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

TL;DR

This paper introduces PARADIS, a physics-inspired neural weather prediction model that explicitly decomposes advection, diffusion, and reaction processes, improving forecast accuracy and spectral fidelity.

Contribution

The paper presents a novel neural architecture with a semi-Lagrangian advection operator and structured decomposition, enhancing interpretability and performance in weather forecasting.

Findings

PARADIS achieves competitive deterministic forecast skill on ERA5 benchmarks.

It exhibits strong short-lead forecast performance.

It maintains better spectral fidelity and forecast activity during medium-range rollouts.

Abstract

Recent machine-learning approaches to weather forecasting often employ a monolithic architecture in which distinct physical mechanisms-advection (long-range transport), diffusion-like mixing, thermodynamic processes, and forcing-are represented implicitly within a single large 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 mitigate this, we present PARADIS, a physics-inspired global weather prediction model that enforces inductive biases on network behavior through a functional decomposition into advection, diffusion, and reaction blocks acting on latent variables. We implement advection through a Neural Semi-Lagrangian operator that performs trajectory-based transport via differentiable interpolation on the sphere, enabling end-to-end learning of both the latent modes to be transported and their characteristic trajectories. Diffusion-like processes are modeled by depthwise-separable spatial mixing, whereas local source terms and vertical interactions are handled via pointwise channel interactions, yielding a physically structured operator decomposition. Evaluated on ERA5 benchmarks, PARADIS achieves competitive deterministic forecast skill, with particularly strong short-lead performance, while preserving substantially better spectral fidelity and forecast activity during medium-range rollouts.