An optimized hybrid block technique framework for partial differential equations by exploring radial basis function neural networks

This article explores recent advances in integrating artificial neural networks (ANNs) with numerical methods, focusing on an optimized two-stage hybrid block method for solving complex partial differential equations (PDEs). The method combines ANNs with traditional solvers to improve computational efficiency and accuracy, using a Radial Basis Function Neural Network (RBFNN) for optimization. This approach enhances stability, convergence, and adaptability, especially in multidimensional problems, and reduces computational costs while maintaining precision in fields like fluid dynamics and electromagnetism. Simulations show the method outperforms conventional solvers, enabling more efficient real-time simulations in engineering and mathematics.