POD-KAN-NO: a physically interpretable neural operator

Yanyu Ke

Keywords: Proper Orthogonal Decomposition, Kol- mogorov–Arnold Networks, neural operator, interpretability

Abstract: POD-KAN-NO is a novel neural operator framework that combines the interpretability of modal decomposition with the expressive power of modern neural networks. By integrating Proper Orthogonal Decomposition (POD) with Kolmogorov–Arnold Networks (KAN), our method facilitates transparent and physically interpretable spatial reconstruction, while preserving strong nonlinear representation capabilities. Compared to traditional empirical models and black-box neural operators, POD-KAN-NO offers a promising balance between interpretability and accuracy. Preliminary results show promising performance in tasks such as spatial reconstruction, highlighting the framework’s capacity to integrate interpretability with nonlinear modeling flexibility.

Submission Number: 66