Generative geospatial modelling with geometric algebra

Area of Science:

• Geospatial Science
• Computational Mathematics
• Artificial Intelligence

Background:

• Generative geospatial modelling (GGM) faces challenges integrating data-driven and knowledge-driven methods due to mathematical incompatibilities.
• Existing frameworks often struggle to fuse heterogeneous data sources and diverse domain knowledge effectively.

Purpose of the Study:

• To propose a novel geometric algebra (GA)-based framework for unifying data-driven and knowledge-driven approaches in GGM.
• To develop a cohesive mathematical perspective for interpretable and constraint-aware GGM.
• To demonstrate the framework's versatility through diverse case studies.

Main Methods:

• Development of a GA-based framework utilizing a unified multi-vector representation.
• Implementation of a task-adaptable, five-stage cycle: representation, reasoning, generation, synthesis, and computation.
• Application and illustration through three case studies: trajectory reconstruction, typhoon intensity prediction, and LLM-based GA code generation.

Main Results:

• Successful fusion of heterogeneous data and diverse knowledge using the unified multi-vector representation.
• Demonstration of structured reasoning and hypothesis generation capabilities.
• Validation of the framework's effectiveness across different GGM applications and implementation levels.

Conclusions:

• The proposed GA-based framework offers a cohesive mathematical solution for integrating disparate approaches in GGM.
• This work provides a conceptual and methodological advancement for interpretable and constraint-aware generative geospatial modelling.
• The framework facilitates enhanced reasoning and hypothesis generation, paving the way for more robust GGM applications.