Residual-Guided Multi-Resolution Refinement of Foundation Models: A Case Study in Drought Forecasting

Large \emph{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: \textbf{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 \textbf{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.

Accurate regional weather prediction requires resolving fine-scale structure while remaining consistent with global dynamics. Traditional limited area models rely on computationally expensive simulations, while many learning-based approaches frame the problem as super-resolution, overlooking statistical and physical mismatches across scales. We propose a foundation-model-driven downscaling framework that learns regional refinements of global forecasts by augmenting a pretrained weather model backbone with lightweight, multi-scale prediction heads operating directly in its latent space. Despite being trained on substantially coarser inputs, the pretrained backbone supports regional adaptation at resolutions corresponding to a two-order-of-magnitude increase in grid-cell resolution, without the need for retraining. The proposed approach uses regional numerical simulations as training targets and is evaluated not only against gridded datasets but also against ground-based weather station observations, enabling analysis of systematic biases between global reanalysis, regional simulations, and in-situ weather station observations. Our experiments show improved accuracy in comparison to NWP on most of the metrics at the fraction of computational cost. Moreover, we observe that building on a latent space of globally pre-trained weather foundation model offers better downscaling capabilities than the standard image-based super-resolution approaches.

Time-series foundation models can forecast across heterogeneous domains without task-specific training, but their forecasts are fixed once produced and cannot directly incorporate task-specific expert feedback. We study expert-guided forecast editing: a frozen foundation model generates candidate future trajectories, and an expensive expert evaluator scores them to guide forecast revision. Under a tight query budget, two natural strategies sit at opposite ends: best-of-$N$ purely exploits the foundation model's predictive distribution, while optimization approaches mostly explore the forecast horizon as an unstructured high-dimensional vector. Each extreme is individually sub-optimal. We introduce \textbf{DEFT}, an expert-guided forecast editing framework that balances the two by first exploiting the foundation model's predictive samples in a decomposed trend--seasonal space, then exploring around them via component-wise refinement. DEFT queries the expert only on complete trajectories, then reuses scores for the trend and seasonal components that appeared in the queried recombinations. This lets each expert query provide structured component-level feedback while keeping the foundation model frozen. We compare DEFT against direct search approaches, including best-of-$N$, cross-entropy methods, and Bayesian optimization, under matched expert-query budgets. Across two forecasting benchmarks consisting of 78 datasets, three time-series foundation models, four feedback types, and seven query budgets, DEFT consistently improves the effectiveness of expert guidance. A molecular-dynamics case study further suggests that the same principle extends to more physically grounded feedback, supporting the hypothesis that sparse test-time guidance should be spent balancing prior exploitation with structured exploration.