TC-KAN: Time-Conditioned Kolmogorov–Arnold Networks with Time-Dependent Activations for Long-Term Time Series Forecasting

Long-term time series forecasting (LTSF) is critical for modern power systems, energy management, and grid planning. Yet virtually all existing forecasting models employ stationary activation functions that apply identical nonlinear mappings regardless of temporal context-a fundamental mismatch with real-world load data, which exhibits strongly regime-dependent dynamics such as summer demand peaks, winter heating patterns, and overnight low-load periods. We address this gap by proposing TC-KAN (Time-Conditioned Kolmogorov-Arnold Network), the first forecasting architecture to augment KAN activation functions with position-aware coefficient parameterisation. The core innovation replaces the static polynomial coefficients in standard KAN activations with position-conditioned coefficients produced by a lightweight positional-embedding MLP, providing additional learnable capacity beyond standard KAN while adding negligible parameter overhead. TC-KAN further integrates a dual-pathway processing block-combining depthwise convolution for local temporal pattern extraction with the time-conditioned KAN layer for enhanced nonlinear transformation-within a channel-independent framework with Reversible Instance Normalisation. Experiments were conducted on four standard ETT benchmark datasets and the high-dimensional Weather dataset. TC-KAN achieves superior or competitive accuracy in most configurations while requiring merely 51K parameters-approximately 40% of DLinear and ∼100× fewer than iTransformer. On ETTh2, TC-KAN reduces the mean squared error by up to 61.4% over DLinear, and matches the current state-of-the-art iTransformer on ETTm2 at a fraction of the computational cost. This extreme parameter reduction circumvents the steep memory bottlenecks endemic to massive Transformer models, positioning TC-KAN as a highly practical architecture tailored precisely for resource-constrained edge deployments-such as on-device load forecasting inside smart grid sensors and industrial IoT controllers.