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We prove that a continuous potential $q$ can be constructively determinedfrom the knowledge of the Dirichlet-to-Neumann map for the perturbed biharmonicoperator $\Delta_g^2+q$ on a conformally transversally anisotropic Riemannianmanifold of dimension $\ge 3$ with boundary, assuming that the geodesic raytransform on the transversal manifold is constructively invertible. This is aconstructive counterpart of the uniqueness result of [51]. In particular, ourresult is applicable and new in the case of smooth bounded domains in the$3$-dimensional Euclidean space as well as in the case of $3$-dimensionaladmissible manifolds.

Reconstructing a potential perturbation of the biharmonic operator on transversally anisotropic manifolds