Advances in graph neural networks for alloy design and properties predictions: a review

Basic definition and characteristics of graphs

A graph is widely used in discrete mathematics for representing objects and their relationships. A graph is typically denoted as G = (V, E), where V represents the set of vertices (or nodes) and E denotes the set of edges, which represent the connections between vertices^[27,28]. Nodes represent specific objects (e.g., atoms), while the edges represent the relationships between these objects (e.g., bonding interactions). Therefore, there are typically three types of tasks in graph learning:

• Node-level tasks focus on the individual nodes in a graph. These tasks include node classification, which aims to assign each node to a specific category, node regression, which involves predicting a continuous value for each node, and node clustering, aimed at grouping nodes into several clusters such that similar nodes are placed together in the same group.

• Edge-level tasks involve edge classification and link prediction, which aim to determine the type of an edge or predict the presence of an edge between two specific nodes. Edge classification assigns labels to edges based on the relationship they represent, while link prediction estimates whether an edge will exist between two nodes in the future.

• Graph-level tasks include graph classification, graph regression, and graph matching, all of which require the model to learn representations of entire graphs. These tasks aim to assign labels, predict continuous values, or find correspondences between graphs by capturing global graph structures and properties.

Depending on the directionality of the edges, graphs can be classified into directed and undirected graphs. Since bonding interactions in materials science are typically undirected, undirected graphs are frequently used to represent material structures. The connectivity between vertices can be represented using an adjacency matrix or an incidence matrix. These vertices and their connections are input into GNNs as feature vectors and adjacency matrices for computation and analysis. Figure 1 converts the Ni₃Al crystal into an undirected graph whose adjacency list and matrix encode atom connections - matrix zeros mark absent self-links, while off-diagonal values 1, 2 and 3 label Ni–Ni, Ni–Al and Al–Al bonds, respectively. For other types of graphs, please refer to Supplementary Table 1.

Figure 1. Various representations of the Ni₃Al crystal structure. (A) Schematic diagram of the Ni₃Al crystal structure, showing the arrangement of Ni and Al atoms in a cubic lattice; (B) Undirected graph representation of Ni₃Al, where nodes represent atoms and edges represent ionic bonds; (C) Adjacency list representation of the Ni₃Al structure, depicting the connections between atoms; (D) Adjacency matrix representation of Ni₃Al, illustrating the connectivity between atoms in matrix form.

The structure of GNN models

Message passing

GNNs operate by recursively aggregating and transforming information from neighboring nodes, thereby learning expressive representations of graph-structured data. Each GNN layer can be viewed as a message-passing process, where each node receives messages from its neighbors and updates its own state accordingly. This concept, generalized by Google through identifying shared principles across various GNN models, extends the forward and backward propagation mechanisms of conventional neural networks to graph structures^[38]. The key lies in defining rules for inter-node message passing: during the forward pass [Figure 2], the features of each node are integrated with those of its neighbors to form a refined local representation. In the context of alloy design, such a mechanism can model interactions among different atoms or elements within an alloy, revealing how these interactions collectively shape the material’s macroscopic properties.

Figure 2. Schematic of the message passing mechanism in GNNs. The input layer contains the original attributes. In the hidden layer, each node gathers information from its immediate neighbors and transforms it, creating an updated feature that fuses its own data with local context. The output layer repeats the aggregation, allowing every node to integrate signals from a wider neighborhood and produce a final, more informative representation. GNNs: Graph neural networks.

Overview and main types of GNNs

GNNs are deep learning architectures specifically designed to process graph-structured data. They can learn representations of both nodes and overall graph structures, enabling tasks such as regression, classification, and clustering. While conventional deep learning models, such as convolutional neural networks (CNNs) and recurrent neural networks (RNNs), target Euclidean domains (e.g., images or text), GNNs extend these techniques to non-Euclidean entities such as atoms, ions, or molecules. In this way, graphs representations provide a flexible framework for capturing spatial coordinates and connectivity patterns that significantly influence material properties. From the perspective of supervision, graph learning tasks can be categorized into three main training paradigms:

• Supervised Learning: In the supervised setting, sufficient labeled data is provided for training, commonly used for tasks such as node classification and link prediction.

• Semi-supervised Learning: A small subset of labeled nodes coexists with a large number of unlabeled nodes. During testing, transductive approaches predict labels for unlabeled nodes in the same graph, while inductive approaches require the model to generalize to previously unseen nodes from the same distribution. This setting is particularly common in node and edge classification tasks.

• Unsupervised Learning: Only unlabeled data is available, and the model must discover latent patterns from the graph structure. A typical example is node clustering, where the model groups nodes based on their similarities without any labeled supervision.

In conclusion, GNNs provided a flexible and robust framework for processing graph-structured data under diverse learning settings, enabling the effective modeling of complex relationships and structures across a wide range of domains.

GNNs encompass various specialized architectures tailored to different applications. For the complete description of the message-passing mechanism, see Section “Message passing”. Hereafter, we will refer to that section and only briefly remind the reader of differences among variants. Recursive GNNs (RecGNNs) iteratively aggregate neighborhood information, emphasizing the hierarchical structure of graphs. This property makes them particularly well-suited for materials science tasks such as predicting the properties of complex alloy networks, where atomic interactions follow nested or hierarchical patterns. In contrast, graph autoencoders (GAEs) are unsupervised models designed to learn efficient graph representations, making them ideal for clustering material structures. Spatial-temporal GNNs (ST-GNNs) extend GNN functionality to data that varies across both space and time-an essential capability for modeling how materials respond dynamically to varying conditions (e.g., thermal or mechanical stress over time).

These GNN variants enable more nuanced and predictive analyses in material design, helping to discover new materials with optimized properties. Several GNN variants are commonly adopted in materials chemistry research, each tailored to capture the unique structural and compositional complexities inherent to different material systems. Supplementary Table 3 provides a summary of several GNN variants and their typical applications. Below is an introduction to the three most basic GNNs.

Graph convolutional networks

Graph convolutional networks (GCNs) are a class of neural network architectures designed for graph-structured data^[41]. Figure 3A illustrates this iterative process. In the first layer, each node updates its feature by referencing its immediate neighbors, as indicated by the adjacency matrix. As subsequent layers are added, the receptive field of each node expands, allowing it to aggregate information from increasingly distant neighbors. By propagating features through successive layers, GCNs effectively capture both local and global dependencies in the graph, facilitating powerful learning from graph data.

Figure 3. Illustration of common GNN architectures. (A) GCN performs spectral convolution, aggregating normalized features from neighboring nodes with shared trainable weights; (B) GraphSAGE samples a fixed-size set of neighbors and aggregates their features (e.g., mean or max-pool) to build updated node representations; (C) GAT assigns attention coefficients to each neighbor, enabling the model to weigh their contributions adaptively during aggregation. GNN: Graph neural network; GCN: graph convolutional network; GAT: graph attention network.

Workflow for constructing GNN tasks

Figure 4 illustrates the entire workflow of a GNN model from input data to final output predictions. Initially, the raw data is divided into training and testing sets, typically at a ratio of 4:1, and k-fold cross-validation can be employed to enhance model robustness. The data is then converted into a graph structure using specific algorithms, which involves defining nodes, edges, and their corresponding features. Feature selection usually emphasizes attributes highly correlated with the target task; for example, the stability of crystals is closely related to their structural features. Next, the GNN architecture is constructed, starting with normalization layers, followed by 3-5 graph convolutional layers. Dropout layers are added to prevent overfitting, and pooling layers are used for extracting essential features. Finally, during training, suitable optimizers, learning rates, and loss functions are established. Predictions are generated through forward propagation for each batch, and the differences between predictions and actual values (losses) drive parameter adjustments via back-propagation until the model converges.

Figure 4. Workflow for constructing GNN tasks. Diagram illustrating data preprocessing, graph construction, GNN building, training, and final property prediction. GNN: Graph neural network.

Characteristics and constraints of GNNs

GNNs offer clear advantages for material research, especially in modeling structure-property relationships. However, the predictive accuracy of state-of-the-art GNNs is still constrained by several inherent architectural and data-related limitations. They naturally model graph-structured data (such as atoms and grain boundaries) by message passing^[23] and aggregating features along edges, which lets them capture the complex relationships that govern material behavior. This end-to-end framework eliminates the need for manual feature engineering^[36], speeding up development. Its multilayer design integrates information from local atomic arrangements all the way up to global microstructural patterns, yielding more accurate property predictions.

Although four key method-level hurdles remain, as shown in Table 2, each has now been met with promising solutions.

Among these constraints, interpretability has received increasing attention. While GNNs offer strong predictive performance, their internal reasoning processes are often opaque. To improve transparency, several techniques have been developed. Attention-based models such as GAT and SAGNN learn importance weights for neighboring nodes, helping identify which parts of the graph most influence predictions. Additionally, methods such as GNNExplainer, gradient-based saliency maps, and feature masking reveal critical substructures or features responsible for specific outcomes. These techniques not only improve trust and understanding but also support model validation and refinement.

Continued advances in these four areas (scalability, representation quality, interpretability, and data efficiency) are the key to unlocking broader, more reliable GNN applications, including material discovery. Yet a critical gap remains: existing architectures rarely achieve all four goals while staying faithful to underlying physics across multiple length scales. The remainder of this review is therefore structured to confront this gap by mapping recent methodological progress, benchmarking their performance on alloy-relevant tasks, and distilling actionable guidelines that can steer the development of future, physics-consistent GNN frameworks for alloy modeling.

Material property prediction and microstructure characterization

In alloy design, predicting material properties is a critical task. Traditional methods for prediction typically rely on extensive experimental data and complex physical models, which are often inadequate for multi-component alloys with intricate interactions. With the advent of GNNs, researchers have started to explore more efficient and accurate ways to map alloy composition to performance, particularly in forecasting key properties such as mechanical performance.

Polycrystal-scale elasticity

Pagan et al. laid the groundwork for grain-level GNN surrogates by training a message-passing network on crystal-elastic finite element method (FEM) data and fine-tuning it with high-energy X-ray diffraction microscopy (HEDM) measurements [Figure 9A]; using grain orientation, directional modulus and volume as node features and shared boundaries as edges. Then their model reproduced the anisotropic stiffness of a low-solvus, high-refractory (LSHR) alloy and Ti-7Al with 5%-10% error^[56].

Figure 9. (A) Pipeline for mapping crystallographic graphs to direction-dependent elastic constants; grains are treated as nodes and grain-boundary misorientations as weighted edges, enabling anisotropic elastic behavior to be learned directly from the topology; (B) Graph-transformation scheme for ferritic steel, in which microstructural snapshots are converted into time-evolving graphs whose updated edge weights capture damage accumulation and allow high-cycle fatigue life to be predicted. These examples illustrate how bespoke graph representations can be tailored to very different mechanical-property targets. Reproduced with permission from Refs.^[56,63]. © 2022 and © 2023 The Authors.

Building on this grain-scale graph representation, Hu et al. introduced AnisoGNN, which augments every node with symmetry aware descriptors such as Schmid factors; a single network therefore recovers elastic moduli and initial yield strength for nickel superalloys and aluminum alloys under arbitrary loading directions with high fidelity^[57]. In parallel, Hestroffer et al. transferred the same architecture to crystal plasticity finite element data for α-titanium^[58], achieving accurate single-axis predictions of yield strength and Young’s modulus while cutting computational cost by orders of magnitude. To explore coupled fields, Dai et al. combined phase field snapshots with a graph network to capture effective magnetostriction in ferromagnetic polycrystals^[59] and later used Fourier perturbation data to predict ionic conductivity together with elastic moduli along three principal directions^[60]. Vlassis et al. advanced the framework further by training a graph network to output a differentiable hyperelastic energy functional, allowing downstream continuum solvers to derive stresses directly from the learned potential^[61]. Finally, Hu et al. added edges to construct a temporal GNN (TGNN) that tracks grain growth and texture evolution across time, successfully reproducing microstructural kinetics at a fraction of the phase field cost^[62].

Taken together, these studies trace an explicit upgrade path-static elasticity, plasticity, multi-physics tensors, energy functional learning, and microstructure dynamics-while retaining the grain graph backbone established by Pagan, underscoring the versatility and scalability of GNNs for polycrystal property prediction.

Crystal-structure graphs for formation energy

The graph-based representation pioneered by Lupo Pasini et al. begins with a rigorously constructed CGCNN that encodes the Ni-Nb binary alloy as an atomistic graph, where each atom is a node and each chemical interaction is an edge; Figure 10 illustrates this conversion in detail. Training on density-functional-theory data, the model reproduces formation energies and bulk moduli with near-DFT accuracy while running three orders of magnitude faster, thereby demonstrating that a properly designed GNN can replace brute-force quantum calculations for routine screening of crystal prototypes^[67,68]. This binary proof-of-concept validates the sufficiency of simple node and edge attributes-atomic number, fractional coordinates and bond distances-to capture the essential physics governing cohesive energy and elasticity.

Figure 10. Binary-alloy structure conversion to a graph representation. The crystalline super-cell is first tiled to expose periodicity, after which each atom is mapped to a node carrying its element type, and every pair of atoms within a chosen cutoff radius is mapped to an edge weighted by inter-atomic distance. The resulting graph preserves both chemical identity and local geometry, providing a compact input for GNNs that predict alloy properties while remaining agnostic to cell size. GNNs: Graph neural networks.

Building on that foundation, subsequent studies progressively expand both chemical scope and task specificity. MEGNet couples the original node-edge graph with a learnable global state vector, enabling a single network to predict more than a dozen properties across most of the periodic table^[69]. Intermetallics graph neural network (IGNN) then fine-tunes this backbone with a density-focused loss to reduce errors on heterogeneous intermetallic datasets^[70]. Building on CGCNN^[23], a variant tailored to battery research integrates electrochemical labels and high-throughput databases to identify over one hundred low-voltage alloy anodes without additional DFT relaxations^[71].

Works above trace a coherent trajectory from a binary demonstrator to a universal backbone and, ultimately, to specialized discovery tools, underscoring the pivotal role of GNNs in converting atomic connectivity into reliable, scalable predictors for alloy design.

Dynamic microstructure evolution

Qin et al. introduced GrainGNN, a dynamic graph-neural surrogate that tracks grain coarsening during rapid solidification by representing every time step as a graph whose nodes are grains and whose edges are shared boundaries^[72]. Grains that merge or vanish are handled through a classifier predicting topological events, while a separate regressor updates boundary motion; the network reproduces phase-field statistics with > 80% pointwise fidelity yet runs 10²-10³ × faster. To visualize these predictions, Figure 11 explains the compression of grain evolution during solidification to a 2D graph representation.

Figure 11. Compression of grain-evolution data during solidification into a two-dimensional graph representation. Successive 3D microstructure snapshots are projected onto a plane; each grain becomes a node whose color encodes crystallographic orientation, while shared grain boundaries are converted to edges weighted by boundary length. This 2D graph retains the essential topological information needed to track grain coalescence and growth kinetics with greatly reduced storage and computational cost. Adapted from Ref.^[72], copyright © 2024 Elsevier Inc.

Meantime, Hu et al. proposed a TGNN that keeps the grain graph fixed but augments each node with time-series features such as orientation tensors^[62]; stacked time-convolution and recurrent units propagate history-dependent information, enabling accurate cross-scale forecasts of texture evolution under mechanical loading. Together, GrainGNN and TGNN cover the two principal facets of microstructural kinetics: GrainGNN excels when grains appear, merge or disappear, whereas TGNN excels when grain identities persist but properties evolve continuously. Used sequentially-first GrainGNN for the as-solidified state, then TGNN for service-time evolution, the two frameworks outline a fully GNN-driven pipeline for process-to-performance alloy design.

Composition design

Scholars have utilized GNNs to assist in alloy composition design. In particular, Long et al. presented a composition-to-property network for bulk metallic glasses (BMGs) that converts an alloy formula into a graph, whose nodes carry elemental descriptors and whose edges encode bond strength^[76]. The end-to-end model learns latent correlations between short-range atomic topology and macroscopic mechanical strength, providing quantitative guidance where empirical rules fail. Figure 12 shows the graph construction pipeline and illustrates how the learned edge features highlight critical element-element interactions that govern BMG toughness.

Figure 12. Graph representation of alloy composition for mechanical-property prediction. Each node denotes an alloying element, and each edge represents the correlation between a pair of elements and the target property. Edge color encodes correlation strength - lighter tones indicate weaker relationships, while darker tones mark stronger ones - and edge width scales with the same metric to aid visual comparison. Adapted from Ref.^[76], copyright © 2024 Elsevier Ltd.

Additionally, Yang et al. extended the paradigm to crystalline systems containing defects^[77]. Using 2,000 graphene biocrystals and three-dimensional Al polycrystals generated by molecular dynamics simulation (MD), they trained a graph network to regress per-atom stresses from connectivity alone, achieving a 5.5% test error. Coupling the trained surrogate with a genetic algorithm enabled inverse design of stress-mitigating local structures, opening a route to defect-centric optimization. Figure 13 depicts the edge-only graph representation and the resulting stress-field prediction around grain boundaries.

Figure 13. Graph-neural model for atomic-stress prediction in defect-containing crystals. Atoms serve as nodes tagged by grain ID, nearest-neighbor bonds form edges, and message passing embeds grain-boundary and defect context before stress read-out. Adapted from Ref.^[77]. © 2022 The Authors.

Furthermore, leveraging density-functional datasets, Zhou et al. built the adsorbate-site GCN (ASGCNN) to model nitrogen adsorption on Heusler surfaces^[78]. Trained on 6,000 active-learning-selected structures, the network ranks candidate surfaces by binding free energy, then filters them with a desorption criterion to expose alloys suited for electrochemical nitrogen reduction. Subsequent DFT verification confirmed the catalytic promise of the top-ranked compositions, underscoring the synergy between graph learning and first-principles data in composition screening.

Unsupervised and self-supervised GNN techniques for alloy design

Beyond representation learning, recent developments have explored generative GNNs that directly synthesize alloy structures with desired properties, forming a natural extension to unsupervised encoders.

Generative and inverse design

Google DeepMind, in collaboration with the Berkeley Lab, developed the advanced active-learning deep learning tool - graph networks for materials exploration (GNoME)^[87], aiming to expedite material discovery by predicting the structure and stability of novel materials-effectively addressing the time- and cost-intensive nature of conventional experimental approaches. The latest public release enumerates > 3.8 × 10⁵ stable phases, expanding the Materials Project catalogue by almost an order of magnitude. Figure 14 illustrates how GNNs, by representing intricate atomic structures as graphs, capture the complex interatomic relationships necessary to accurately forecast material stability. The trained GNN model rapidly generates large volumes of candidate materials without requiring real-world experimentation, drastically reducing the initial screening phase.

Figure 14. GNoME framework. GNNs are employed to efficiently predict both the properties and structural stability of candidate crystals. Reproduced from Ref.^[87], copyright © 2023, The Author(s). GNoME: Graph networks for materials exploration; GNNs: graph neural networks.

Moreover, the AI4S group from Microsoft introduced MatterGen^[88], a framework that employs a diffusion-based generative process to iteratively refine atomic types, coordinates, and periodic lattices to construct crystal structures. In this approach, GNNs represent and process the crystal lattice, enabling MatterGen to generate new structures that meet specified property constraints; the model can then be fine-tuned for particularly performance requirements, functioning as a form of high-throughput virtual experimentation. In parallel, discriminative GNNs which are exemplified by the CGCNN^[23] remain invaluable for rapid post-generation triage; recent work achieved a true-positive rate of 95% when predicting the synthesizability of double-halide perovskites^[89].

GNN surrogates for quantum calculations

Beyond generation, GNNs increasingly substitute conventional quantum calculations. The universal interatomic potential M3GNet attains near-DFT accuracy across the periodic table while being three orders of magnitude faster, enabling large-scale molecular-dynamics simulations that were previously infeasible^[53]. Comparable all-periodic-table performance has recently been reported for the equivariant CHGNet potential^[90]. Park et al. further demonstrated that a direct-force GNN architecture delivers ab-initio-quality forces while outperforming classical potentials in both accuracy and scalability for large systems^[91]. Finally, M3GNet-guided cluster-expansion workflows have been applied to multi-component and HEAs, reducing the configurational-averaging cost by roughly an order of magnitude without sacrificing phase-stability predictions^[92].

High-throughput discovery and screening with GNNs

High-throughput methods accelerate materials discovery by enabling automated evaluation of vast design spaces, and their integration with GNNs offers a scalable solution for predicting materials properties with near-DFT accuracy but at a fraction of the computational cost.

Wu et al. coupled CGCNN with van-der-Waals DFT screening to evaluate 5,000+ 2D monolayers for catalytic and electronic properties^[93]. Elrashidy et al. combined ALIGNN with a variational autoencoder to generate 11,000 magnetic candidates, successfully validating 167 new 2D magnets^[94]. Sibi et al. used ALIGNN to predict work functions for thousands of 2D materials, achieving high accuracy and transferability to MXenes^[95]. Rahman et al. applied GNNs to screen over 10,000 bulk and surface structures for defect information energies using a DFT-trained surrogate model^[96]. Google DeepMind’s GNoME framework predicted stability for over 390,000 hypothetical inorganic crystals, expanding the Materials Project database by nearly 10 times^[87]. Microsoft’s MatterGen used a GNN-guided diffusion model to generate crystal structures matching predefined property constraints. Vazquez et al. integrated GNN surrogates with cluster expansion methods for HEA phase screening, reducing DFT computation time by an order of magnitude^[92].

Multiscale dynamics and physics-informed models

Graph-based surrogates are now being extended beyond static property prediction to capture time-dependent phenomena across multiple length scales, thereby complementing or replacing computationally intensive physics solvers.

At the mesoscale, Qin et al. encoded the evolving grain topology that arises during rapid solidification of HEAs as a dynamic graph and trained GrainGNN on phase-field trajectories; the network reproduces grain-growth kinetics while delivering speed-ups of two to three orders of magnitude relative to conventional phase-field integrations^[72]. Moving to the atomistic regime, Ehsan et al. coupled hybrid Monte-Carlo/MD simulations with a graph-convolutional network that predicts the potential energy landscape of medium-entropy alloys, demonstrating that a local chemical ordering signal extracted from GCNN embeddings can faithfully track thermodynamic equilibration over a wide temperature range^[97]. At still larger scales, Tian et al. introduced a physics-informed GNN equipped with uncertainty quantification that learns dislocation-mobility laws directly from large ensembles of molecular-dynamics simulations of body-centered-cubic metals; the resulting constitutive relation surpasses phenomenological models in both accuracy and transferability while providing calibrated epistemic error bars that guide additional data acquisition^[98].

Taken together, these studies illustrate a coherent progression: graph surrogates first replicate mesoscale grain evolution, then atomistic energetics, and finally bridge to continuum-scale constitutive behavior through physics-aware loss functions.

Knowledge integration and autonomous agents

Recent studies highlight how graph-based surrogates can be embedded in higher-level reasoning frameworks to unlock autonomous decision-making in alloy research. Ghafarollahi and Buehler coupled a property-predicting GNN with a suite of large-language-model (LLM) agents^[99]; the LLMs handle task planning and hypothesis generation, while the GNN supplies rapid estimates of Peierls barriers and dislocation–solute interactions, enabling the multi-agent system to chart the Nb–Mo–Ta design space with a fraction of the computational cost required by direct atomistic simulation. Complementing this top-down strategy, Qi et al. introduced knowledge-driven graph convolutional network (KD-GCN)^[100], which embeds steel-making heuristics in a knowledge graph and feeds them into a GCN encoder; the model attains high predictive fidelity on limited data, showing that domain ontology can compensate for sparse labels when mapping composition-process variables to mechanical properties At the catalyst scale, the deconstruction and reconstruction (DR-Label) supervision scheme by Wang decomposes node-wise labels into edge-wise constraints before reconstruction^[101], tightening the learning signal and yielding state-of-the-art adsorption-energy predictions on OC20 and Cu single-atom-alloy benchmarks.

A summary of recent cutting-edge GNN applications in alloy design is provided in Table 5.

GNNs integrating different alloy design data and models to build graphs

Below are several approaches for data representation:
(1) Converting images to graph-structured data: (a) Three-dimensional phase field patterns. Researchers spatially compress 3D phase-field pattern transitions and material microstructural characteristics^[72]. These images typically describe phase transition processes and the microstructure of materials. By converting them into abstract graphs, the model can effectively capture the spatial distribution and evolutionary behavior between different phases; (b) EBSD and SEM images. By combining EBSD images and scanning electron microscopy (SEM) images^{[60,63,64,66]}, grain orientation and alloy microstructure can be further characterized.

(2) Directly abstracting grain or alloy phase structures using graph structure. Each grain is treated as a node in the graph, while edges reflect grain boundaries or phase boundaries, thus depicting microscopic topological relations^{[67,69-71,74]}. Furthermore, mapping these graph structures to first-principles models allows for atomic-level insights into materials behavior. Incorporating DFT results into GNN training can significantly boost the accuracy of alloy property predictions.

(3) Graph-based representation of elastic FEM data. In FEM, this allows the model to capture the material’s localized stress concentration and relaxation effects^{[56,57,61,62,65]}. Some researchers have also converted phase field data into graph-structured data for the prediction of material properties^[59].

(4) Transfer learning method. The graph-based model is pretrained on material datasets that are related to the target task but have different data distributions, and then fine-tuned on a specific material system. This method enables the model to learn general microstructural representations from different material systems and transfer this knowledge to new material design and prediction tasks. However, it is worth noting that careful consideration is required to avoid the negative transfer, which occurs when knowledge from general datasets impacts model performance on specific alloys. Approaches such as domain adaptation techniques or selective transfer learning can mitigate this risk.

(5) Computational data and experimental data. Some researchers have improved model accuracy through multi-source data fusion. Certain studies have integrated thermodynamic data from widely used phase diagram handbooks with first-principles calculation results to construct prediction models for alloy solid-liquid phase boundary temperatures^[73]. Other researchers have incorporated process data, such as tempering temperature and cooling rate from the steel processing industry, into the input features of GNNs, achieving correlation analysis between processing parameters and material phase transformation behaviors. Verification results indicate that this approach, which fuses physics-based data with practical engineering information, yields predictions that closely match experimental data^[100].

(6) Incorporating equivariance through equivariant graph neural networks (EGNNs). EGNNs embed rotational and translational symmetry directly into their architecture, ensuring that predictions remain consistent under spatial transformations^[102,103]. This is critical for alloy design, where capturing structure-property relationships necessitates robust invariance^[104]. By distinguishing genuine compositional or bonding effects from mere orientation artifacts, EGNNs improve data-efficiency and predictive accuracy^[103]. For example, MatTen accurately predicts entire elasticity tensors across crystal classes by preserving rotational frame independence, enabling the discovery of alloys with exceptional mechanical performance^[105]. Overall, by incorporating physical symmetry constraints, EGNNs yield predictions that align more closely with underlying laws, significantly accelerating the search for high-performance alloys.

Overall, these strategies underscore the flexibility and efficacy of GNNs in alloy design. By adapting their graph representations to heterogeneous data-including images, phase-field simulations, FEM and process parameters, as illustrated in Figure 15, so that researchers can more accurately model, predict, and optimize the complex interplay of phases and properties in advanced alloy systems.

Figure 15. Different GNN data representation methods. Representative data types referenced in the literature. GNN: Graph neural network.

The role of multiscale modeling and data integration in GNNs and alloy design

After identifying the different scales/modes of graph representation, the next step is to consider how to integrate this information at the multiscale level. Multiscale modeling enables a comprehensive representation of material behavior by integrating information from different scales, such as atomic, microstructural, mesoscopic and macroscopic performance levels. In multiscale modeling, GNNs can capture the complex relationships between atomic-scale chemical bonding and macroscopic mechanical properties, offering more comprehensive and accurate predictions for alloy design. This is the key role GNNs are expected to play in alloy development.

As shown in Figure 16, GNNs fulfill distinct roles at various scales. At the atomic level, GNNs can effectively capture atomic interactions and establish mappings between atomic-level attributes and alloy-phase properties. Researchers have integrated molecular and atomic information computed using the DFT method with GNN models to predict microscopic-scale properties and study morphological evolution. At the microstructural level, GNNs can represent the distribution and evolution of grain boundaries, phase boundaries, and other microstructures, often aided by DFT calculations. At the mesoscopic level, GNNs integrate phase field data or finite element data to achieve cross-scale alloy performance prediction. At the macroscopic level, GNNs, integrating multiscale information, can predict the macroscopic mechanical properties of materials, providing guidance for practical material applications.

Figure 16. Multiscale perspective on GNNs, showing how they map atoms, grains, and entire components to graph representations and enable property prediction from the atomic to the macroscopic level. GNNs: Graph neural networks.

Nevertheless, relying solely on multiscale modeling is not sufficient to fully cover the complex information required for alloy design. Data integration therefore becomes pivotal. By merging datasets from diverse sources, GNNs can construct robust predictive models supported by broader data foundations. Such fused data not only boosts model reliability but also broadens its scope of applicability^[14]. Therefore, uniting multiscale modeling and data integration enables GNNs to efficiently realize accurate alloy designs across multiple dimensions, significantly reducing development cycles, cutting costs, and paving the way for next-generation intelligent material design.

Challenges

The scarcity of high-quality data and alloys’ multiscale complexity - especially under extreme conditions - still hinder effective GNN training. Converting alloy-specific data (e.g., microstructure, crystallography, grain boundaries, defects) into graph formats lacks standardized methods, restricting accurate representation. Predicting alloy behaviors under extreme conditions, characterized by complex, nonlinear properties, also remains challenging.

Future directions

Future research should prioritize enhanced data collection and model refinement. Data augmentation techniques, few-shot learning, and generative models can address data scarcity. Validation methods must ensure realism in synthetic data.

For unsupervised learning, clearer evaluation metrics and physically informed augmentation strategies are necessary to ensure accurate, transferable representations across alloy systems.

Customized GNN architectures for specific alloys and cross-scale modeling to link microstructures and macroscopic properties will be vital. Expanding GNN applications, integrating alloy physical properties and processing conditions, and establishing multiscale simulation frameworks will enhance predictive accuracy.

Sampling schemes, graph sparsification, and graphics processing units (GPU)/tensor processing units (TPU) acceleration have already reduced training costs by 1-2 orders of magnitude for large-scale graphs. However, the astronomically large compositional space of multi-component alloys still poses a search challenge. Another promising avenue is to leverage quantum ML to further accelerate combinatorial searches.

Standardized evaluation protocols, benchmark suites, and open repositories will support robust model assessment. Integrating GNN predictions with high-throughput experimental workflows will accelerate validation and refinement. Federated and privacy-preserving collaborative training will further strengthen datasets and foster transparent, reproducible alloy informatics.