PDE Model

Partial differential equation (PDE) models are being revolutionized by data-driven approaches, aiming to improve the efficiency and accuracy of solving these equations across diverse scientific and engineering domains. Current research focuses on developing novel neural network architectures, such as transformer-based models and physics-informed neural networks (PINNs), often incorporating techniques like multiscale operator learning and boundary integral methods to handle complex geometries and high-dimensional data. These advancements enable faster and more robust solutions for problems ranging from fluid dynamics and robotics to subsurface flow modeling and biological systems, ultimately accelerating scientific discovery and technological innovation.