Solvers have each demonstrated significant success in distinct domains, such as imaging sciences and the solution of Partial Differential Equations (PDEs). In this presentation, we introduce a novel framework that integrates DL with these classical solvers to enhance the accuracy of DL in addressing certain ill-posed inverse problems. Specifically, we explore how solutions to a PDE involving a fractional (learnable) Laplace–Beltrami operator on the boundary can be mapped to corresponding images. We demonstrate that the fractional order of the operator can be optimally learned to improve accuracy.