AIPHAD, an active learning web application for visual understanding of phase diagrams

Phase diagrams are crucial in materials science, mapping phases and their transformations under varying thermodynamic conditions. However, constructing multidimensional phase diagrams is resource-intensive, requiring numerous experiments or simulations. Data-driven approaches, particularly machine learning, offer a promising solution to expedite this process. This research addresses the challenges of efficient phase diagram construction by developing AIPHAD, a web application designed to leverage active learning techniques to guide experimental efforts and provide intuitive visualizations. The application aims to drastically reduce the time, cost, and human effort typically associated with comprehensive phase diagram determination, thereby accelerating materials discovery and development. The importance of efficient phase diagram construction is underscored by the extensive use of phase diagrams in various materials research areas, ranging from alloy development to condensed-matter physics studies focusing on magnetic structures and critical phenomena. While significant progress has been made in the creation of various phase diagrams, the process is still limited by the large number of experiments or simulations required, making it a time-consuming and costly endeavor. Machine learning offers the potential to transform this field by enabling predictive modeling of phase diagrams based on existing data, reducing the need for extensive experimental verification. The development of AIPHAD directly responds to this need, bridging the gap between machine learning capabilities and the practical requirements of materials scientists working with phase diagrams. The application's intuitive interface and open-source nature are expected to promote its adoption across the broader materials science community.

Existing literature highlights the significant challenges associated with generating comprehensive phase diagrams, particularly for multicomponent systems. The traditional methods are resource-intensive, demanding considerable time, cost, and human expertise. Recent studies have demonstrated the potential of machine learning to address these limitations, with applications in predicting phase formation in high-entropy alloys, stability of quasicrystals, coexisting phases in ternary sections, and phase boundaries in binary systems. Data-driven techniques have also been applied in condensed-matter physics to analyze simulation-based phase diagrams, specifically in research on critical phenomena involving strongly correlated fermions and topological quantum systems. These studies pave the way for more efficient phase diagram construction using active learning and uncertainty sampling, which allow for targeted experimentation and reduction in the overall number of experiments needed. However, these methodologies often lack user-friendly interfaces, which restricts broader adoption in the materials science community. Therefore, the development of AIPHAD, which combines advanced machine learning algorithms with an accessible web application, fills a critical gap in current materials research.

AIPHAD utilizes the PDC (Phase Diagram Construction) algorithm, which incorporates active learning principles, specifically uncertainty sampling. The algorithm starts with a discretized phase diagram space and an initial set of labeled data points (from pre-existing data or preliminary experiments). Phase estimation for unlabeled data is performed using machine learning techniques: Label Propagation (LP) and Label Spreading (LS). Both methods use a fully connected graph representing the data points, with edge weights defined by an RBF kernel. LP propagates labels from labeled data to estimate probabilities for each unlabeled point belonging to different phases, while LS allows for label adjustments in labeled data, offering robustness to noise. Uncertainty sampling identifies the most uncertain points for informative experiments using different uncertainty scores (Least Confident, Margin Sampling, and Entropy-based Approach). The AIPHAD web application allows users to select between LP and LS, and choose among the different uncertainty score methods, as well as to adjust hyperparameters (γ for LP, γ and α for LS). The algorithm iteratively estimates phases, proposes experiments based on uncertainty, and incorporates new experimental data, refining the phase diagram iteratively. The application supports five diagram types: two-variable, three-variable diagrams, ternary sections, ternary phase diagrams, and quaternary sections. AIPHAD also incorporates thermodynamic considerations, utilizing information about coexisting phases and the Gibbs phase rule to enhance efficiency, focusing experimentation on crucial areas of the phase space. AIPHAD is available as both a web application and a Python package, providing flexibility to users. The Python version provides full control over parameters, allowing users to customize the algorithm for specific needs. The basic steps are: Importing necessary libraries; Defining parameters for pdc_sampler (estimation method, sampling method, number of proposals); Preparing the dataset (candidate points and label data); Performing phase diagram estimation (using pdc.fit(X, y)); And performing uncertainty sampling (using pdc.us()). In the multiple proposal case, the user can specify which method (only uncertainty score ranking or neighbor exclusion method) they wish to use.

The efficacy of AIPHAD was demonstrated through the investigation of the Fe-Ti-Sn ternary system, focusing on the Heusler phase, a material with potential thermoelectric applications. Starting with seven initial experiments, AIPHAD effectively guided subsequent experiments, leading to a refined understanding of the phase boundaries. The study involved both isothermal section analysis at 900 °C and the construction of a ternary phase diagram across a temperature range. The Label Spreading (LS) method, coupled with the Least Confident (LC) uncertainty score, proved particularly effective in identifying phase boundaries within the Fe-Ti-Sn system. Different uncertainty score methods (LC, MS, EA) were compared under both LP and LS estimations. While the proposed points varied significantly under the LP method, LS consistently identified the most uncertain point, with clearer delineation of phase boundaries. Analysis at 900 °C showcased the algorithm's iterative refinement, where the proposed experiments clustered around the predicted phase boundaries, enhancing the accuracy of the phase diagram. Analysis of the full ternary phase diagram across a range of temperatures (initially 700-1000 °C, later refined to 800-1000 °C) revealed three new phase regions (FeSn, FeSn₂, and Fe+Ti) at lower temperatures, demonstrating AIPHAD's effectiveness in uncovering complex phase relationships. A targeted search for the Heusler phase's stable region at 900 °C, guided by the probability of each phase, successfully pinpointed its compositional range. Four out of six experiments suggested by AIPHAD confirmed the presence of the Heusler phase. The results indicated that AIPHAD significantly reduces the number of experiments required to construct phase diagrams, especially when starting with minimal prior knowledge of the system. The metastable nature of the produced phase diagrams was acknowledged, resulting from the relatively short heat treatment times employed in the experimental process. Supplementary data for each stage of the process, including data compatible with the AIPHAD web application, are provided.

The successful application of AIPHAD to the Fe-Ti-Sn system demonstrates its potential to significantly accelerate phase diagram determination. The use of active learning, combined with the intuitive web application and flexible Python package, makes the tool accessible to a wide range of users. The ability of AIPHAD to incorporate thermodynamic considerations, utilize coexisting phase information, and incorporate the Gibbs phase rule further enhances its efficiency. The study highlights the synergy between machine learning and traditional experimental techniques in materials research. The ability to effectively target specific phase regions, as demonstrated by the Heusler phase search, adds a significant advantage over traditional approaches. The open-source nature of AIPHAD encourages community involvement and further development, paving the way for future enhancements and broader applications. The results obtained using AIPHAD highlight the potential for significant advancements in materials discovery and optimization.

AIPHAD, an open-source toolbox comprising a user-friendly web application and a flexible Python package, significantly accelerates phase diagram construction using active learning and machine learning. Its effectiveness was demonstrated through the detailed mapping of the Fe-Ti-Sn ternary system, efficiently identifying the Heusler phase. AIPHAD's intuitive interface and integration with existing experimental workflows promise to streamline phase diagram research across diverse materials systems. Future work could focus on expanding AIPHAD's capabilities to handle even more complex systems and incorporating advanced machine learning models to improve prediction accuracy.

The current version of AIPHAD relies on the accuracy of the initial experimental data and the chosen machine learning model. Inaccuracies in initial data or limitations of the model could affect the prediction accuracy. While the study demonstrates AIPHAD's effectiveness on the Fe-Ti-Sn system, further validation across a wider range of materials systems is necessary to fully assess its generalizability. The metastable phase diagrams produced are a result of the short heat treatment times; longer heat treatments might reveal differences in the equilibrium phase diagram.