Parameter Identification in a Three-Compartment Pharmacokinetic Model: Sensitivity Analysis, Gradient Boosting and Numerical Verification

This study investigates parameter estimation in a linear three-compartment pharmacokinetic model with absorption. Peripheral-compartment permutation symmetry is explicitly separated from local practical conditioning. Singular-value analysis is supplemented by noise-weighted local design comparisons. XGBoost and LightGBM are trained on 10,000 independently sampled parameter vectors, with clean and noise-augmented training evaluated separately. A bounded, scaled, three-start nonlinear least-squares (NLS) baseline is evaluated on the same held-out observations. On 1000 noise-free test vectors, mean relative parameter errors are 4.2460% and 4.3232% for clean-trained XGBoost and LightGBM, compared with 0.0158% for NLS. Noise experiments use 100 independent parameter vectors and 20 realizations per vector at each nonzero noise level. Bias, conditional standard deviation and RMSE are reported per parameter. The machine learning models exploit the parameter distribution within the ±20% training domain, whereas the bounded NLS baseline includes no explicit penalty toward the domain center. Therefore, their lower errors under noisy observations may partly reflect this prior information rather than an advantage specific to gradient boosting. The results distinguish accurate curve fitting from stable parameter recovery and do not establish universal superiority of gradient boosting over optimization. Conclusions are restricted to the stated synthetic parameter domain.