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The problem of identifying the cause from the result is called the inverse problem, which is an important ill-posed problem in the mathematical sciences. In addition, it is attracting attention as a tool for understanding the background of physical phenomena in detail. I study the inverse problem of determining the governing system of equations from information on the solutions of partial differential equations. In particular, I am interested in the analysis of inverse problems for hyperbolic partial differential equations using geometric analysis on pseudo-Riemannian manifolds with indefinite metrics. I would like to understand the analytical aspect of inverse problems from the viewpoint of geometry as well.