SA-GAT-SR: Self-Adaptable Graph Attention Networks with Symbolic Regression for high-fidelity material property prediction

TL;DR

A novel computational paradigm—Self-Adaptable Graph Attention Networks integrated with Symbolic Regression (SA-GAT-SR)—that synergistically combines the predictive capability of GNNs with the interpretative power of symbolic regression is introduced.

Abstract

Recent advances in machine learning have demonstrated an enormous utility of deep learning approaches, particularly Graph Neural Networks (GNNs) for materials science. These methods have emerged as powerful tools for high-throughput prediction of material properties, offering a compelling enhancement and alternative to traditional first-principles calculations. While the community has predominantly focused on developing increasingly complex and universal models to enhance predictive accuracy, such approaches often lack physical interpretability and insights into materials behavior. Here, we introduce a novel computational paradigm, Self-Adaptable Graph Attention Networks integrated with Symbolic Regression (SA-GAT-SR), that synergistically combines the predictive capability of GNNs with the interpretative power of symbolic regression. Our framework employs a self-adaptable encoding algorithm that automatically identifies and adjust attention weights so as to screen critical features from an expansive 180-dimensional feature space while maintaining O(n) computational scaling. The integrated SR module subsequently distills these features into compact analytical expressions that explicitly reveal quantum-mechanically meaningful relationships, achieving 23 times acceleration compared to conventional SR implementations that heavily rely on first principle calculations-derived features as input. This work suggests a new framework in computational materials science, bridging the gap between predictive accuracy and physical interpretability, offering valuable physical insights into material behavior.

Figures (3)

• Figure 1: The SA-GAT-SR model for materials prediction.a The flowchart of SA-GAT-SR model encompasses four sequential stages: data acquisition (blue), preliminary GNN prediction (yellow), feature screening (pink), and symbolic regression (brown). The combination of GNN prediction and reserved features in the feature screening step is used as the input features of SR module. b The architecture of the GNN module. In the self-adaptable encoding (SAE) algorithm, the raw feature vector consists of scalar properties associated with atoms and unit cells from the crystal structure. The SAE assigns a weight to each characteristic and generates the initial feature vector. The blue and orange circles represent atomic and global node features, respectively. The message-passing layers include stacked node update modules, as illustrated, allowing iterative updating of feature vectors through the GNN architecture.
• Figure 2: The performance of the SA-GAT-SR model across three datasets.a Dependence of the SR derivation time on the number of input features. While keeping the dimensionality and complexity of the final expressions constant, the derivation time shows exponential growth as the number of input features increases. b The bandgap MAE performance of the SA-GAT model with different hidden feature dimensions across three datasets. c-d The performance of all methods—including SA-GAT-SR, SA-GAT, ALIGNN, CGCNN, SR, and GAT—on bandgap and formation energy prediction is evaluated. SA-GAT corresponds to the GNN module within SA-GAT-SR, while SR uses the same feature set as SA-GAT-SR but excludes the GNN-predicted output. e-g Bandgap prediction performance, comparing the SA-GAT-SR model with and without the GNN module across three datasets as the number of reserved features increases. e, f, and g present the results of our study on the $\mathrm{ABO}_3$, $\mathrm{ABX}_3$ and $\mathrm{AB(O|X)}_3$ datasets, respectively.
• Figure 3: The impact of the GNN module in both ICs Computation and formation energy prediction.a-c The ICs derived by the SAE algorithm within the GNN module, where a, b, and c correspond to the ICs results for $\mathrm{ABO}_3$, $\mathrm{ABX}_3$, and $\mathrm{AB(O|X)}_3$, respectively. For each property prediction task, the IC reflects the significance of a specific feature within its feature set. In the figures, $E_{F}$, $E_{gap}$, and $E_{T}$ denote formation energy, bandgap, and total energy, respectively, for convenience. d-f Comparison of the GNN model with different three feature embedding algorithms in formation energy prediction on the $\mathrm{AB(O|X)}_3$ dataset. The blue diamonds and red dots represent the results on the training set and testing set, respectively. The GNN model with the fully connected network (FCN) embedding algorithm serves as a baseline, reflecting standard performance. The model with the CGCNN embedding algorithm utilizes one-hot encoding followed by the FCN to generate feature vectors.