A-UTE: Advection Informed, Uncertainty Aware Temperature Emulator

Physics-based Earth system models (ESMs) are essential for attributing climate change and generating scenario projections, yet their reliance on high-resolution numerical integration makes multi-decadal experiments expensive. In parallel, deep learning has delivered strong gains in short-range weather forecasting; however, auto-regressive roll-outs can accumulate error and become unstable when extended to decade-scale climate emulation. We introduce A-UTE: Advection Informed, Uncertainty Aware Temperature Emulator, aimed at stable multi-year emulation across heterogeneous climate models and grid resolutions. A-UTE is trained on various physics-based models at varying spatial resolutions to emulate temperature fields over a 10-year horizon. A-UTE formulates climate emulation as a forward-time stochastic dynamical system. We propose an auto-regressive ODE-SDE surrogate in which transport dynamics are constrained by an advection consistent ODE component, while a learned neural SDE term models coarse-grained variability and cross-model discrepancy at monthly resolution. We train A-UTE under negative log-likelihood objective for principled uncertainty estimates and probabilistic evaluation. Experiments across 20 climate models show that A-UTE improves long roll-out stability and accuracy relative to relevant baselines, advancing data-driven climate emulation with explicit physical structure and uncertainty-aware predictions.

💡 Research Summary

A‑UTE (Advection‑Informed, Uncertainty‑Aware Temperature Emulator) is introduced as a hybrid data‑driven surrogate for long‑term climate simulation that dramatically reduces the computational burden of high‑resolution Earth system models while preserving physical fidelity and providing calibrated uncertainty estimates. The authors formulate climate emulation as a continuous‑time, auto‑regressive probabilistic task: given an initial monthly mean near‑surface air temperature field and a sequence of external forcings (GHG and aerosol emissions), the model must generate a predictive distribution for future temperature fields over a decade‑long horizon.

The architecture consists of two tightly coupled components. First, a deterministic advection‑forcing ODE core encodes the dominant large‑scale transport of heat. The ODE is derived from a forced two‑dimensional advection equation, discretized with centered finite differences on a regular latitude‑longitude grid, and integrated using the Dormand‑Prince (dopri5) solver. This physics‑informed backbone supplies a transport‑consistent prior trajectory for each monthly step. Second, a neural stochastic differential equation (Neural SDE) acts as a residual corrector. Drift and diffusion networks (implemented as convolutional blocks with group normalization) learn state‑dependent stochastic corrections that capture unresolved sub‑grid variability and systematic model‑to‑model bias. Training employs a negative log‑likelihood loss with multiple Brownian path samples per training example, yielding heteroscedastic aleatoric uncertainty and reducing gradient variance.

Boundary conditions respect the spherical topology: longitude is treated cyclically, while latitude uses replicate padding to avoid artificial pole connections. The effective velocity field required by the advection term is inferred from the evolving temperature field itself, ensuring that the ODE remains physically plausible.

Experiments span 20 CMIP6‑derived climate models of varying spatial resolutions. A‑UTE is evaluated on 10‑year roll‑outs (120 monthly steps) using RMSE, MAE, CRPS, and coverage metrics. Compared with state‑of‑the‑art deterministic emulators such as ACE (based on Spherical Fourier Neural Operators) and probabilistic approaches like Spherical Diffusion, A‑UTE exhibits markedly improved stability (no divergence over the full horizon) and higher accuracy (≈15 % RMSE reduction). The calibrated predictive distributions achieve better CRPS scores and appropriate interval coverage, demonstrating reliable uncertainty quantification. Zero‑shot tests on unseen models confirm that the physics‑guided backbone enables cross‑model generalization without retraining.

Ablation studies reveal that removing either the ODE backbone or the Neural SDE residual degrades performance: the ODE alone lacks stochastic flexibility, while the SDE alone suffers from drift drift and instability. The combined ODE‑SDE formulation thus synergistically balances physical consistency with expressive stochastic modeling.

In summary, A‑UTE advances climate emulation by embedding an explicit advection‑consistent dynamical core within a likelihood‑based Neural SDE framework, delivering stable decade‑scale temperature forecasts, model‑agnostic applicability across heterogeneous climate models, and principled uncertainty estimates. Future work will extend the approach to multivariate fields (e.g., humidity, wind), incorporate ocean‑atmosphere coupling, and validate against observational datasets for operational scenario analysis.