PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems
PVD-ONet is an operator learning model that maps initial conditions directly to solutions for boundary layer problems without retraining. It generalizes PVD-Net by using multiple DeepONet modules—two for leading-order and five for high-order approximations—to achieve fast, accurate predictions. This method relies only on governing equations, bypassing the need for training data.