Numerical Experiment

Numerical experiments are computational studies used to validate and explore mathematical models, particularly those involving partial differential equations (PDEs). Current research focuses on improving the accuracy and efficiency of these experiments, often employing machine learning techniques like physics-informed neural networks (PINNs), generative adversarial networks (GANs), and various deep learning architectures to solve or approximate PDE solutions. These advancements are crucial for tackling complex scientific problems across diverse fields, from fluid dynamics and materials science to inverse problems and uncertainty quantification, where analytical solutions are often intractable. The resulting improvements in computational efficiency and accuracy directly impact the reliability and scope of scientific modeling and simulation.