ChemODE: A Physics-Informed Neural Surrogate for Robust Pharmacokinetics and Biochemical Dynamics

Abstract The automated discovery of governing kinetic laws from observational data is a critical challenge in systems biology, pharmacology, and chemical engineering. In these experimental domains, data-driven mechanism discovery is complicated by sparse sampling, measurement noise (e.g., blood assays), and the prevalence of nonlinear saturation limits (Michaelis-Menten kinetics). Existing symbolic regression methods, such as SINDy, rely on polynomial basis functions that fundamentally fail to extrapolate physical saturation, and their reliance on numerical differentiation degrades catastrophically in high-noise regimes (>5%). In this work, we introduce ChemODE, a physics-informed gray-box framework tailored for biochemical and pharmacokinetic (PK) networks. ChemODE integrates (1) Constrained Rational Layers to autonomously enforce physical saturation laws, (2) On-the-fly Feature Normalization to resolve magnitude bias in multicompartment scale separations, and (3) a noise-robust integral-based optimization scheme. We validate ChemODE on fundamental biological benchmarks, including the nonlinear Brusselator limit cycle and a synthetic 3-compartment pharmacokinetic model. To demonstrate clinical applicability, ChemODE successfully extracts physiological absorption and elimination rates from real-world human theophylline pharmacokinetic assays. Furthermore, rigorous uncertainty quantification (10-seed ensembles) proves that ChemODE recovers enzyme kinetics with high precision (Vmax error ≈ 1%), significantly outperforming unconstrained baselines. This work establishes that integral-based minimization, combined with rational architectural constraints and a neural residual paradigm, provides a robust surrogate modeling path for interpretable mechanism discovery in noise-dominated biochemical settings.