Neural advection-diffusion equation for long-term climate dynamics

초록

Climate and weather prediction has traditionally relied on computationally demanding numerical simulations grounded in atmospheric physics, yet deep-learning approaches are emerging as transformative alternatives. Existing methods, however, are often purely data-driven and physics-agnostic, lacking explicit physics-aware structures and struggling to generalize. To address these challenges, we present the Physics-Aware Tensor Field Neural PDE (PA-TFNP), a forecasting framework that embeds rotation-equivariant tensor-field neural operators directly on the sphere, couples them with a numerically rigorous gradient operator based on spherical transforms and physically consistent boundary treatment, and augments the learned dynamics with diffusion terms derived from the atmospheric primitive equations. These innovations enable our model to achieve superior performance through physics-aware inductive biases and efficient learning. The proposed PA-TFNP achieves state-of-the-art performance in global and regional weather prediction, outperforming ClimODE by 78.92% on global hourly data while using significantly fewer parameters. On regional forecasting tasks, our model achieves consistently strong performance with a comparable number of parameters.

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