🤖 AI Summary
This work addresses the challenges of time series forecasting under test-time distribution shifts, where sparse or noisy observation prefixes lead to weak identifiability, error accumulation, and unstable long-term correction. To this end, it formulates test-time adaptation for the first time as a Dirichlet boundary value problem on a temporal manifold. By treating known prefix errors as boundary conditions, the approach combines a local solver for error propagation with a global solver that retrieves cross-window error memory, and introduces Spatio-Temporal Manifold Fusion (SMF) to generate a smooth, bounded correction field. Evaluated across six benchmark datasets and four frozen backbones, the method achieves an average 26.82% relative reduction in MSE over standard baselines and improves upon the strongest baseline by 12.77%, demonstrating remarkable robustness under sparse and corrupted prefix conditions.
📝 Abstract
Test-Time Adaptation (TTA) aims to improve time series forecasting under distribution shifts by using limited observations revealed during inference. However, forecasting TTA must operate in a source-free online setting, where the adaptation signal is short, temporally correlated, and potentially noisy. Existing methods can therefore suffer from weak identifiability, error accumulation, and unstable long-horizon corrections when the revealed prefix is sparse or contaminated. To address these issues, we propose STEPS, a Smooth Temporal Error Propagation Solver for TTA in time-series forecasting. STEPS reformulates forecasting TTA as a Dirichlet Boundary Value Problem on a temporal manifold, where the revealed prefix error serves as the boundary condition for the unknown future error field. Then, STEPS solves a smooth and bounded correction field in prediction space: a Local Solver propagates prefix errors under temporal smoothness, a Global Solver retrieves stable cross-window error memory and Spatiotemporal Manifold Fusion (SMF) integrates both solutions into the final correction. Across six standard benchmarks and four frozen backbones, STEPS achieves an average relative MSE reduction of 26.82% over the zero-shot backbone, exceeding the strongest compared TTA baseline by 12.77%. Additional sparse prefix and contamination tests confirm the robustness of STEPS under limited and noisy prefixes.