Material intelligent visualization design via two-dimensional symbolic feature generation

Machine learning for complex materials problems suffers from high-dimensionality data, while traditional “black-box” dimensionality reduction techniques typically lack the capability to balance predictive accuracy with visualization and interpretability. This work presents a novel method named Two-Dimensional Symbolic Feature Generation, based on symbolic regression and genetic algorithms. This approach facilitates machine learning by providing quantifiable interpretability and enabling visualization-driven materials design. Evaluated across diverse classification and regression tasks in materials science, the proposed method demonstrates notable success in three critical aspects: First, it significantly improved the predictive accuracy. Specifically, classification accuracy for ferroelectric perovskites and high-entropy alloy phases improved from 85.6% and 84.5% to 94.2% and 88.4%, respectively. Correspondingly, prediction errors for shape memory alloys and copper alloys were reduced from 2.9 K, 5.9% and 9.7% to 1.1 K, 3.7% and 6.2%. Second, the method ensures interpretability by constructing explicit mathematical expressions that transform the original high-dimensional features into two new symbolic ones, avoiding opaque spatial transformations. Third, it enables model visualization through two-dimensional contour maps that relate the constructed features to the target property, thereby offering intuitive insight into feature-property relationships. Leveraging these “design roadmaps,” a refractory high-entropy alloy with a single-phase solid solution and a precipitation-strengthened copper alloy with an optimized property trade-off were successfully designed. The two-dimensional symbolic feature generation framework thus addresses key limitations in accuracy, interpretability, and visualization within materials informatics, establishing a new paradigm for transparent and visual materials design.