Parametric Numerical Integration with (Differential) Machine Learning

Álvaro Leitao; Jonatan Ráfales

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arXiv · 2512.11530

Parametric Numerical Integration with (Differential) Machine Learning

Álvaro Leitao·Jonatan Ráfales

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Abstract

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.

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Álvaro Leitao, Jonatan Ráfales. 2025-12-12. Parametric Numerical Integration with (Differential) Machine Learning. https://arxiv.org/abs/2512.11530

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