GeoCert: Certified Geometric AI for Reliable Forecasting

2026-04-25

AI Summary

Existing scientific prediction methods struggle to simultaneously achieve high accuracy, physical consistency, and verifiable reliability, often facing a trade-off between scalability and interpretability. This work proposes GeoCert, a geometric AI framework that formulates prediction as an evolutionary process on hyperbolic manifolds, leveraging negative curvature–induced contractive dynamics to unify forecasting, physical reasoning, and formal verification within a single differentiable architecture. By innovatively embedding formal verification into the learned geometric structure and hierarchically separating universal physical laws from domain-specific dynamics through constrained layers, GeoCert enables certifiably generalizable predictions across diverse domains. Evaluated on energy, climate, finance, and transportation systems, GeoCert attains state-of-the-art accuracy with a 97.5% reduction in computational cost and substantially improved certification success rates, advancing scientific AI toward a paradigm of verifiable reasoning.

Technology Category

• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Machine Learning: Calibration & Uncertainty Quantification
• Humans and AI: Human-Aware Planning and Behavior Prediction

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Search and Retrieval-Augmented AI: Vertical and domain-specific search

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.

Problem

• forecasting
• physical consistency
• formal verification
• reliability
• scalability

Innovation

• geometric AI
• hyperbolic manifold
• formal verification
• differentiable forecasting
• certifiable robustness