Numerical Method

Numerical methods, encompassing both classical techniques and emerging machine learning approaches, aim to efficiently and accurately solve mathematical problems, particularly partial differential equations (PDEs), crucial in numerous scientific and engineering fields. Current research heavily focuses on integrating physics-informed neural networks (PINNs), extreme learning machines (ELMs), and other neural network architectures with traditional methods like finite difference or finite element methods, often employing techniques like domain decomposition and preconditioning to improve accuracy and efficiency. These advancements offer the potential for more robust, accurate, and computationally efficient solutions to complex problems across diverse scientific disciplines and engineering applications, bridging the gap between data-driven and model-based approaches.