos |
| author_facet | Williams, Emily Howard, Amanda Meuris, Brek Stinis, Panos |
| contents | Physics-informed deep operator networks (DeepONets) have emerged as a promising approach toward numerically approximating the solution of partial differential equations (PDEs). In this work, we aim to develop further understanding of what is being learned by physics-informed DeepONets by assessing the universality of the extracted basis functions and demonstrating their potential toward model reduction with spectral methods. Results provide clarity about measuring the performance of a physics-informed DeepONet through the decays of singular values and expansion coefficients. In addition, we propose a transfer learning approach for improving training for physics-informed DeepONets between parameters of the same PDE as well as across different, but related, PDEs where these models struggle to train well. This approach results in significant error reduction and learned basis functions that are more effective in representing the solution of a PDE. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_18459 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | What do physics-informed DeepONets learn? Understanding and improving training for scientific computing applications Williams, Emily Howard, Amanda Meuris, Brek Stinis, Panos Machine Learning Numerical Analysis Physics-informed deep operator networks (DeepONets) have emerged as a promising approach toward numerically approximating the solution of partial differential equations (PDEs). In this work, we aim to develop further understanding of what is being learned by physics-informed DeepONets by assessing the universality of the extracted basis functions and demonstrating their potential toward model reduction with spectral methods. Results provide clarity about measuring the performance of a physics-informed DeepONet through the decays of singular values and expansion coefficients. In addition, we propose a transfer learning approach for improving training for physics-informed DeepONets between parameters of the same PDE as well as across different, but related, PDEs where these models struggle to train well. This approach results in significant error reduction and learned basis functions that are more effective in representing the solution of a PDE. |
| title | What do physics-informed DeepONets learn? Understanding and improving training for scientific computing applications |
| topic | Machine Learning Numerical Analysis |
| url | https://arxiv.org/abs/2411.18459 |