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

TL;DR

This work introduces TimeGS, a novel framework that fundamentally shifts the forecasting paradigm from regression to 2D generative rendering, and utilizes the inherent anisotropy of Gaussian kernels to adaptively model complex variations with flexible geometric alignment.

Abstract

Time series forecasting (TSF) remains a challenging problem due to the intricate entanglement of intraperiod-fluctuations and interperiod-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 continuous latent 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 performance.

Figures (11)

• Figure 1: Comparison of 2D Period–based modeling. (a) TimesNet wu2022timesnet and (b) PDF pdf may can break temporal adjacency at row boundaries by using grid-based 2D operators. By contrast, (c) our TimeGS can avoid boundary artifacts by leveraging anisotropic Gaussians and continuous rendering to adapt to information density. (X: period index, Y: phase within a period, Z: value).
• Figure 2: The architecture of TimeGS. (a) Overall Structure: The model processes time series through a generative rendering paradigm. (b) Channel-Adaptive Aggregation: Fuses the rendered outputs from different branches using a channel-wise adaptive weighting mechanism to ensure robust multivariate forecasting. (c) 2D Variation Feature Extraction: Extracts 2D variation features using UNet-based encoder on reshaped temporal tensors. (d) Multi-Basis Gaussian Kernel Generation: Generates composite Gaussian kernels by predicting intensities and weights for the Gaussian Basis Bank.
• Figure 3: Illustration of the chronologic discontinuity problem caused by topological mismatch and our proposed Chronologically Continuous Rasterization.
• Figure 4: Analysis on the number of branches ($K$) and the number of components ($P$) on the ETTh1 dataset.
• Figure 5: Analysis on the look back window ($I$) on the ETTh1 and the Weather dataset.