Learning and Transferring Physical Models through Derivatives
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911392701874176 |
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| author | Trenta, Alessandro Cossu, Andrea Bacciu, Davide |
| author_facet | Trenta, Alessandro Cossu, Andrea Bacciu, Davide |
| contents | We propose Derivative Learning (DERL), a supervised approach that models physical systems by learning their partial derivatives. We also leverage DERL to build physical models incrementally, by designing a distillation protocol that effectively transfers knowledge from a pre-trained model to a student one. We provide theoretical guarantees that DERL can learn the true physical system, being consistent with the underlying physical laws, even when using empirical derivatives. DERL outperforms state-of-the-art methods in generalizing an ODE to unseen initial conditions and a parametric PDE to unseen parameters. We also design a method based on DERL to transfer physical knowledge across models by extending them to new portions of the physical domain and a new range of PDE parameters. This introduces a new pipeline to build physical models incrementally in multiple stages. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_01391 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Learning and Transferring Physical Models through Derivatives Trenta, Alessandro Cossu, Andrea Bacciu, Davide Machine Learning We propose Derivative Learning (DERL), a supervised approach that models physical systems by learning their partial derivatives. We also leverage DERL to build physical models incrementally, by designing a distillation protocol that effectively transfers knowledge from a pre-trained model to a student one. We provide theoretical guarantees that DERL can learn the true physical system, being consistent with the underlying physical laws, even when using empirical derivatives. DERL outperforms state-of-the-art methods in generalizing an ODE to unseen initial conditions and a parametric PDE to unseen parameters. We also design a method based on DERL to transfer physical knowledge across models by extending them to new portions of the physical domain and a new range of PDE parameters. This introduces a new pipeline to build physical models incrementally in multiple stages. |
| title | Learning and Transferring Physical Models through Derivatives |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2505.01391 |