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.
| Comments: | 15 pages, 4 figures |
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2604.23474 [cs.LG] |
| (or arXiv:2604.23474v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2604.23474 arXiv-issued DOI via DataCite (pending registration) |
From: Zongru Li [view email]
[v1]
Sat, 25 Apr 2026 23:54:41 UTC (1,005 KB)
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