CondensNet: Self-adaptive physical constraints for stable long-term hybrid climate simulations

Accurate and efficient climate simulations are crucial for understanding Earth’s evolving climate. However, current General Circulation Models (GCMs) face challenges in capturing unresolved physical processes, such as cloud and convection. A common solution is to adopt Cloud-Resolving Models (CRMs), which provide more accurate results than the standard subgrid parameterization schemes typically used in GCMs. However, CRMs (also referred to as super-parameterizations, such as SPCAM) remain computationally prohibitive. Hybrid modeling, which integrates deep learning with equation-based GCMs, offers a promising alternative but often struggles with long-term stability and accuracy issues. In this work, we find that water vapor oversaturation during condensation is a key factor compromising the stability of hybrid modeling. To address this, we introduce CondensNet, a novel neural network architecture that embeds a self-adaptive physical constraint to correct unphysical condensation processes. CondensNet effectively mitigates water vapor oversaturation, enhancing simulation stability while maintaining accuracy and improving computational efficiency compared to super-parameterization schemes. We integrate CondensNet into a GCM to form PCNN-GCM (Physics-Constrained Neural Network GCM), a hybrid deep learning framework designed for long-term stable climate simulations under real-world conditions (AMIP setting). PCNN-GCM enables stable simulations over decades and achieves up to 370× speed-up compared with SPCAM, while also being faster than traditional CAM5 under GPU acceleration or CPU-only. Beyond stability and efficiency, PCNN-GCM demonstrates greater skill in capturing complex climate variability than CAM5, including tropical precipitation extremes and the Madden-Julian Oscillation (MJO), yielding results that align more closely with observations or reanalyses (e.g., ERA5, TRMM) than conventional parameterization schemes.