Lightweight Physics-Informed KAN: An Efficient Edge Intelligence Framework for Spatio-Temporal Traffic Forecasting

Abstract

Traffic forecasting on IoT edges faces strict computational limits and unreliable sensor data. We propose a Lightweight Physics-Informed Kolmogorov-Arnold Network (PI-KAN) for efficient spatio-temporal forecasting. PI-KAN embeds the kinematic wave partial differential equation (PDE) into a graph-based KAN, utilizing B-splines for efficient feature extraction while strictly enforcing macroscopic physical laws. Native evaluations on a resource-constrained x86 edge node (acting as an industrial RSU surrogate) using the METR-LA and PEMS-BAY datasets demonstrate that PI-KAN achieves highly competitive accuracy. Crucially, it attains significant parameter reductions compared to standard recurrent architectures, maintaining ultra-low real-time inference latency (under 1.0 ms). Furthermore, multi-run statistical evaluations reveal that PDE regularization actively tightens prediction variance under severe data loss (up to 40%) and acts as a strict physical boundary on unseen test data. By establishing a direct positive correlation between physical violations and prediction errors, PI-KAN proves that bounding physical residuals fundamentally restricts the upper bound of forecasting errors. Consequently, PI-KAN provides a reliable, physically consistent, and ultra-lightweight intelligence solution for real-time vehicular edge computing.