Taming the Century: A Theoretical Framework for Long-Term Uncertainty Quantification in Hybrid AI-Physics Climate Models

Background: Hybrid artificial intelligence-physics (AI-physics) climate models promise transformative advances in computational efficiency and predictive accuracy, yet their ability to maintain stable, physically consistent projections over century-long timescales—essential for climate adaptation planning—remains fundamentally unproven. While deep learning models achieve remarkable short-term forecasting skill, error accumulation through chaotic dynamics, conservation law violations, and feedback instabilities has historically limited stable integration to weeks or months.

Objective: This paper develops a unified theoretical framework for understanding and ensuring long-term uncertainty evolution in hybrid climate models, addressing the critical gap between current decade-long stability achievements and century-scale requirements for policy-relevant climate projections.

Methods: We synthesize dynamical systems theory, conservation law mathematics, chaos theory, and recent empirical breakthroughs to construct four interconnected theoretical frameworks: (1) Conservation-Stability Theory, (2) Attractor Manifold Stability, (3) Lyapunov-Based Error Decomposition, and (4) Data Assimilation for Extended Integration. We formalize the Conservation-Stability Theorem establishing sufficient conditions for indefinite stability and analyze the CondensNet breakthrough achieving decade-long stable simulations through targeted physical constraints.

Results: We prove that architectural enforcement of energy, mass, and momentum conservation laws guarantees bounded error growth, preventing exponential instability. The proposed unified uncertainty decomposition U(t) = U_chaos(t) + U_model(t) + U_constraint(t) + U_feedback(t) distinguishes irreducible chaotic error from model-induced error, enabling targeted mitigation strategies. Empirical validation through CondensNet demonstrates decade-long stability via adaptive condensation constraints, representing a 50-100× improvement over unconstrained networks.

Conclusions: Century-scale climate AI stability is theoretically achievable through systematic application of physics-informed architectural constraints, attractor manifold enforcement, and ensemble-based uncertainty quantification. We provide a 10-year roadmap (2026-2035) progressing from consolidated decade-long stability to operational century-scale probabilistic climate projections, with strategic recommendations for researchers, model developers, and policymakers.