Minrui Cao

Title: FunKAN: Interpretable Kolmogorov–Arnold Networks for Learning
Date: Wednesday, August 26th
Time: 9am
Location: Zoom
Supervised by: Jiguo Cao

Abstract: Learning nonlinear mappings between functional inputs and functional outputs is a fundamental problem in functional data analysis, particularly when functional observations are noisy, sparsely or irregularly sampled, and related through complex nonlinear mechanisms. In this work, we propose FunKAN, an interpretable neural framework based on Kolmogorov–Arnold networks for nonlinear functional learning. FunKAN organizes functional prediction into a unified framework consisting of functional representation, nonlinear mapping, function reconstruction, and structural regularization, allowing functional information to be preserved throughout the learning process while maintaining model flexibility and interpretability. The framework further incorporates adaptive spline refinement and attribution-guided pruning to improve approximation accuracy, model sparsity, and computational efficiency within a common architecture. It naturally accommodates dense, sparse, and irregular functional observations, and smoothness regularization can be incorporated to preserve the structural properties of predicted functions. Extensive simulation studies and real-data applications demonstrate that FunKAN consistently outperforms conventional functional regression models and multilayer perceptrons under nonlinear functional relationships while remaining competitive in simpler settings. These results establish FunKAN as a flexible and interpretable methodology for learning nonlinear mappings between functional inputs and functional outputs.