Domain Knowledge Constrained Symbolic Regression for Optimising Dermal Drug Formulations

PURPOSE: Interpretable dynamic models that remain physically admissible under extrapolation are essential for dermal formulation optimisation. Mechanistic models are often labour-intensive to derive, whereas unconstrained data-driven models may violate physical constraints and degrade beyond observed conditions. METHODS: We developed a domain knowledge constrained symbolic regression (DKC-SR) framework to discover compact, interpretable dynamic models for cumulative release directly from time-series experiments. Domain knowledge was embedded through a restricted operator set and feasibility constraints over the bounded optimisation domain. Candidate expressions were evaluated by numerically solving the dynamic differential equations and selected using an information-criterion trade-off across a level-wise set of complexity-controlled models. The final surrogate was coupled with the covariance matrix adaptation evolution strategy for formulation optimisation. RESULTS: In an ibuprofen formulation case study, the selected model provided a formulation ranking that, combined with experimental validation, guided the optimiser to a narrow high-performing region; a representative optimum was experimentally confirmed to exceed the historical best. Although the surrogate was more reliable for ranking and optimisation guidance than for exact quantitative calibration, it remained physically admissible and numerically stable across the design space. CONCLUSIONS: DKC-SR provides a compact, interpretable, and optimisation-ready route to modelling dermal release under bounded design constraints.