PDE System

Partial differential equation (PDE) systems are fundamental to modeling diverse physical phenomena, and current research focuses on developing efficient and accurate methods for solving them, particularly in complex scenarios with high nonlinearity or limited data. Prominent approaches leverage neural operators, physics-informed neural networks (PINNs), and Gaussian processes, often incorporating techniques like backstepping control and meta-learning to improve performance and generalization. These advancements are significantly impacting scientific computing by enabling faster and more robust solutions to complex PDE systems, with applications ranging from fluid dynamics and traffic flow control to materials science and robotics.