GeoCert: Certified Geometric AI for Reliable Forecasting

TL;DR

GeoCert is a unified geometric AI framework that enhances forecasting accuracy, physical consistency, and formal verification, enabling scalable and trustworthy scientific AI across various domains.

Contribution

It introduces a novel differentiable geometric approach that integrates forecasting, physical reasoning, and formal verification in a single model.

Findings

Achieves state-of-the-art accuracy in forecasting tasks.

Reduces computational cost by 97.5%.

Maintains superior certification rates across domains.

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.