Generative geospatial modelling with geometric algebra.

The integration of data-driven and knowledge-driven approaches in generative geospatial modelling (GGM) is often hindered by their mathematical incompatibilities. Here, we propose a geometric algebra (GA)-based framework that employs a unified multi-vector representation to fuse heterogeneous data and diverse knowledge. The framework facilitates structured reasoning and hypothesis generation through a task-adaptable, five-stage cycle: representation, reasoning, generation, synthesis and computation. We illustrate this design through three case studies covering constrained trajectory reconstruction, typhoon intensity prediction and large language model-based GA code generation, which instantiate different components and implementation levels of the proposed framework. By offering a cohesive mathematical perspective, our work provides a conceptual and methodological framework for interpretable and constraint-aware GGM. This article is part of the theme issue 'Modern applications of geometric algebra'.