Md Rezwan Jaher

Many critical decision-making processes in healthcare and engineering are challenged by the inability to measure key underlying parameters. These scenarios often formulate as mechanistically hierarchical inverse problems, where the observable macroscopic output is multiplicatively entangled with intrinsic micro-scale physics and unmeasurable spatial geometry. Solving such severely underdetermined problems via standard Bayesian inference or simulation-based calibration requires millions of forward evaluations, rendering patient-specific inference computationally intractable at the clinical point-of-care. Conversely, standard black-box empirical models fail to resolve the structural non-identifiability, indiscriminately absorbing structural variance and collapsing to the population mean. To address these coupled clinical and computational challenges, we propose a novel two-stage architectural decomposition. Instead of a monolithic mapping, we functionally separate the inverse problem according to its governing physics. The first stage acts as a constrained inverse surrogate, isolating the intrinsic biophysical parameter by learning the inverse mapping over an idealized reference manifold. The second stage performs empirical structural calibration, learning an effective geometric factor to bridge the idealized physics with in vivo macroscopic reality. To train this architecture under extreme data scarcity, we introduce Physics-Calibrated Data Scaling (PCDS), a highly scalable data generation strategy that dynamically corrects the systematic bias between low-fidelity analytical surrogates and high-fidelity finite element simulations. We demonstrate this framework on the clinical diagnosis of glaucoma, successfully deconstructing a single, routine intraocular pressure (IOP) measurement into its latent hydrodynamic root causes (tissue permeability and outflow facility). By propagating population-level epistemic uncertainty through our trained operators via Monte Carlo sampling, the framework generates a continuous, empirical push-forward distribution of the patient’s physiological state. Our results confirm that while standard data-driven baselines achieve only 37% classification accuracy, our hierarchical decomposition achieves 92.5% diagnostic accuracy, offering a generalizable blueprint for solving ill-posed, data-scarce inverse problems across the physical and biological sciences