Domain Knowledge Constrained Symbolic Regression for Optimising Dermal Drug Formulations

Area of Science:

• Pharmacokinetics and Drug Delivery
• Computational Modeling and Simulation
• Formulation Science

Background:

• Developing interpretable dynamic models for dermal formulation optimization is crucial.
• Mechanistic models are time-consuming, while data-driven models may lack physical constraints.
• Ensuring physical admissibility under extrapolation is essential for reliable optimization.

Purpose of the Study:

• To develop a novel framework for discovering compact, interpretable dynamic models for cumulative dermal release.
• To embed domain knowledge into the model discovery process to ensure physical admissibility.
• To create an optimization-ready modeling route for dermal formulations.

Main Methods:

• Developed a domain knowledge constrained symbolic regression (DKC-SR) framework.
• Embedded domain knowledge via restricted operator sets and feasibility constraints.
• Evaluated candidate expressions by numerically solving differential equations and using information criteria for selection.
• Coupled the final surrogate model with a covariance matrix adaptation evolution strategy for optimization.

Main Results:

• The DKC-SR framework successfully identified a compact, interpretable dynamic model for ibuprofen dermal release.
• The model provided a reliable formulation ranking, guiding the optimizer to a high-performing region.
• An experimentally confirmed optimum exceeded historical best performance.
• The surrogate model demonstrated physical admissibility and numerical stability across the design space.

Conclusions:

• DKC-SR offers a powerful and efficient method for developing interpretable dynamic models in dermal release studies.
• The framework ensures models are physically admissible and suitable for optimization tasks.
• This approach streamlines the optimization of dermal formulations under bounded design constraints.