Neural PDE

Neural Partial Differential Equations (Neural PDEs) leverage machine learning to efficiently solve complex partial differential equations (PDEs) that model diverse physical phenomena. Current research emphasizes improving model robustness and accuracy, particularly under data scarcity, through techniques like adversarial training and pretraining on lower-dimensional problems. Popular architectures include neural operators, graph neural networks, and variations of U-Nets, often incorporating physics-informed constraints or probabilistic representations to enhance performance and uncertainty quantification. This field promises significant advancements in scientific computing by accelerating simulations across various disciplines, from fluid dynamics and electromagnetics to materials science and climate modeling.