PIPE: Physics-Informed Position Encoding for Alignment of Satellite Images and Time Series

Abstract: Multimodal time series forecasting is foundational in various fields, such as utilizing satellite imagery and numerical data for predicting typhoons in climate science. However, existing multimodal approaches primarily focus on utilizing text data to help time series forecasting, leaving the visual data in existing time series datasets untouched. Furthermore, it is challenging for models to effectively capture the physical information embedded in visual data, such as satellite imagery's temporal and geospatial context, which extends beyond images themselves. To address this gap, we propose physics-informed positional encoding (PIPE), a lightweight method that embeds physical information into vision LLMs (VLMs). PIPE introduces two key innovations: (1) a physics-informed positional indexing scheme for mapping physics to positional IDs, and (2) a variant-frequency positional encoding mechanism for encoding frequency information of physical variables and sequential order of tokens within the embedding space. By preserving both the physical information and sequential order information, PIPE significantly improves multimodal alignment and forecasting accuracy. Through the experiments on the most representative and the largest open-sourced satellite image dataset, PIPE achieves state-of-the-art performance in both deep learning forecasting and climate domain methods, demonstrating superiority across benchmarks, including a 12% improvement in typhoon intensity forecasting over prior works. Our code is provided in the supplementary material.