Forecasting as Rendering: A 2D Gaussian Splatting Framework for Time Series Forecasting

arXiv:2603.02220v2 Announce Type: replace Abstract: Time series forecasting remains a challenging problem due to the intricate entanglement of intra-period fluctuations and inter-period trends. While recent advances have attempted to reshape 1D sequences into 2D period-phase representations, they suffer from two principal limitations. Firstly, treating reshaped tensors as static images results in a topological mismatch, as standard spatial operators sever chronological continuity at grid boundaries. Secondly, relying on uniform fixed-size representations allocates modeling capacity inefficiently and fails to provide the adaptive resolution required for compressible, non-stationary temporal patterns. To address these limitations, we introduce TimeGS, a novel framework that fundamentally shifts the forecasting paradigm from regression to 2D generative rendering. By reconceptualizing the future sequence as a latent 2D temporal surface, TimeGS utilizes the inherent anisotropy of Gaussian kernels to adaptively model complex variations with flexible geometric alignment. To realize this, we introduce a Multi-Basis Gaussian Kernel Generation (MB-GKG) block that synthesizes kernels from a fixed dictionary to stabilize optimization, and a Multi-Period Chronologically Continuous Rasterization (MP-CCR) block that enforces strict temporal continuity across periodic boundaries. Comprehensive experiments on standard benchmark datasets demonstrate that TimeGS attains state-of-the-art or competitive performance. The code is at https://github.com/yixinwang1/TimeGS.