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

• URL: http://arxiv.org/abs/2601.21151v1
• Date: Thu, 29 Jan 2026 01:20:21 GMT
• Title: Learning to Advect: A Neural Semi-Lagrangian Architecture for Weather Forecasting
• Authors: Carlos A. Pereira, Stéphane Gaudreault, Valentin Dallerit, Christopher Subich, Shoyon Panday, Siqi Wei, Sasa Zhang, Siddharth Rout, Eldad Haber, Raymond J. Spiteri, David Millard, Emilia Diaconescu,
• Abstract summary: Recent machine-learning approaches to weather forecasting often employ a monolithic architecture.<n>We present PARADIS, a physics-inspired global weather prediction model that imposes inductive biases on network behavior.<n>We implement advection through a Neural Semi-Lagrangian operator that performs trajectory-based transport via differentiable on the sphere.<n>Diffusion-like processes are modeled through depthwise-separable spatial mixing, while local source terms and vertical interactions are modeled via pointwise channel interactions.
• Score: 6.433158386048011
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Recent machine-learning approaches to weather forecasting often employ a monolithic architecture, where distinct physical mechanisms (advection, transport), diffusion-like mixing, thermodynamic processes, and forcing are represented implicitly within a single large network. This representation is particularly problematic for advection, where long-range transport must be treated with expensive global interaction mechanisms or through deep, stacked convolutional layers. To mitigate this, we present PARADIS, a physics-inspired global weather prediction model that imposes 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 through depthwise-separable spatial mixing, while local source terms and vertical interactions are modeled via pointwise channel interactions, enabling operator-level physical structure. PARADIS provides state-of-the-art forecast skill at a fraction of the training cost. On ERA5-based benchmarks, the 1 degree PARADIS model, with a total training cost of less than a GPU month, meets or exceeds the performance of 0.25 degree traditional and machine-learning baselines, including the ECMWF HRES forecast and DeepMind's GraphCast.

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