# Climate modeling

Rescene-ESM freezes an AI weather model trained only for medium-range forecasting as its atmosphere and builds observation-constrained physical ocean, sea-ice, land, river, carbon-cycle and energy-balance components around it. A coupling ladder shows that stochastic SST forcing and the land's moisture flux raise El Niño–Southern Oscillation amplitude and teleconnections step by step toward observed levels while the mean climate barely moves. The full model simulates about 1,000 years per day on one GPU, holds a thousand-year control without drift, and carries emissions scenarios through rivers to population heatwave exposure.

Rescene-ESM freezes an AI weather model trained only for medium-range forecasting as its atmosphere and builds observation-constrained physical ocean, sea-ice, land, river, carbon-cycle and energy-balance components around it. A coupling ladder shows that stochastic SST forcing and the land's moisture flux raise El Niño–Southern Oscillation amplitude and teleconnections step by step toward observed levels while the mean climate barely moves. The full model simulates about 1,000 years per day on one GPU, holds a thousand-year control without drift, and carries emissions scenarios through rivers to population heatwave exposure.

Partially observed dynamical systems expose only coarse-grained slow variables, while unresolved fast variables enter as random effects, so data-driven climate emulators must be probabilistic, yet generative models such as diffusion models lack stability guarantees over long autoregressive rollouts. Forced-dissipative stochastic interpolants write the energy injection and dissipation structure of turbulence into the drift network as a hard constraint, and a Foster–Lyapunov drift condition for the Markov chain proves geometric ergodicity of the emulator. On the two-scale Lorenz-96 prototype, the emulator stays stable over long integrations and under finite-amplitude external forcing, and accurately predicts the forced response of both mean and variance.

Partially observed dynamical systems expose only coarse-grained slow variables, while unresolved fast variables enter as random effects, so data-driven climate emulators must be probabilistic, yet generative models such as diffusion models lack stability guarantees over long autoregressive rollouts. Forced-dissipative stochastic interpolants write the energy injection and dissipation structure of turbulence into the drift network as a hard constraint, and a Foster–Lyapunov drift condition for the Markov chain proves geometric ergodicity of the emulator. On the two-scale Lorenz-96 prototype, the emulator stays stable over long integrations and under finite-amplitude external forcing, and accurately predicts the forced response of both mean and variance.