Learning to Advect: A Neural Semi-Lagrangian Architecture for Weather Forecasting
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| Main Authors: | , , , , , , , , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866913128196866048 |
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| author | Pereira, Carlos A. Gaudreault, Stéphane Dallerit, Valentin Subich, Christopher Panday, Shoyon Wei, Siqi Zhang, Sasa Rout, Siddharth Haber, Eldad Spiteri, Raymond J. Millard, David Diaconescu, Emilia |
| author_facet | Pereira, Carlos A. Gaudreault, Stéphane Dallerit, Valentin Subich, Christopher Panday, Shoyon Wei, Siqi Zhang, Sasa Rout, Siddharth Haber, Eldad Spiteri, Raymond J. Millard, David Diaconescu, Emilia |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_21151 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Learning to Advect: A Neural Semi-Lagrangian Architecture for Weather Forecasting Pereira, Carlos A. Gaudreault, Stéphane Dallerit, Valentin Subich, Christopher Panday, Shoyon Wei, Siqi Zhang, Sasa Rout, Siddharth Haber, Eldad Spiteri, Raymond J. Millard, David Diaconescu, Emilia Machine Learning Atmospheric and Oceanic Physics 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. |
| title | Learning to Advect: A Neural Semi-Lagrangian Architecture for Weather Forecasting |
| topic | Machine Learning Atmospheric and Oceanic Physics |
| url | https://arxiv.org/abs/2601.21151 |