用几何方法统一预测与验证，让科学预测更可靠且高效
GeoCert: Certified Geometric AI for Reliable Forecasting
- 将预测建模为双曲流形上的演化过程，利用负曲率实现内在鲁棒性
- 在多个领域达到顶尖精度，计算成本降低97.5%，认证成功率更高
- 适合需要可验证、物理一致性的科研与工程场景
科学领域的预测系统必须准确、符合物理规律且可认证可靠。现有模型通常分别处理预测、约束强制和验证，限制了可扩展性和可解释性。我们提出GeoCert，一种统一预测、物理推理与形式化验证的几何人工智能框架。该框架将预测建模为双曲流形上的演化过程，负曲率带来收缩动力学、内在鲁棒性及对数时间认证。分层约束架构将通用物理定律与特定领域动态分离，实现跨能源、气候、金融和交通系统的可认证泛化。GeoCert在保持更高认证率的同时，达到当前最优预测精度，并将计算成本降低97.5%。通过将验证嵌入学习的几何结构，该框架将预测从经验近似转变为形式化验证推断，为可信、可复现、物理基础坚实的科学人工智能提供可扩展范式。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。