Galvanic corrosion, a significant challenge in engineering, involves the degradation of dissimilar metals in contact under corrosive environments. The corrosion rate is highly dependent on numerous factors, including environmental parameters (temperature, humidity, salt concentration), material properties, and geometric configurations. Traditional experimental methods for determining the cathodic current (a key indicator of corrosion susceptibility) are expensive and time-consuming due to the need to vary and measure each parameter. Finite Element (FE) simulations can help, but they require experimentally derived boundary conditions (BCs), adding further to the cost and complexity. This necessitates a more efficient approach to predict corrosion behavior across a wide range of conditions. Machine learning (ML) surrogate models offer a potential solution by rapidly estimating the cathodic current for diverse input configurations. However, even with ML, a considerable upfront investment is required to generate the simulation and experimental data necessary to calibrate the model. Active learning (AL) is proposed as a methodology to optimize the process by strategically selecting the most informative data points to include in model training. This iterative process reduces the cost associated with acquiring both experimental BCs and running FE simulations. The current research focuses on developing and validating an AL framework to specifically tackle this high-dimensional problem in the context of galvanic corrosion.

Prior work has explored the use of ML and AL in various applications, including materials science and engineering. Studies have used different acquisition functions (e.g., predictive uncertainty, expected improvement, expected information gain) to guide the selection of data points in AL. While the utility of AI and AL in materials degradation models, specifically in corrosion, is evident, limited prior work has addressed problems with stratified environmental and geometric variations in a systematic manner. Existing AL protocols often search the entire input domain, which is inefficient in this context where obtaining experimental BCs is costly. The existing methods also typically identify only a single input configuration at each iteration, neglecting the potential benefits of selecting multiple configurations to better balance exploration and exploitation of the input space. Moreover, extrapolating model predictions beyond the initial input domain can lead to poor accuracy. Therefore, there's a need for a more advanced AL framework tailored to the challenges of galvanic corrosion.

This research develops a two-step AL framework to improve the prediction accuracy of the cathodic current in a galvanic couple (AA7075-SS304) using FE simulations. The framework utilizes a Gaussian Process (GP) and a Neural Network (NN) as surrogate models, combining their predictions through an information fusion technique. Initially, a dataset of 2520 FE simulations is used, obtained using a hypercube sampling strategy. The dataset is split into training and testing sets. An initial batch of training data is selected using the MaxPro approach, which aims for uniformity across lower-dimensional projections of the input space. A GP model is then trained on this initial data and used to calculate an acquisition function (either predictive standard deviation or expected information gain). The first step of the staggered approach focuses on selecting the optimal temperatures and salt concentrations by marginalizing over the geometric parameters (cathode length and water layer thickness) within the GP model. The acquisition function is maximized (using weighted K-means clustering to identify multiple configurations) to identify additional temperatures and salt concentrations for experimental measurements of polarization curves. In the second step, with the temperature and salt concentrations fixed at values identified in the first step, the acquisition function is recalculated considering only the geometric parameters and is again maximized (using weighted K-means clustering) to identify optimal geometric parameters for additional FE simulations. This two-step approach iteratively refines the surrogate model, maximizing information gain with minimal data acquisition. The performance of the framework is evaluated using 10-fold cross-validation (CV) error and mean absolute error (MAE) on both the training and testing sets. Finally, the framework’s ability to extrapolate to out-of-distribution points is tested on an independent dataset, and an additional AL iteration is performed on an expanded input domain to further enhance the model's predictive power.

The developed AL framework significantly improved the accuracy and efficiency of predicting cathodic current in a galvanic couple. The results demonstrate that the active learning approach, using either the predictive standard deviation or the expected information gain as the acquisition function, led to substantial reductions in the computational costs (approximately 50% reduction compared to random selection) while achieving comparable prediction accuracy to a model trained on the full dataset. The expected information gain (EI) acquisition function consistently outperformed the predictive standard deviation (PS) function, particularly in out-of-distribution predictions. The initial model, trained on a subset of datapoints (using MaxPro approach), yielded a 10-fold CV error of approximately 5 mA/m and MAE of 3.7-3.2 mA/m for the test set for PS and EI respectively. After incorporating data from the active learning iterations, the out-of-distribution prediction error on an extrapolation dataset (2885 data points from previous studies) was substantially reduced by nearly 50% (from 0.017 mA/m to 0.009 mA/m) when using EI, showing the effectiveness of the framework in extrapolating beyond the initial input domain. The analysis of probability density functions indicated that the optimal design points identified during the active learning iterations were not uniformly distributed across the input space, indicating that the AL framework effectively prioritized data points with high information content.

The developed two-step AL framework successfully addresses the challenges associated with predicting galvanic corrosion in a high-dimensional parameter space. By strategically selecting additional experimental and simulation data points, the framework efficiently calibrates a surrogate model that accurately predicts cathodic current, significantly reducing the computational cost and time compared to traditional methods. The superior performance of the expected information gain acquisition function highlights the importance of selecting an appropriate acquisition function for optimal exploration and exploitation of the input space. The ability of the framework to extrapolate predictions to out-of-distribution points further demonstrates its value in exploring a wider range of conditions. The staggered approach allows for efficient integration of both experimental and simulation data, addressing situations where different sets of factors control these responses. The successful application of the framework to a galvanic corrosion problem suggests its broader applicability to other materials degradation studies.

This study presents a novel two-step active learning framework for efficient and accurate prediction of galvanic corrosion. The framework combines FE simulations, experimental measurements, and advanced ML techniques to minimize computational costs while maximizing prediction accuracy. The results demonstrate significant improvements in model performance, particularly when using the expected information gain as the acquisition function. This approach offers a powerful tool for accelerating the design and optimization of materials and systems subjected to corrosive environments. Future research could explore the application of this framework to other types of corrosion or different materials systems, and could focus on optimizing the parameters of the acquisition function selection.

The current study focused on a specific galvanic couple (AA7075-SS304) and a simplified two-dimensional FE model. The generalizability of the framework to other material combinations and more complex geometries needs further investigation. The accuracy of the extrapolation is dependent on the underlying assumptions of the surrogate model and the choice of the kernel function used in the GP model. Additional research is needed to assess the robustness and sensitivity of the framework to different model parameters and data characteristics. Finally, although the study reduced costs significantly, further iterations of active learning might yield even better results.