# A posteriori learning of quasi-geostrophic turbulence parametrization: an experiment on integration steps

arXiv: https://arxiv.org/abs/2111.06841 · HTML: https://mlsanity.com/paper/2111.06841/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 27 references that are in the map.
- First posted on arXiv 12 Nov 2021.

## Builds on (most cited first, 7 of 7)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [VoxelNet: End-to-End Learning for Point Cloud Based 3D Object Detection](https://mlsanity.com/paper/1711.06396/) (2017)
- [End to End Learning for Self-Driving Cars](https://mlsanity.com/paper/1604.07316/) (2016)
- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [FSRNet: End-to-End Learning Face Super-Resolution with Facial Priors](https://mlsanity.com/paper/1711.10703/) (2017)
- [Learning to Control PDEs with Differentiable Physics](https://mlsanity.com/paper/2001.07457/) (2020)
- [Physical invariance in neural networks for subgrid-scale scalar flux modeling](https://mlsanity.com/paper/2010.04663/) (2020)

## Built on by (most cited first, 1 of 1)

- [Jacobian Regularization Stabilizes Long-Term Integration of Neural Differential Equations](https://mlsanity.com/paper/2602.04608/) (2026)

## Abstract (arXiv)

Modeling the subgrid-scale dynamics of reduced models is a long standing open problem that finds application in ocean, atmosphere and climate predictions where direct numerical simulation (DNS) is impossible. While neural networks (NNs) have already been applied to a range of three-dimensional flows with success, two dimensional flows are more challenging because of the backscatter of energy from small to large scales. We show that learning a model jointly with the dynamical solver and a meaningful textita posteriori-based loss function lead to stable and realistic simulations when applied to quasi-geostrophic turbulence.