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Simultaneous Recovery of Wave Speeds and Initial Sources on Graphs via Redundant Frontier Propagation

  • Amir Moradifam
  • Oliver P. Waite
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Abstract

We study the simultaneous recovery of an unknown initial signal and unknown vertex wave speeds for the wave equation on a finite graph from time-dependent measurements on a prescribed set of vertices. With the graph geometry known, we first show that a single experiment determines both quantities under a new two-witness zero forcing condition and generic nondegeneracy assumptions. We then develop a more general frontier-propagation framework in which the redundancy required for simultaneous recovery is distributed across successive graph contours rather than localized at individual forcing vertices. We derive Lipschitz stability estimates for the frontier propagation problem. We also show the recovery and stability results extend to positively weighted graphs.

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Cite

BibTeXRIS
BibTeX
@misc{moradifam2026simultaneous,
  title = {{Simultaneous Recovery of Wave Speeds and Initial Sources on Graphs via Redundant Frontier Propagation}},
  author = {Amir Moradifam and Oliver P. Waite},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.36106},
  eprint = {2610.36106},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.36106},
}
RIS
TY  - UNPB
TI  - Simultaneous Recovery of Wave Speeds and Initial Sources on Graphs via Redundant Frontier Propagation
AU  - Amir Moradifam
AU  - Oliver P. Waite
PY  - 2026
DA  - 2026/10/26
PB  - arXiv
DO  - 10.48550/arxiv.2610.36106
UR  - https://arxiv.org/abs/2610.36106
AB  - We study the simultaneous recovery of an unknown initial signal and unknown vertex wave speeds for the wave equation on a finite graph from time-dependent measurements on a prescribed set of vertices. With the graph geometry known, we first show that a single experiment determines both quantities under a new two-witness zero forcing condition and generic nondegeneracy assumptions. We then develop a more general frontier-propagation framework in which the redundancy required for simultaneous recovery is distributed across successive graph contours rather than localized at individual forcing vertices. We derive Lipschitz stability estimates for the frontier propagation problem. We also show the recovery and stability results extend to positively weighted graphs.
ER  -