MACHINE LEARNING–DRIVEN ALGORITHM SELECTION FOR NUMERICAL INTEGRATION UNDER ACCURACY–COST TRADE-OFFS

Numerical integration is a fundamental component of scientific and engineering computation, playing a critical role in simulation, modeling, and optimization pipelines. However, the performance of classical quadrature methods strongly depends on the structural properties of the integrand, and no single integration strategy is universally optimal when numerical accuracy and computational cost are considered simultaneously. This limitation becomes particularly relevant in heterogeneous engineering problems involving repeated integration under varying numerical conditions. This paper presents a machine learning–driven framework for the adaptive selection of numerical integration methods. The proposed approach formulates numerical integration as a supervised algorithm selection problem under a composite accuracy–cost objective. A portfolio of integration techniques is considered, including Simpson’s rule, Gauss–Legendre quadrature, Romberg integration, neural network–based integrators, and physics-informed schemes. Each integration instance is represented through a set of interpretable features capturing smoothness, curvature, oscillatory behavior, variability, and singularity characteristics of the integrand. Based on these features, supervised learning models are trained to predict the most suitable integration method prior to execution. The proposed framework is evaluated on a comprehensive benchmark suite comprising 1,000 integration instances grouped into five families, covering smooth, oscillatory, singular, boundary-layer, and physics-based integrals. Experimental results demonstrate that no fixed integration method dominates across all problem classes. The machine learning–based selector achieves a classification accuracy of 90.67% on unseen test instances and significantly improves the accuracy–cost trade-off compared to fixed-strategy approaches. Statistical validation using Friedman and Wilcoxon nonparametric tests confirms the robustness and effectiveness of the proposed method.