Parametric Numerical Integration with (Differential) Machine Learning
By: Álvaro Leitao, Jonatan Ráfales
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.
Similar Papers
Deep Neural Networks Inspired by Differential Equations
Machine Learning (CS)
Makes smart computer programs easier to understand.
Learning Solution Operators for Partial Differential Equations via Monte Carlo-Type Approximation
Machine Learning (CS)
Makes computer models solve problems faster and cheaper.
Learning functions through Diffusion Maps
Machine Learning (CS)
Makes computers learn from less data better.