Mixed-dimensional partial differential equations (PDEs), characterized by couplings between operators defined on domains of different dimensionality, pose significant computational challenges due to their inherent ill-conditioning. Moreover, the computational cost increases substantially when such problems must be solved repeatedly to address multiple instances of the low-dimensional component, which in many practical applications correspond to varying configurations of fracture, fiber, or vascular networks. In this work, we develop a novel training strategy for neural preconditioners that leverages the geometric structure of Krylov subspace methods. The core contribution is the formulation of a dynamic training algorithm in which the loss functional directly optimizes the angles between Krylov subspaces that govern the convergence behavior of iterative solvers. The proposed approach retains the advantages of unsupervised learning, such as straightforward data generation and independence from ground-truth solutions, while introducing a transparent, solver-integrated performance metric. A differentiable formulation of the Flexible GMRES algorithm enables efficient gradient-based optimization via backpropagation through the solver’s iterative process. The resulting dynamic loss captures the alignment between the residual vector and the Krylov subspace at each iteration, providing a geometrically meaningful proxy for the convergence rate. The performance of this solver-aware training strategy is validated through numerical experiments, which demonstrate a significant acceleration of iterative solver convergence. The method generalizes across different topological configurations of one-dimensional graphs and adapts to variations in problem discretization without requiring retraining. These results confirm the effectiveness of the proposed training strategy in enabling the neural preconditioner to directly influence Krylov subspace geometry and, consequently, to accelerate the convergence of iterative solvers.