Discovering Closed-Form Pharmacokinetic Relationships with Symbolic Regression to Improve Interpretability, Mechanistic Plausibility, and Extrapolation Beyond Black-Box Prediction

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Machine-learning models can predict pharmacokinetic quantities and concentration–time profiles with increasing flexibility, yet prediction alone does not reveal whether the learned relation is dimensionally coherent, pharmacologically plausible, stable under perturbation, or transferable beyond the training domain. This methodological framework examines symbolic regression as a route to explicit pharmacokinetic equations while treating interpretability as a constrained scientific objective rather than a by-product of algebraic compactness. The proposed approach separates equation discovery from mechanistic attribution and requires candidate expressions to preserve measurement level, units, temporal structure, biological directionality where justified, and the distinction between molecular, physiological, and population-level variables. Mechanistic knowledge is introduced as an admissibility constraint or structural prior rather than as proof that the recovered expression is causal. The framework further proposes multi-criterion model selection based on predictive adequacy, parsimony, dimensional validity, stability, mechanistic plausibility, uncertainty, and performance under predefined extrapolation tests. Black-box predictors, population pharmacokinetic models, physiologically based pharmacokinetic models, and hybrid scientific-machine-learning approaches remain necessary comparators because symbolic transparency does not guarantee superior prediction or extrapolation. The central contribution is therefore a validation-oriented strategy for discovering closed-form relationships that can be inspected, challenged, and rejected. Its scope is methodological: recovered equations remain hypotheses conditioned on data quality, identifiability, chemical and population coverage, model specification, and external validation, and should not be interpreted as mechanistic laws or implementation-ready dosing rules without independent evidence.