Two-point boundary value problems (BVPs) are foundational to numerous applications in science and engineering. However, as systems become nonlinear, chaotic, or stochastic, traditional solvers face instability due to their sensitivity to initial guesses and discretization errors. In this research, we propose a hybrid framework combining established numerical methods with modern machine learning (ML) techniques capable of learning from successful computations and failures. The approach not only enforces boundary conditions using analytic priors but also incorporates uncertainty quantification through Bayesian methods. Although our primary focus is on enhancing the robustness of BVP solvers, we aim to demonstrate the practical relevance of this work by applying it to simulate aspects of chronic kidney disease (CKD) dynamics, thereby bridging a significant numerical challenge with a real-world biomedical problem.