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Physics-guided machine learning (PGML) has become a prevalent approach in studying scientific systems due to its ability to integrate scientific theories for enhancing machine learning (ML) models. However, most PGML approaches are tailored to isolated and relatively simple tasks, which lim- its their applicability to complex systems involving multiple interacting processes and numerous influencing features. In this paper, we propose a Physics-Guided Foundation Model (PGFM) that combines pre-trained ML models and physics- based models and leverages their complementary strengths to improve the modeling of multiple coupled processes. To effectively conduct pre-training, we construct a simulated en- vironmental system that encompasses a wide range of influ- encing features and various simulated variables generated by physics-based models. The model is pre-trained in this sys- tem to adaptively select important feature interactions guided by multi-task objectives. We then fine-tune the model for each specific task using true observations, while maintaining con- sistency with established physical theories, such as the prin- ciples of mass and energy conservation. We demonstrate the effectiveness of this methodology in modeling water temper- ature and dissolved oxygen dynamics in real-world lakes. The proposed PGFM is also broadly applicable to a range of sci- entific fields where physics-based models are being used. 

Human-generated Spatial-Temporal Data (HSTD), represented as trajectory sequences, has undergone a data revolution, thanks to advances in mobile sensing, data mining, and AI. Previous studies have revealed the effectiveness of employing attention mechanisms to analyze massive HSTD. However, traditional attention models face challenges when managing lengthy and noisy trajectories as their computation comes with large memory overheads. Furthermore, attention scores within HSTD trajectories are sparse (i.e., most of the scores are zeros), and clustered with varying lengths (i.e., consecutive tokens clustered with similar scores). To address these challenges, we introduce an innovative strategy named Memory-efficient Trajectory Attention (MeTA). We leverage complicated spatial-temporal features (e.g., traffic speed, proximity to PoIs) and design an innovative feature-based trajectory partition technique to shrink trajectory length. Additionally, we present a learnable dynamic sorting mechanism, with which attention is only computed between sub-trajectories that have prominent correlations. Empirical validations using real-world HSTD demonstrate that our approach not only yields competitive results but also significantly lowers memory usage compared with state-of-the-art methods. Our approach presents innovative solutions for memory-efficient trajectory attention, offering valuable insights for handling HSTD efficiently. 

Abstract At the end of its mission, the MESSENGER spacecraft's orbit intersected Mercury's nightside magnetic equator at low altitudes below 420 km, enabling the first in situ observations of this region, where the magnetic field strength is typically sub‐dipolar. We present 5 events from these orbits where MESSENGER encountered Earth‐like dipolarization regions characterized by enhanced field strengths up to 20 nT above the intrinsic planetary field, and an average decrease and increase in plasma proton density and temperature, respectively, for 1–2 min periods, comparable to Hermean substorm timescales. The events span local times of 1.5 hr pre‐ and post‐midnight, and are present from the magnetic equator up to magnetic latitudes of at least north. Supported by estimates of decreased flux tube entropy during these events, we suggest these dipolarization regions are formed by the pileup of dipolarization fronts and formation of a substorm current wedge.