@article{manifoldorthogonaldualspectrumextrapolat,
  title = {Manifold-Orthogonal Dual-spectrum Extrapolation for Parameterized Physics-Informed Neural Networks},
  author = {Zhangyong Liang and Huanhuan Gao},
  year = {2026},
  eprint = {2603.13751},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2603.13751},
}