Uncertainty-Aware Test-Time Adaptation for Cross-Region Spatio-Temporal Fusion of Land Surface Temperature

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.

Test-Time Domain Adaptation (TTDA) aims to adapt Deep Neural Networks to distribution shifts using only streaming, unlabeled test data in real time. Current methods for semantic segmentation tasks suffer from critical limitations. Entropy minimization techniques require costly backpropagation, risking catastrophic forgetting and producing noisy segmentation boundaries. Memory-bank methods, while backpropagation-free, exhibit slow adaptation, requiring numerous samples to converge and struggle to handle continuous domain shifts. We introduce TestMate, a novel, real-time, and backpropagation-free TTDA framework that overcomes these issues. TestMate leverages generalization capability of a lightweight Visual Foundation Model to guide the adaptation. We use a zero-shot instance segmentation YOLOv8-seg based model to generate unlabeled mask proposals for objects and their parts at multiple scales in real time. These proposals are fused with the primary model via a heuristic, size-ordered competitive scheme, where small, high-confidence regions dominate and refine predictions in surrounding larger, less certain areas. This paremeter-free mechanism enables immediate adaptation from the first frame, inherently avoids catastrophic forgetting and effectively preserves fine object details and boundaries, even for small objects. TestMate can be used as a standalone, efficient refinement module or seamlessly integrated into existing TTDA methods to significantly boost their performance. We demonstrate state-of-the-art results across two benchmark datasets, proving TestMate's effectiveness in three distinct adaptation tasks: TTDA, Source-Free Domain Adaptation (SFDA), and online-TTDA. Code is available.

Large Time Series Foundation Models (TSFMs) demonstrate strong zero-shot forecasting capabilities across diverse domains. However, their application to regional climate forecasting faces practical challenges: model weights are often proprietary, local training records are limited, and computational budgets are constrained, making traditional fine-tuning approaches infeasible. To address these constraints, we introduce a lightweight, black-box adaptation framework (requiring no access to backbone parameters and no backbone fine-tuning) that enhances frozen TSFMs at inference time through two plug-and-play wrappers: SMR\textsuperscript{2} (Stationarity aware multi-resolution Residual), which decomposes the input into multi-resolution temporal views, learns stride specific residual corrections that capture regional dynamics, then adaptively ensembles them into a single forecast, and MBB (Moving Block Bootstrap), which preserves temporal dependencies through block resampling and ensembles over temporally coherent residual perturbations to stabilize the point forecast. Both wrappers instantiate the same bagging style principle: they build diverse views of the input or its residuals, forecast each with the same frozen backbone, and aggregate, so all adaptation comes from inference time ensembling rather than any weight update. Evaluated on one month ahead Standardized Precipitation Evapotranspiration Index (SPEI) prediction across multiple sites in South Australia, our framework consistently improves forecasting performance across several backbone models, demonstrating up to 26% mean squared error (MSE) reduction over the corresponding frozen backbone while enabling practical deployment in resource constrained regional forecasting systems.