A generative deep learning framework for inverse design of compositionally complex bulk metallic glasses

Bulk metallic glasses (BMGs) are attractive materials due to their unique properties. However, traditional trial-and-error methods for BMG discovery are inefficient and costly. Machine learning (ML) offers a promising alternative, but existing ML models primarily rely on supervised learning, which struggles with the high-dimensional compositional space of complex BMGs. This research addresses this limitation by developing a generative deep-learning framework (GDLF) based on an unsupervised GAN algorithm. The GDLF directly generates compositionally complex BMG compositions, improving efficiency and overcoming the limitations of supervised learning methods in high-dimensional compositional spaces.

The design of BMGs has traditionally relied on time-consuming and inefficient trial-and-error approaches guided by empirical rules like the eutectic point rule and the confusion principle. Recently, data-driven approaches using machine learning (ML) have gained popularity in alloy design. However, most ML-based BMG design methods employ supervised learning, requiring human input to navigate the high-dimensional compositional space. While effective for less complex alloys, this approach becomes impractical for compositionally complex BMGs, such as high-entropy BMGs. This paper aims to overcome these limitations by proposing an unsupervised generative deep learning approach.

The proposed GDLF combines a generative adversarial network (GAN) for data generation with a supervised boosted trees algorithm for data evaluation. The researchers explored three types of data descriptors: compositional information (D1), empirical parameters (D2) commonly used in previous studies (such as atomic size difference, mixing enthalpy, etc.), and recently developed glass-forming ability (GFA) models (D3). These descriptors were used both individually and in combination to create compound descriptors (CD1 and CD2). The GAN consists of a generator (G) and a discriminator (D). The generator produces new BMG compositions and their attributes (e.g., thermal properties), while the discriminator distinguishes between real and generated data. A surrogate model, a well-trained boosted tree classifier trained on a large dataset of known metallic glasses and non-metallic glasses, was used to further evaluate the generated compositions. The GDLF was trained on four datasets of BMGs (Zr-, La-, Fe-, and Ti-based), and the performance of the model was evaluated using various metrics, including generator loss, the ability of the surrogate model to identify the generated compositions as glass-forming alloys, principal component analysis (PCA) to visualize data distributions, and Wasserstein distances to quantify the difference between the generated and literature data. Hierarchical clustering was used to analyze the diversity within each dataset. The study also investigated the use of an expanded dataset combining multiple types of BMGs to improve the generation of more diverse compositions. Experimental validation of generated BMG compositions was conducted using arc-melting and Cu-mold casting, followed by X-ray diffraction (XRD) and energy-dispersive X-ray spectroscopy (EDX) analysis. For inverse design, the GDLF was modified by incorporating relevant thermal properties (Tg, Tx, Tl) into the data descriptor, enabling the generation of BMG compositions with targeted properties. These generated compositions were also experimentally verified using XRD and differential scanning calorimetry (DSC).

The GDLF successfully generated novel BMG compositions, significantly improving the efficiency of BMG discovery compared to traditional methods. The choice of data descriptors significantly affected the model's performance. Combining compositional information with theory-guided descriptors (CD1) proved superior to using empirical descriptors (CD2) for generating diverse and realistic BMG compositions. The use of an expanded dataset further enhanced the diversity of generated compositions, resulting in the generation of a multi-principal element BMG composition, resembling high-entropy alloys, which was successfully synthesized and characterized. The GDLF also successfully enabled inverse design, where the model generated BMG compositions with pre-defined thermal properties (Tg, Tx, Tl). The generated compositions were experimentally verified, showcasing the framework's potential for targeted BMG design. The Wasserstein distance calculations quantified the closeness of the generated data distributions to the original data distributions, confirming the efficacy of the proposed method. The generated compositions exhibited amorphous nature as confirmed by XRD, consistent with the expected BMG structure. The EDX mapping confirmed the homogeneity of element distribution within the experimentally produced BMGs. The DSC analysis confirmed the targeted thermal properties of the inverse designed BMGs.

The GDLF offers a significant advancement in BMG design, particularly for compositionally complex systems. Unlike previous supervised learning approaches, the unsupervised nature of the GAN allows for the generation of BMG compositions that are not present in the training data, exploring uncharted territories in the compositional space. The superior performance of theory-guided descriptors over empirical descriptors highlights the importance of incorporating physical understanding into machine learning models. The successful generation and experimental validation of a novel multi-principal element BMG exemplifies the potential of this method for discovering new materials with enhanced properties. The ability to perform inverse design based on targeted properties opens up exciting possibilities for tailoring BMGs for specific applications. The results suggest that this framework could be extended to other complex material systems, accelerating the pace of materials discovery and design.

This research successfully demonstrates a generative deep-learning framework (GDLF) capable of generating novel and compositionally complex BMGs, including multi-principal element compositions resembling high-entropy alloys. The study highlights the importance of selecting appropriate data descriptors and showcases the framework's ability to perform inverse design, enabling the targeted creation of BMGs with desired properties. Future research could explore the application of this GDLF to other material systems and further refine the data descriptors to improve prediction accuracy and explore broader compositional spaces. The framework shows great promise for accelerating the discovery and design of advanced materials.

The study's reliance on existing literature data for training the model might limit the exploration of entirely novel compositions outside the currently known compositional space. The size of the available BMG dataset was relatively small compared to other material datasets, potentially affecting the model's generalizability. Further investigation is needed to assess the model’s performance with significantly larger and more diverse datasets. The computational cost of training the GAN model can be substantial, particularly with very large datasets.