Numerical Scheme

Numerical schemes are algorithms for approximating solutions to mathematical equations, particularly those describing complex physical phenomena or processes that lack analytical solutions. Current research focuses on improving the accuracy and efficiency of these schemes, particularly through the integration of machine learning techniques, such as convolutional neural networks and recurrent graph neural networks, to create data-driven or physics-informed models. This leads to advancements in areas like fluid dynamics simulation, image processing (e.g., medical image segmentation), and solving partial differential equations, offering more accurate and computationally efficient solutions for a wide range of scientific and engineering problems.