2023/06/08 by Emilia Blåsten, Hiroshi Isozaki, Matti Lassas +1 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics
paper · doi:10.1137/21m1439936
openalex publication_date 2023/06/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/11
.We study the inverse problem of determining a finite weighted graph \((X,E)\) from the source-to-solution map on a vertex subset \(B⊂ X\) for heat equations on graphs, where the time variable can be either discrete or continuous. We prove that this problem is equivalent to the discrete version of the inverse interior spectral problem, provided that there does not exist a nonzero eigenfunction of the weighted graph Laplacian vanishing identically on \(B\) . In particular, we consider inverse problems for discrete-time random walks on finite graphs. We show that under a novel geometric condition (called the Two-Points Condition), the graph structure and the transition matrix of the random walk can be uniquely recovered from the distributions of the first passing times on \(B\) , or from the observation on \(B\) of one realization of the random walk.Keywordsinverse problem for random walkinverse spectral problemheat equationunique continuationMSC codes05C5005C8105C22