Order Differential Operator

Order differential operators are mathematical tools crucial for modeling diverse physical phenomena through partial differential equations (PDEs). Current research focuses on efficiently solving these equations using neural networks, particularly addressing challenges in handling high-order derivatives and ensuring stable training, with methods like Physics-Informed Neural Networks (PINNs) and novel architectures designed for operator splitting being explored. These advancements aim to improve the accuracy, speed, and interpretability of PDE solutions, impacting fields ranging from fluid dynamics to materials science through more efficient and robust computational modeling.