A general and transferable deep learning framework for predicting phase formation in materials

The study addresses how to efficiently predict phase formation in materials (e.g., crystalline vs. amorphous phases, and BCC/FCC/HCP structures) when only small datasets are available and mechanisms are unclear. Conventional machine learning in materials requires task-specific descriptors selected via trial-and-error and often depends on imprecise or difficult-to-measure properties, limiting performance and transferability. The authors propose a general and transferable deep learning framework that uses end-to-end feature extraction from structured pseudo-image representations (notably a periodic table representation) to improve accuracy and enable transfer learning across related tasks. Predicting glass-forming ability (GFA) and high-entropy alloy (HEA) phases are chosen as testbeds due to their importance and difficulty, with the goal of demonstrating improved performance and generalization, especially with limited data.

Prior work shows machine learning has been widely used to predict materials properties such as formation energies, superconducting critical temperatures, phases, and various properties. Conventional approaches rely on manual features (e.g., Magpie descriptors, physically motivated metrics like mixing enthalpy/entropy, atomic size mismatch, electronegativity differences, VEC). For GFA, Ward et al. employed 145–210 descriptors (including general-purpose and domain-specific ones). For HEAs, traditional models (SVMs, shallow neural networks) using manual features typically distinguish only BCC vs. FCC or intermetallics vs. solid solutions, with difficulty handling HCP due to scarce data. Transfer learning has been highlighted for data-scarce domains, and deep learning’s integrated feature extractors make it suitable for knowledge transfer. Recent CNN-based representations (atom table, randomized layouts) have been explored, but embedding domain knowledge (periodic trends) directly into representations remains an opportunity to enhance generalization on small datasets.

General and Transferable Deep Learning (GTDL) framework: Raw materials data (composition and processing parameters) are mapped to 2-D pseudo-images. The primary representation is a periodic table representation (PTR): a 9×18 grid with 108 element-specific pixels holding atomic percentages and additional gray pixels for unused positions; one gray pixel encodes processing (0 for melt-spun, 100 for copper mold casting). Two alternative mappings were used for comparison: (1) Atom table representation (11×11) placing elements sequentially by atomic number; (2) Randomized PTR with elements randomly arranged in the periodic table area. CNN architecture: A compact VGG-like CNN with three convolutional blocks (3×3 kernels, stride 1, zero-padding of one), channel sizes 8→16→32, ReLU activations, and pooling layers after each conv block, followed by a fully connected layer and softmax classifier. Total trainable parameters ≈6274 to mitigate overfitting on limited data. CNNs were implemented in Keras/TensorFlow. SNN baselines used 20 neurons in the hidden layer. Datasets: GFA dataset assembled from multiple sources: Sun’s binary (≈3000), Ward’s ternary (≈6000), BMG (≈800), Miracle’s GFA (≈300), plus 800+ conventional crystalline metallic materials to balance classes. Original GFA dataset size 10,440; after converting to a binary task (AM vs. CR) by including processing parameter, dataset size 16,250. HEA dataset: 355 experimentally synthesized HEAs with phase labels (41 BCC, 24 FCC, 14 HCP, 59 amorphous, 217 multi-phase) spanning 50 elements with imbalanced distributions. Training and evaluation for GFA: Compared four shallow neural networks (SNNs) using various manual/composition features and three CNNs using the three representations (atom table, randomized PTR, PTR). Used categorical cross-entropy loss, 2000 epochs with early stopping, and 10-fold cross-validation. For generalization, performed leave-one-system-out (LOSO) tests on 160 ternary systems and specifically on Al-Ni-Zr (with 5151 composition points as ground truth). Additional external validation used newly reported BMG systems and binary outliers. Transfer learning to HEAs: Reused trained CNN feature extractors (convolutional layers) from GFA models (CNN1/2/3). Fed HEA compositions into these CNNs to extract high-dimensional features. Trained a new classifier (random forest via scikit-learn, with stratified splits) on these features to predict five HEA phase classes (BCC, FCC, HCP, amorphous, mixture). Fivefold cross-validation was used to report accuracy, precision, recall, and F1. Feature analysis used PCA to visualize learned elemental relationships and alloy feature clustering. Comparators: Manual feature sets included composition vectors, Magpie descriptors, and domain-specific metrics (mixing entropy/enthalpy, atomic size difference, electronegativity difference, VEC, and statistics of elemental properties).

- On GFA (binary AM vs. CR), the PTR-based CNN (CNN3) achieved the highest 10-fold cross-validation testing accuracy of 96.3%, outperforming SNN baselines (≈89.9–93.5%) and other CNNs without periodic structure (CNN1 atom table: 95.0%; CNN2 randomized PTR: 94.9%). - In the Al-Ni-Zr ternary system, CNN3 reproduced three amorphous regions and their boundaries most faithfully compared with experimental ground truth, showing superior generalization to SNN3 and CNN2. - LOSO tests on unseen alloy systems showed PTR-based CNN (CNN3) had markedly better generalization; on Al-Ni-Zr LOSO, CNN3 reached 80.3% accuracy versus lower scores for other models. Across 160 ternary systems, CNN-based models outperformed SNNs (PTR model best; table shows CNN superiority by about 7% over SNN4). - External validation on newly reported or challenging systems: CNN3 predicted 27/28 for Ir-Ni-Ta-(B), Mg-Cu-Yb, and S-bearing BMGs; 10/13 for RE6Fe72B22 substitutions; and 16/18 for binary alloy outliers, outperforming SNNs and non-PTR CNNs. - Transfer learning to HEAs (five phases): Using features transferred from GFA CNN3 with PTR and a random forest classifier achieved average fivefold CV scores: accuracy 0.935, precision 0.940, recall 0.935, F1 0.934. Models transferred from non-PTR CNNs performed worse (randomized PTR accuracy 0.854; atom table accuracy 0.884). - Feature visualization revealed that PTR enables the CNN to learn periodic trends and cluster elements by groups/periods, even for sparsely represented elements, aiding generalization. HEA alloy features clustered by phase, supporting the efficacy of transfer learning.

The findings demonstrate that embedding domain knowledge via the periodic table representation (PTR) and leveraging deep learning’s automatic feature extraction significantly improve prediction accuracy and, crucially, generalization to unseen compositions and systems. CNN3’s superior performance on LOSO tests and external validations indicates that PTR captures periodic trends and elemental relationships that manual features or non-structured representations miss, especially under data scarcity. Transfer learning from GFA to HEA phase prediction succeeds because the input domains overlap (similar element sets and compositional descriptors) and the CNN’s learned features encode relevant chemistry and physics. The strong HEA performance across five classes, despite small and imbalanced data, underscores the practicality of reusing feature extractors trained on larger related datasets. Overall, the approach directly addresses the research goal: accurate, generalizable phase prediction with small datasets by transferring knowledge across related materials tasks.

This work introduces a general and transferable deep learning framework that maps compositions and processing conditions to periodic-table-based pseudo-images, enabling automatic feature learning and knowledge transfer. The PTR-based CNN achieves state-of-the-art accuracy for glass-forming ability prediction and superior generalization to unseen systems and newly reported alloys. By transferring learned features to HEA phase prediction, the framework accurately discriminates five phase types using a small, imbalanced dataset without manual feature engineering. The study shows that embedding domain knowledge in data representations enhances model robustness under data scarcity and facilitates reusability across related problems. The framework can be readily applied to new materials development by reusing well-trained feature extractors; future work could extend to other materials classes, integrate additional processing variables, and explore end-to-end fine-tuning strategies for target tasks.

- Data limitations and imbalance: The HEA dataset is small (355 samples) with uneven class distributions and rare elements, which challenges model training and evaluation. The GFA dataset required augmentation of crystalline entries to mitigate bias. - Potential overfitting risks: Small input images and limited data necessitated a compact CNN to curb overfitting; results may still be sensitive to dataset splits and class imbalance. - Label and mechanism uncertainty: GFA labels simplify complex phenomena (e.g., AMR vs. BMG distinctions depend on processing and incomplete records), and physical property inputs in manual baselines rely on simplified models (e.g., ideal solution for enthalpy), which can introduce noise. - Representation dependence: Performance gains rely on the PTR; alternative mappings without embedded periodic structure showed weaker generalization, suggesting sensitivity to representation design.