Learning to Advect: A Neural Semi-Lagrangian Architecture for Weather Forecasting

Abstract

Machine-learning approaches to weather forecasting often employ a monolithic architecture in which distinct physical mechanisms, such as advection, diffusive mixing, thermodynamic processes, and forcing, are represented implicitly within a single large neural network. This is particularly problematic for advection, where long-range transport typically requires expensive global interaction mechanisms or deep stacks of local convolutional layers. To address this limitation, we introduce a physics-inspired neural architecture that decomposes latent-state evolution into dedicated advection, diffusion, and reaction operators. Its central component is a Neural Semi-Lagrangian operator that performs trajectory-based transport via differentiable interpolation on the sphere, allowing the network to learn both a compressed set of latent modes to be transported and their characteristic trajectories. The atmospheric state is projected into latent space and spatially coarsened to a processor grid, where advection, diffusion, and reaction operators jointly evolve the representation. Diffusive mixing and unresolved dissipation are represented by depthwise-separable spatial mixing, while local source terms and vertical interactions are handled through pointwise channel interactions. We evaluate a reference implementation of the proposed architecture on global weather forecasting. Evaluated on ERA5 benchmarks, the reference model achieves competitive deterministic forecast skill, with particularly strong performance at short to medium lead times, while preserving improved spectral fidelity and forecast activity relative to several leading data-driven baselines.