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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.01763 |
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| _version_ | 1866913628517564416 |
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| author | Le, Vu-Anh Dik, Mehmet |
| author_facet | Le, Vu-Anh Dik, Mehmet |
| contents | This paper presents a mathematics-informed approach to neural operator design, building upon the theoretical framework established in our prior work. By integrating rigorous mathematical analysis with practical design strategies, we aim to enhance the stability, convergence, generalization, and computational efficiency of neural operators. We revisit key theoretical insights, including stability in high dimensions, exponential convergence, and universality of neural operators. Based on these insights, we provide detailed design recommendations, each supported by mathematical proofs and citations. Our contributions offer a systematic methodology for developing next-gen neural operators with improved performance and reliability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_01763 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | How Analysis Can Teach Us the Optimal Way to Design Neural Operators Le, Vu-Anh Dik, Mehmet Numerical Analysis Machine Learning Functional Analysis This paper presents a mathematics-informed approach to neural operator design, building upon the theoretical framework established in our prior work. By integrating rigorous mathematical analysis with practical design strategies, we aim to enhance the stability, convergence, generalization, and computational efficiency of neural operators. We revisit key theoretical insights, including stability in high dimensions, exponential convergence, and universality of neural operators. Based on these insights, we provide detailed design recommendations, each supported by mathematical proofs and citations. Our contributions offer a systematic methodology for developing next-gen neural operators with improved performance and reliability. |
| title | How Analysis Can Teach Us the Optimal Way to Design Neural Operators |
| topic | Numerical Analysis Machine Learning Functional Analysis |
| url | https://arxiv.org/abs/2411.01763 |