KAN-Matrix: Visualizing Nonlinear Pairwise and Multivariate Contributions for Physical Insight

Abstract: Interpreting complex datasets remains a major challenge for scientists, particularly due to high dimensionality and collinearity among variables. We introduce a novel application of Kolmogorov-Arnold Networks (KANs) to enhance interpretability and parsimony beyond what traditional correlation analyses offer. We present two interpretable, color-coded visualization tools: the Pairwise KAN Matrix (PKAN) and the Multivariate KAN Contribution Matrix (MKAN). PKAN characterizes nonlinear associations between pairs of variables, while MKAN serves as a nonlinear feature-ranking tool that quantifies the relative contributions of inputs in predicting a target variable. These tools support pre-processing (e.g., feature selection, redundancy analysis) and post-processing (e.g., model explanation, physical insights) in model development workflows. Through experimental comparisons, we demonstrate that PKAN and MKAN yield more robust and informative results than Pearson Correlation and Mutual Information. By capturing the strength and functional forms of relationships, these matrices facilitate the discovery of hidden physical patterns and promote domain-informed model development.