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PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems
Physics-informed neural networks and physics-informed DeepONet excel at solving partial differential equations but often struggle with singularly perturbed problems. To address this limitation, we propose two novel data-free frameworks: the Prandtl--Van Dyke neural network(PVD-Net) and its operator-
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