Leray-Schauder Mappings for Operator Learning
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866915826166136832 |
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| author | Zappala, Emanuele |
| author_facet | Zappala, Emanuele |
| contents | We present an algorithm for learning operators between Banach spaces, based on the use of Leray-Schauder mappings to learn a finite-dimensional approximation of compact subspaces. We show that the resulting method is a universal approximator of (possibly nonlinear) operators. We demonstrate the efficiency of the approach on two benchmark datasets showing it achieves results comparable to state of the art models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_01746 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Leray-Schauder Mappings for Operator Learning Zappala, Emanuele Machine Learning Numerical Analysis We present an algorithm for learning operators between Banach spaces, based on the use of Leray-Schauder mappings to learn a finite-dimensional approximation of compact subspaces. We show that the resulting method is a universal approximator of (possibly nonlinear) operators. We demonstrate the efficiency of the approach on two benchmark datasets showing it achieves results comparable to state of the art models. |
| title | Leray-Schauder Mappings for Operator Learning |
| topic | Machine Learning Numerical Analysis |
| url | https://arxiv.org/abs/2410.01746 |