Constraint-Aware Machine Learning Framework for Hydrogel Formulation and Reverse Design

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Hydrogel formulation is governed by complex and nonlinear relationships between compositional variables, physicochemical interactions, and experimentally imposed feasibility constraints, making the rational identification of high-performing mixtures a challenging task in practice. In this work, we present a constraint-aware computational framework for the prediction and optimization of hydrogel formulation under ordinal experimental assessment. The proposed approach integrates ordinal neural network models, specifically CORAL and CORN, with treebased ensemble learners, including Random Forest, HistGradientBoosting, and XGBoost, within a unified pipeline that combines predictive modeling, feasible-region Monte Carlo sampling, probabilistic mixture inference, and explainable artificial intelligence. Formulations are represented through normalized component fractions subject to bounded ranges, compositional conservation, and hydrogel-specific logical constraints, enabling direct exploration of experimentally meaningful solution spaces. The results show that explicitly accounting for ordinal structure improves predictive reliability, while ensemble methods provide strong robustness and capture nonlinear compositional effects with high accuracy and substantial ordinal agreement. In particular, gradient-boosting-based models achieved the strongest overall performance, whereas ordinal neural models contributed smoother and more consistent probability distributions across adjacent quality categories. SHAP-based interpretability analysis revealed that hydrogel quality is primarily governed by a limited subset of influential variables and that most model behavior is predominantly additive, with only a small number of meaningful interactions. Beyond prediction, the framework enables reverse design by identifying regions of the formulation space associated with a high probability of achieving the target performance category and by providing both compositional ranges and percentage-based candidate formulations suitable for experimental implementation. The entire workflow is deployed as an interactive web-based application, allowing users to train models, define constraints, explore feasible regions, and iteratively improve the system as new experimental data and feedback become available. Together, these results establish a practical and adaptive decision-support framework for hydrogel formulation and provide a generalizable methodology for constrained ordinal optimization in chemical and materials design.

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