Physics-Informed Kolmogorov-Arnold Networks for Power System Dynamics

TL;DR

This paper addresses the challenge of accurately learning power-system dynamics with limited labeled data by introducing physics-informed Kolmogorov-Arnold Networks (PIKANs). By integrating KANs, which use edge-activated splines inspired by the Kolmogorov-Arnold representation, with PINN concepts, PIKANs efficiently approximate swing-equation-based DAEs and enable parameter identification. The authors demonstrate that PIKANs achieve higher accuracy with substantially fewer parameters than traditional MLP-based PINNs on SMIB and a 4-bus, 2-generator system, including precise inertia and damping estimation from trajectory data. The work suggests significant practical potential for fast, data-efficient grid dynamic modeling and uncertainty quantification, with avenues for further speedups and interpretability enhancements.

Abstract

This paper presents, for the first time, a framework for Kolmogorov-Arnold Networks (KANs) in power system applications. Inspired by the recently proposed KAN architecture, this paper proposes physics-informed Kolmogorov-Arnold Networks (PIKANs), a novel KAN-based physics-informed neural network (PINN) tailored to efficiently and accurately learn dynamics within power systems. The PIKANs present a promising alternative to conventional Multi-Layer Perceptrons (MLPs) based PINNs, achieving superior accuracy in predicting power system dynamics while employing a smaller network size. Simulation results on a single-machine infinite bus system and a 4-bus 2- generator system underscore the accuracy of the PIKANs in predicting rotor angle and frequency with fewer learnable parameters than conventional PINNs. Furthermore, the simulation results demonstrate PIKANs capability to accurately identify uncertain inertia and damping coefficients. This work opens up a range of opportunities for the application of KANs in power systems, enabling efficient determination of grid dynamics and precise parameter identification.

Figures (12)

• Figure 1: Illustration of a 3-layer KAN having a shape of $[2, 3, 3, 1]$.
• Figure 2: General structure of a PINN misyris2020physicsraissi2017physics: it predicts the output $\textbf{u}(t, \textbf{x})$ given inputs $\textbf{x}$ and $t$.
• Figure 3: Physics-Informed Kolmogorov-Arnold Network (PIKAN) for power system dynamics.
• Figure 4: Testing systems: (a) SMIB power system, (b) 4-bus system with two generator.
• Figure 5: Training convergence process of the PIKAN-I algorithm for capturing SMIB system frequency dynamics. The LBFGS optimizer was employed, with parameter maximum iteration set to 20. Thus, each optimization step in the figure contains 20 iterations.