GeoCert: Certified Geometric AI for Reliable Forecasting

Abstract

Forecasting systems in science must be accurate, physically consistent, and certifiably reliable. Most existing models address prediction, constraint enforcement, and verification separately, limiting scalability and interpretability. We introduce GeoCert, a geometric AI framework that unifies forecasting, physical reasoning, and formal verification within a single differentiable computation. GeoCert formulates forecasting as evolution along a hyperbolic manifold, where negative curvature induces contraction dynamics, intrinsic robustness, and logarithmic-time certification. A hierarchical constraint architecture separates universal physical laws from domain-specific dynamics, enabling certified generalization across energy, climate, finance, and transportation systems. GeoCert achieves state-of-the-art accuracy while reducing computational cost by 97.5% and maintaining better certification rates. By embedding verification into the geometry of learning, GeoCert transforms forecasting from empirical approximation to formally verified inference, offering a scalable foundation for trustworthy, reproducible, and physically grounded scientific AI.