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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.11530 |
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| _version_ | 1866912760038686720 |
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| author | Leitao, Álvaro Ráfales, Jonatan |
| author_facet | Leitao, Álvaro Ráfales, Jonatan |
| contents | In this work, we introduce a machine/deep learning methodology to solve parametric integrals. Besides classical machine learning approaches, we consider a differential learning framework that incorporates derivative information during training, emphasizing its advantageous properties. Our study covers three representative problem classes: statistical functionals (including moments and cumulative distribution functions), approximation of functions via Chebyshev expansions, and integrals arising directly from differential equations. These examples range from smooth closed-form benchmarks to challenging numerical integrals. Across all cases, the differential machine learning-based approach consistently outperforms standard architectures, achieving lower mean squared error, enhanced scalability, and improved sample efficiency. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_11530 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Parametric Numerical Integration with (Differential) Machine Learning Leitao, Álvaro Ráfales, Jonatan Machine Learning Numerical Analysis 68T07, 65D30, 65C05 G.1.4; G.3 In this work, we introduce a machine/deep learning methodology to solve parametric integrals. Besides classical machine learning approaches, we consider a differential learning framework that incorporates derivative information during training, emphasizing its advantageous properties. Our study covers three representative problem classes: statistical functionals (including moments and cumulative distribution functions), approximation of functions via Chebyshev expansions, and integrals arising directly from differential equations. These examples range from smooth closed-form benchmarks to challenging numerical integrals. Across all cases, the differential machine learning-based approach consistently outperforms standard architectures, achieving lower mean squared error, enhanced scalability, and improved sample efficiency. |
| title | Parametric Numerical Integration with (Differential) Machine Learning |
| topic | Machine Learning Numerical Analysis 68T07, 65D30, 65C05 G.1.4; G.3 |
| url | https://arxiv.org/abs/2512.11530 |