Robust Pharmacokinetic Parameter Estimation via Differentiable ODE Solvers with Physics-Informed Optimization

Abstract

This paper presents a differentiable ODE solver framework for robust parameter estimation in a two-compartment pharmacokinetic (PK) model with first-order absorption. Five model parameters are estimated from noisy concentration–time data using a PyTorch-based fourth-order Runge–Kutta (RK4) solver with sigmoid-bounded constraints and adaptive weighted regularization. A comprehensive Monte Carlo evaluation with 50 independent noise realizations at each of five noise levels (1%, 5%, 10%, 15%, and 20%) provides statistically rigorous performance assessment. The proposed method is compared against Levenberg–Marquardt (LM), Differential Evolution (DE), and Gauss–Seidel (GS) algorithms. Results demonstrate that the differentiable solver approach achieves the lowest median average relative error at noise levels ≥10%, with a median ARE of 8.42% at 10% noise compared to 47.63% (LM), 12.18% (DE), and 68.91% (GS). At 20% noise, the proposed method maintains a median ARE of 29.15%, outperforming all baselines. The Monte Carlo framework reveals that classical methods exhibit high variance and frequent catastrophic failures, while the proposed approach provides consistent, reliable estimates across diverse noise realizations.