Physics-informed learning under mixing: How physical knowledge speeds up learning
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918150620053504 |
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| author | Scampicchio, Anna Toso, Leonardo F. Rickenbach, Rahel Anderson, James Zeilinger, Melanie N. |
| author_facet | Scampicchio, Anna Toso, Leonardo F. Rickenbach, Rahel Anderson, James Zeilinger, Melanie N. |
| contents | A major challenge in physics-informed machine learning is to understand how the incorporation of prior domain knowledge affects learning rates when data are dependent. Focusing on empirical risk minimization with physics-informed regularization, we derive complexity-dependent bounds on the excess risk in probability and in expectation. We prove that, when the physical prior information is aligned, the learning rate improves from the (slow) Sobolev minimax rate to the (fast) optimal i.i.d. one without any sample-size deflation due to data dependence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_24801 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Physics-informed learning under mixing: How physical knowledge speeds up learning Scampicchio, Anna Toso, Leonardo F. Rickenbach, Rahel Anderson, James Zeilinger, Melanie N. Machine Learning Systems and Control A major challenge in physics-informed machine learning is to understand how the incorporation of prior domain knowledge affects learning rates when data are dependent. Focusing on empirical risk minimization with physics-informed regularization, we derive complexity-dependent bounds on the excess risk in probability and in expectation. We prove that, when the physical prior information is aligned, the learning rate improves from the (slow) Sobolev minimax rate to the (fast) optimal i.i.d. one without any sample-size deflation due to data dependence. |
| title | Physics-informed learning under mixing: How physical knowledge speeds up learning |
| topic | Machine Learning Systems and Control |
| url | https://arxiv.org/abs/2509.24801 |