# Acceleration of horizontal numerical advection for atmospheric modeling through surrogate modeling with temporal coarse-graining

arXiv: https://arxiv.org/abs/2605.10956 · HTML: https://mlsanity.com/paper/2605.10956/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 44 references that are in the map.
- First posted on arXiv 30 Apr 2026.

## Builds on (most cited first, 9 of 9)

- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [Categorizing Variants of Goodhart's Law](https://mlsanity.com/paper/1803.04585/) (2018)
- [Enhancing Computational Fluid Dynamics with Machine Learning](https://mlsanity.com/paper/2110.02085/) (2021)
- [Learned Coarse Models for Efficient Turbulence Simulation](https://mlsanity.com/paper/2112.15275/) (2021)
- [Weak baselines and reporting biases lead to overoptimism in machine learning for fluid-related partial differential equations](https://mlsanity.com/paper/2407.07218/) (2024)
- [Stiff Neural Ordinary Differential Equations](https://mlsanity.com/paper/2103.15341/) (2021)
- [Extreme Event Prediction with Multi-agent Reinforcement Learning-based Parametrization of Atmospheric and Oceanic Turbulence](https://mlsanity.com/paper/2312.00907/) (2023)
- [Decomposing weather forecasting into advection and convection with neural networks](https://mlsanity.com/paper/2405.06590/) (2024)

## Abstract (arXiv)

Machine-learned surrogate modeling of advection may accelerate geoscientific models, but existing approaches have either achieved limited speedup or have sacrificed spatial resolution compared to the model they are trained to emulate. We developed a machine-learned solver that speeds up advection simulations without sacrificing spatial resolution through the use of temporal coarse-graining, where the model is trained to take larger integration steps than dictated by the Courant-Friedrich-Lewy (CFL) condition. Our solver framework includes a convolutional neural network that takes concentrations and CFL numbers as inputs and outputs mass flux. Our solvers emulate 10-day ground-level horizontal advection simulations with r2 values against the baseline ranging from 0.60--0.98 with temporal coarsening factors of 4 to 32 times the baseline integration time step. Speed increases and accuracy decreases with increased coarsening, with r2 = 0.24 in accuracy lost for every factor of 10 gained in speed, reaching a maximum 92× speedup while maintaining r2 = 0.60. We deliberately trained our solvers only on January ground-level wind data to examine their ability to generalize across seasons and vertical heights. The 4×-coarsened learned solver successfully reproduces simulations over 72 vertical levels. The 8×--16× solvers (but not 32×) emulate most vertical levels. The learned solvers also generalize well across seasons, except for instabilities in June and October. With additional fine-tuning, these learned solvers could be appropriate for operational use where trading accuracy for speed could be advantageous, such as in screening tools, in ensemble simulations, or with data assimilation.