Training Stiff Neural Ordinary Differential Equations with Implicit Single-Step Methods
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916426043883520 |
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| author | Fronk, Colby Petzold, Linda |
| author_facet | Fronk, Colby Petzold, Linda |
| contents | Stiff systems of ordinary differential equations (ODEs) are pervasive in many science and engineering fields, yet standard neural ODE approaches struggle to learn them. This limitation is the main barrier to the widespread adoption of neural ODEs. In this paper, we propose an approach based on single-step implicit schemes to enable neural ODEs to handle stiffness and demonstrate that our implicit neural ODE method can learn stiff dynamics. This work addresses a key limitation in current neural ODE methods, paving the way for their use in a wider range of scientific problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_05592 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Training Stiff Neural Ordinary Differential Equations with Implicit Single-Step Methods Fronk, Colby Petzold, Linda Numerical Analysis Artificial Intelligence Computational Engineering, Finance, and Science Stiff systems of ordinary differential equations (ODEs) are pervasive in many science and engineering fields, yet standard neural ODE approaches struggle to learn them. This limitation is the main barrier to the widespread adoption of neural ODEs. In this paper, we propose an approach based on single-step implicit schemes to enable neural ODEs to handle stiffness and demonstrate that our implicit neural ODE method can learn stiff dynamics. This work addresses a key limitation in current neural ODE methods, paving the way for their use in a wider range of scientific problems. |
| title | Training Stiff Neural Ordinary Differential Equations with Implicit Single-Step Methods |
| topic | Numerical Analysis Artificial Intelligence Computational Engineering, Finance, and Science |
| url | https://arxiv.org/abs/2410.05592 |