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

arXiv: https://arxiv.org/abs/2601.21151 · HTML: https://mlsanity.com/paper/2601.21151/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 47 references that are in the map.
- First posted on arXiv 29 Jan 2026.

## Builds on (most cited first, 19 of 19)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [MiniCPM: Unveiling the Potential of Small Language Models with Scalable Training Strategies](https://mlsanity.com/paper/2404.06395/) (2024)
- [FuXi: A cascade machine learning forecasting system for 15-day global weather forecast](https://mlsanity.com/paper/2306.12873/) (2023)
- [Neural General Circulation Models for Weather and Climate](https://mlsanity.com/paper/2311.07222/) (2023)
- [WeatherBench 2: A benchmark for the next generation of data-driven global weather models](https://mlsanity.com/paper/2308.15560/) (2023)
- [Spherical Fourier Neural Operators: Learning Stable Dynamics on the Sphere](https://mlsanity.com/paper/2306.03838/) (2023)
- [Forecasting Global Weather with Graph Neural Networks](https://mlsanity.com/paper/2202.07575/) (2022)
- [ClimODE: Climate and Weather Forecasting with Physics-informed Neural ODEs](https://mlsanity.com/paper/2404.10024/) (2024)
- [Dion: Distributed Orthonormalized Updates](https://mlsanity.com/paper/2504.05295/) (2025)
- [Prithvi WxC: Foundation Model for Weather and Climate](https://mlsanity.com/paper/2409.13598/) (2024)
- [SEEDS: Emulation of Weather Forecast Ensembles with Diffusion Models](https://mlsanity.com/paper/2306.14066/) (2023)
- [Fixing the Double Penalty in Data-Driven Weather Forecasting Through a Modified Spherical Harmonic Loss Function](https://mlsanity.com/paper/2501.19374/) (2025)
- [ExtremeCast: Boosting Extreme Value Prediction for Global Weather Forecast](https://mlsanity.com/paper/2402.01295/) (2024)
- [Numerical models outperform AI weather forecasts of record-breaking extremes](https://mlsanity.com/paper/2508.15724/) (2025)
- [KARINA: An Efficient Deep Learning Model for Global Weather Forecast](https://mlsanity.com/paper/2403.10555/) (2024)
- [Utilizing Strategic Pre-training to Reduce Overfitting: Baguan -- A Pre-trained Weather Forecasting Model](https://mlsanity.com/paper/2505.13873/) (2025)
- [Advection Augmented Convolutional Neural Networks](https://mlsanity.com/paper/2406.19253/) (2024)

## Built on by (most cited first, 4 of 4)

- [Examining Fast Radiatively Driven Responses Using Machine-Learning Weather Emulators](https://mlsanity.com/paper/2602.16090/) (2026)
- [Bridging short- and medium-range weather forecasting with machine learning](https://mlsanity.com/paper/2608.26822/) (2026)
- [Towards a Foundation Model for the Martian Atmosphere](https://mlsanity.com/paper/2605.28851/) (2026)
- [Green-Routed Neural Operators: Physics Determines Where the Network Reads](https://mlsanity.com/paper/2610.05337/) (2026)

## Abstract (arXiv)

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.