Title: Physics-Aware Tensor Field Neural PDE for Climate and Weather Prediction
Primary area: applications to physical sciences (physics, chemistry, biology, etc.)
Keywords: Weather Prediction, Neural ODE, Physics-Informed Machine Learning, Tensor Field Neural, Partial Differential Equations

Abstract: 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, overlooking essential physical principles 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 strict physical fidelity 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 with a comparable number of parameters.

TL;DR: We introduce PA-TFNP, a physics-aware tensor-field neural PDE framework for weather and climate forecasting.