Epoxy (EP) resins are widely used for corrosion protection due to their strong adhesion, high corrosion resistance, excellent mechanical properties, and low cost. However, cracks can reduce their performance over time. Self-healing coatings offer a cost-effective solution to improve the durability of metallic structures. Intrinsic self-healing, based on reversible bonds like hydrogen bonds, is particularly promising due to its high reversibility and mild repair conditions. Electrochemical impedance spectroscopy (EIS) at 0.01 Hz (Z0.01Hz) is used to assess corrosion resistance, with higher values indicating better barrier ability. An ideal self-healing coating should have a Z0.01Hz value close to that of the intact coating, excellent barrier ability (Z0.01Hz > 1010 Ω·cm²), and long-term stability. Conventional trial-and-error methods for coating formulation are time-consuming. Machine learning offers a promising alternative for materials design and optimization, especially for complex systems. Active learning and Bayesian optimization are particularly suitable for scenarios with limited data. This study employs a machine learning framework to develop a self-healing composite coating using an EP resin, polyetheramines, amino-terminated urea-pyrimidinone monomers (UPy-D400), and ZIF-8@Ca microfillers. The four parameters investigated were: molecular weight of polyetheramine, molar ratio of polyetheramine to EP, UPy-D400 content, and ZIF-8@Ca content. The lg|Z0.01Hz| value of scratched coatings served as the output variable.

Existing literature highlights the challenges of designing self-healing epoxy coatings with high efficiency and long-term corrosion protection. Several studies focus on using reversible covalent bonds (disulfide bonds, Diels-Alder reactions, hydrazone bonds) or non-covalent interactions (metal-ligand, hydrogen bonding) for self-healing. The use of hydrogen bonds has shown promising results due to their high reversibility. Traditional trial-and-error methods are time-consuming and inefficient in optimizing complex multi-component systems. Machine learning, including active learning and Bayesian optimization, has emerged as a valuable tool for accelerating material discovery and optimization by efficiently exploring large design spaces. Several studies have successfully applied machine learning to predict material properties with limited datasets, including applications in polymer science and epoxy adhesive strength prediction.

The study utilized a machine learning framework involving data acquisition, active learning, and Bayesian optimization. **Data Acquisition:** An orthogonal Latin square method was employed to design experiments, generating 32 initial datasets that cover a wide range of the four parameters. These datasets provided the initial training data for machine learning models. **Active Learning:** Five common machine learning models (Random Forest (RF), Linear Regression (LR), Artificial Neural Network (ANN), Support Vector Regression (SVR), and Decision Tree (DT)) were trained and compared using the 32 initial datasets. The RF model showed the best prediction accuracy (R² = 0.709, MAPE = 0.081, RMSE = 0.685) and was selected for the active learning process. In each active learning cycle, the RF model predicted the lg|Z0.01Hz| values for all untested experimental conditions (256 total conditions, 32 initial, leaving 224 untested), selecting the top five best predicted formulations for laboratory testing. The results of these experiments were then added to the dataset, and the RF model was retrained. This process was repeated for five cycles. **Bayesian Optimization:** After the active learning stage, Bayesian optimization was used to refine the search space further. Focusing on a more concentrated region around the high-performing candidates identified during active learning, Bayesian optimization refined the experimental conditions with specific increments. The algorithm used a random forest as the surrogate model and expected improvement (EI) as the acquisition function to suggest promising new experiments and efficiently searched for the global optimum. This stage involved 1000 iterations. **Coating Preparation and Testing:** The self-healing epoxy coatings were prepared by mixing ZIF-8@Ca microfillers with E51 epoxy resin, polyetheramine curing agent, and UPy-D400 monomers. EIS measurements were conducted on both intact and scratched coatings immersed in 3.5 wt.% NaCl solution to evaluate their corrosion resistance. Salt spray tests (ASTM B117/D1654 standard) were performed to assess the long-term corrosion resistance and adhesion strength. The pull-off test measured adhesion strength before and after salt spray exposure.

The active learning process significantly improved the accuracy of the RF model, increasing R² by 246%, reducing MAPE by 51%, and reducing RMSE by 47% after five cycles. Bayesian optimization successfully identified a coating formulation with an exceptionally high lg|Z0.01Hz| value of 11.58 (corresponding to (4.40 ± 2.04) × 10¹¹ Ω·cm²), significantly higher than values reported in previous studies. EIS measurements confirmed the excellent self-healing ability of the optimized coating, with a repaired Z0.01Hz value almost identical to the intact coating. Salt spray testing showed minimal corrosion and only a 3.3% adhesion loss after 60 days, in stark contrast to the 79.4% adhesion loss observed in the pure EP coating. The optimal coating formulation involved relatively low molecular weight polyetheramine, a high molar ratio of polyetheramine to EP, and moderate amounts of UPy-D400 and ZIF-8@Ca microfillers. These findings highlight the effectiveness of the machine learning framework in discovering superior self-healing epoxy coatings.

The results demonstrate the successful application of a machine learning framework for the design and optimization of self-healing epoxy coatings. The combination of active learning and Bayesian optimization efficiently navigated the complex parameter space, leading to the discovery of a high-performance coating with significantly improved corrosion resistance and self-healing capabilities compared to existing formulations. The superior performance of the optimized coating is attributed to a synergistic effect of the selected components and their optimized ratios. The active learning strategy effectively guided the experimental process by prioritizing the most promising candidates, while Bayesian optimization ensured an efficient exploration of the design space while managing uncertainty. The findings underscore the potential of machine learning to accelerate the development of high-performance materials in various applications. The use of EIS and salt spray testing provided robust validation of the coating's performance.

This study successfully demonstrated a machine learning-driven approach to designing highly efficient self-healing epoxy coatings for corrosion protection. The integrated workflow combining active learning and Bayesian optimization enabled the discovery of an optimal formulation exceeding the performance of previously reported coatings. The resulting coating displayed exceptional self-healing capabilities and long-term corrosion resistance. This work highlights the significant potential of machine learning in accelerating materials discovery and optimizing material properties, particularly in complex systems like self-healing coatings.

The study focused on a specific type of self-healing epoxy coating with a defined set of components and parameters. The generalizability of the findings to other types of coatings or different self-healing mechanisms requires further investigation. The sample size used for the initial dataset, while efficiently selected using orthogonal methods, might still be considered relatively small. Future work could explore the applicability of this methodology with larger initial datasets. The long-term durability of the optimized coating under various environmental conditions could be studied in more detail.