P1-KAN: an effective Kolmogorov-Arnold network with application to hydraulic valley optimization
For researchers in function approximation and engineering optimization, this work offers a more effective KAN variant for irregular functions, though improvements over existing KANs are incremental.
The paper proposes P1-KAN, a new Kolmogorov-Arnold network for approximating high-dimensional irregular functions, providing error bounds and universal approximation theorems. It outperforms MLPs and other KAN variants in accuracy and convergence speed, achieving similar accuracy to spline-based KAN on smooth functions, and demonstrates effectiveness in a hydraulic valley optimization task.
A new Kolmogorov-Arnold network (KAN) is proposed to approximate potentially irregular functions in high dimensions. We provide error bounds for this approximation, assuming that the Kolmogorov-Arnold expansion functions are sufficiently smooth. When the function is only continuous, we also provide universal approximation theorems. We show that it outperforms multilayer perceptrons in terms of accuracy and convergence speed. We also compare it with several proposed KAN networks: it outperforms all networks for irregular functions and achieves similar accuracy to the original spline-based KAN network for smooth functions. Finally, we compare some of the KAN networks in optimizing a French hydraulic valley.