Efficiently Parameterized Neural Metriplectic Systems
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
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| _version_ | 1866910800338223104 |
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| author | Gruber, Anthony Lee, Kookjin Lim, Haksoo Park, Noseong Trask, Nathaniel |
| author_facet | Gruber, Anthony Lee, Kookjin Lim, Haksoo Park, Noseong Trask, Nathaniel |
| contents | Metriplectic systems are learned from data in a way that scales quadratically in both the size of the state and the rank of the metriplectic data. Besides being provably energy conserving and entropy stable, the proposed approach comes with approximation results demonstrating its ability to accurately learn metriplectic dynamics from data as well as an error estimate indicating its potential for generalization to unseen timescales when approximation error is low. Examples are provided which illustrate performance in the presence of both full state information as well as when entropic variables are unknown, confirming that the proposed approach exhibits superior accuracy and scalability without compromising on model expressivity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_16305 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Efficiently Parameterized Neural Metriplectic Systems Gruber, Anthony Lee, Kookjin Lim, Haksoo Park, Noseong Trask, Nathaniel Machine Learning Metriplectic systems are learned from data in a way that scales quadratically in both the size of the state and the rank of the metriplectic data. Besides being provably energy conserving and entropy stable, the proposed approach comes with approximation results demonstrating its ability to accurately learn metriplectic dynamics from data as well as an error estimate indicating its potential for generalization to unseen timescales when approximation error is low. Examples are provided which illustrate performance in the presence of both full state information as well as when entropic variables are unknown, confirming that the proposed approach exhibits superior accuracy and scalability without compromising on model expressivity. |
| title | Efficiently Parameterized Neural Metriplectic Systems |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2405.16305 |