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Encoding geospatial objects is fundamental for geospatial artificial intelligence (GeoAI) applications, which leverage machine learning (ML) models to analyze spatial information. Common approaches transform each object into known formats, like image and text, for compatibility with ML models. However, this process often discards crucial spatial information, such as the object’s position relative to the entire space, reducing downstream task effectiveness. Alternative encoding methods that preserve some spatial properties are often devised for specific data objects (e.g., point encoders), making them unsuitable for tasks that involve different data types (i.e., points, polylines, and polygons). To this end, we propose POLY2VEC, a polymorphic Fourier-based encoding approach that unifies the representation of geospatial objects, while preserving the essential spatial properties. POLY2VEC incorporates a learned fusion module that adaptively integrates the magnitude and phase of the Fourier transform for different tasks and geometries. We evaluate POLY2VEC on five diverse tasks, organized into two categories. The first empirically demonstrates that POLY2VEC consistently outperforms objectspecific baselines in preserving three key spatial relationships: topology, direction, and distance. The second shows that integrating POLY2VEC into a state-of-the-art GeoAI workflow improves the performance in two popular tasks: population prediction and land use inference. 

Human mobility modeling from GPS-trajectories and synthetic trajectory generation are crucial for various applications, such as urban planning, disaster management and epidemiology. Both of these tasks often require filling gaps in a partially specified sequence of visits, – a new problem that we call “controlled” synthetic trajectory generation. Existing methods for next-location prediction or synthetic trajectory generation cannot solve this problem as they lack the mechanisms needed to constrain the generated sequences of visits. Moreover, existing approaches (1) frequently treat space and time as independent factors, an assumption that fails to hold true in real-world scenarios, and (2) suffer from challenges in accuracy of temporal prediction as they fail to deal with mixed distributions and the inter-relationships of different modes with latent variables (e.g., day-of-the-week). These limitations become even more pronounced when the task involves filling gaps within sequences instead of solely predicting the next visit. We introduce TrajGPT, a transformer-based, multi-task, joint spatiotemporal generative model to address these issues. Taking inspiration from large language models, TrajGPT poses the problem of controlled trajectory generation as that of text infilling in natural language. TrajGPT integrates the spatial and temporal models in a transformer architecture through a Bayesian probability model that ensures that the gaps in a visit sequence are filled in a spatiotemporally consistent manner. Our experiments on public and private datasets demonstrate that TrajGPT not only excels in controlled synthetic visit generation but also outperforms competing models in next-location prediction tasks–Relatively, TrajGPT achieves a 26-fold improvement in temporal accuracy while retaining more than 98% of spatial accuracy on average.