Quadrature Rule

Quadrature rules are numerical methods for approximating definite integrals, crucial for various scientific and engineering applications. Current research focuses on developing efficient and accurate quadrature rules for high-dimensional spaces and complex integrands, including those arising in machine learning (e.g., Gaussian process regression), control theory (e.g., integral reinforcement learning), and partial differential equations. These advancements improve the scalability and accuracy of algorithms across diverse fields, from option pricing to geophysical image reconstruction, by enabling more precise and computationally feasible solutions to integral-based problems. The development of optimal quadrature rules, often leveraging machine learning techniques, is a key area of ongoing investigation.