Analytic Solution

Analytic solutions, aiming to find exact mathematical expressions for problems rather than numerical approximations, are a focus of current research across diverse scientific domains. Recent work explores analytic solutions for complex systems, including neural networks (analyzing covariance propagation and network depth effects), robotic path planning (e.g., 3D Dubins paths), and differential equations (using symbolic regression and physics-informed neural networks). These advancements offer improved accuracy, efficiency, and interpretability compared to purely numerical methods, impacting fields ranging from machine learning and robotics to acoustic modeling and healthcare data analysis.