Neural Conjugate Flows: Physics-informed architectures with flow structure
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913577145729024 |
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| author | Bizzi, Arthur Nissenbaum, Lucas Pereira, João M. |
| author_facet | Bizzi, Arthur Nissenbaum, Lucas Pereira, João M. |
| contents | We introduce Neural Conjugate Flows (NCF), a class of neural network architectures equipped with exact flow structure. By leveraging topological conjugation, we prove that these networks are not only naturally isomorphic to a continuous group, but are also universal approximators for flows of ordinary differential equation (ODEs). Furthermore, topological properties of these flows can be enforced by the architecture in an interpretable manner. We demonstrate in numerical experiments how this topological group structure leads to concrete computational gains over other physics informed neural networks in estimating and extrapolating latent dynamics of ODEs, while training up to five times faster than other flow-based architectures. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_08326 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Neural Conjugate Flows: Physics-informed architectures with flow structure Bizzi, Arthur Nissenbaum, Lucas Pereira, João M. Machine Learning Numerical Analysis We introduce Neural Conjugate Flows (NCF), a class of neural network architectures equipped with exact flow structure. By leveraging topological conjugation, we prove that these networks are not only naturally isomorphic to a continuous group, but are also universal approximators for flows of ordinary differential equation (ODEs). Furthermore, topological properties of these flows can be enforced by the architecture in an interpretable manner. We demonstrate in numerical experiments how this topological group structure leads to concrete computational gains over other physics informed neural networks in estimating and extrapolating latent dynamics of ODEs, while training up to five times faster than other flow-based architectures. |
| title | Neural Conjugate Flows: Physics-informed architectures with flow structure |
| topic | Machine Learning Numerical Analysis |
| url | https://arxiv.org/abs/2411.08326 |