# DeepClouds.ai: Deep learning enabled computationally cheap direct numerical simulations

arXiv: https://arxiv.org/abs/2208.08956 · HTML: https://mlsanity.com/paper/2208.08956/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 32 references that are in the map.
- First posted on arXiv 18 Aug 2022.

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

- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [Machine Learning for Fluid Mechanics](https://mlsanity.com/paper/1905.11075/) (2019)
- [Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solvers](https://mlsanity.com/paper/2007.00016/) (2020)
- [Deep Learning Methods for Reynolds-Averaged Navier-Stokes Simulations of Airfoil Flows](https://mlsanity.com/paper/1810.08217/) (2018)
- [Prediction of Aerodynamic Flow Fields Using Convolutional Neural Networks](https://mlsanity.com/paper/1905.13166/) (2019)
- [Physics-based Deep Learning](https://mlsanity.com/paper/2109.05237/) (2021)
- [Reservoir computing model of two-dimensional turbulent convection](https://mlsanity.com/paper/2001.10280/) (2020)

## Built on by (most cited first, 2 of 2)

- [Differentiable modeling to unify machine learning and physical models and advance Geosciences](https://mlsanity.com/paper/2301.04027/) (2023)
- [Prototype-enhanced prediction in graph neural networks for climate applications](https://mlsanity.com/paper/2504.17492/) (2025)

## Abstract (arXiv)

Simulation of turbulent flows, especially at the edges of clouds in the atmosphere, is an inherently challenging task. Hitherto, the best possible computational method to perform such experiments is the Direct Numerical Simulation (DNS). DNS involves solving non-linear partial differential equations for fluid flows, also known as Navier-Stokes equations, on discretized grid boxes in a three-dimensional space. It is a valuable paradigm that has guided the numerical weather prediction models to compute rainfall formation. However, DNS cannot be performed for large domains of practical utility to the weather forecast community. Here, we introduce DeepClouds.ai, a 3D-UNET that simulates the outputs of a rising cloud DNS experiment. The problem of increasing the domain size in DNS is addressed by mapping an inner 3D cube to the complete 3D cube from the output of the DNS discretized grid simulation. Our approach effectively captures turbulent flow dynamics without having to solve the complex dynamical core. The baseline shows that the deep learning-based simulation is comparable to the partial-differential equation-based model as measured by various score metrics. This framework can be used to further the science of turbulence and cloud flows by enabling simulations over large physical domains in the atmosphere. It would lead to cascading societal benefits by improved weather predictions via advanced parameterization schemes.