Measurement-Dependent Parameter Recoverability in Neural Cardiovascular LPN Inference

Estimating cardiovascular lumped-parameter network (LPN) parameters from limited hemodynamic observations is a potentially non-unique inverse problem in cardiovascular model personalization. We investigated how parameter recoverability depends on measurement availability and noise, and whether poor recovery reflects limitations of neural inference or insufficient observational information. We developed Mada (measurement-availability and difficulty-aware), a probabilistic neural framework that provides parameter estimates and predictive uncertainty under incomplete observations. Using a closed-loop, four-chamber cardiovascular LPN with time-varying elastance, we generated a synthetic population of 650,000 cases comprising 20 chamber-mechanics and vascular parameters and up to 30 hemodynamic and timing observations. Under complete observations, Mada achieved macro R2 = 0.862, maintaining competitive accuracy across neural baselines while providing parameter-specific uncertainty. Recoverability varied substantially across parameters, with atrial active elastances remaining particularly difficult. For mask-aware Mada, macro R2 ranged from 0.066 with basic clinical measurements to 0.751 with a rich clinical set and 0.842 with all measurements, while uncertainty generally increased as informative measurements were removed. Bounded direct optimization achieved substantially smaller hemodynamic residuals but did not consistently recover the generating parameters. Complementary profile and local-sensitivity analyses revealed case-specific parameter compensation and weak observational directions, while target-specific fine-tuning offered little improvement for difficult atrial parameters. Increasing measurement noise degraded both parameter recovery and predictive-interval coverage, and similar trends were observed with a simpler probabilistic ResMLP. These findings demonstrate that accurate reconstruction of observed hemodynamics does not necessarily imply accurate recovery of the underlying LPN parameters, highlighting the importance of assessing parameter recoverability and predictive uncertainty when physiologically meaningful parameter estimates are sought.