In this project, we investigate test‑time adaptation (TTA) of vision‑language models (VLMs) for remote sensing applications. VLMs such as CLIP exhibit strong zero‑shot generalization, but their performance often degrades on remote sensing imagery due to substantial domain shifts—including differences in sensors, spatial resolution, spectral bands, and seasonal variations. TTA provides a promising pathway by allowing the model to adapt during inference using only unlabeled test data, without requiring retraining. Prior approaches, such as test‑time prompt tuning and cache‑based methods, have shown effectiveness on zero‑shot tasks in general computer vision. However, remote sensing datasets typically present larger distribution shifts than standard vision benchmarks, making adaptation more difficult. Nonetheless, building on recent advances, we consider this challenge tractable. Our work will focus on designing efficient and robust TTA algorithms tailored to remote sensing, and on developing theoretical foundations from a computational mathematics perspective, grounded in insights drawn from numerical experiments.