An efficient method for reconstructing the potential in the fractional Calderón problem with a single measurement

@misc{liu2026efficient,
  title = {{An efficient method for reconstructing the potential in the fractional Calderón problem with a single measurement}},
  author = {Yun-Long Liu and Jin Wen and Jun-Liang Fu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.34175},
  eprint = {2610.34175},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.34175},
}

TY  - UNPB
TI  - An efficient method for reconstructing the potential in the fractional Calderón problem with a single measurement
AU  - Yun-Long Liu
AU  - Jin Wen
AU  - Jun-Liang Fu
PY  - 2026
DA  - 2026/10/25
PB  - arXiv
DO  - 10.48550/arxiv.2610.34175
UR  - https://arxiv.org/abs/2610.34175
AB  - In this paper, we develop a numerical method for determining the potential function in one-dimensional and two-dimensional fractional-order Calderón problems through a single measurement. The fractional Laplacian is discretized using the finite difference method, and the POD-RBF method is used to construct the forward problem surrogate model that can provide the predicted value and its exact gradient in time. The inverse problem is solved using Tikhonov regularization and the conjugate gradient method. The efficiency and effectiveness of the developed method are demonstrated through numerical experiments, and the theoretical results are verified.
ER  -