# Latent Space Subdivision: Stable and Controllable Time Predictions for Fluid Flow

arXiv: https://arxiv.org/abs/2003.08723 · HTML: https://mlsanity.com/paper/2003.08723/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Mar 2020.

## Built on by (most cited first, 13 of 13)

- [Eagle: Large-Scale Learning of Turbulent Fluid Dynamics with Mesh Transformers](https://mlsanity.com/paper/2302.10803/) (2023)
- [Learning to Accelerate Partial Differential Equations via Latent Global Evolution](https://mlsanity.com/paper/2206.07681/) (2022)
- [DL4SciVis: A State-of-the-Art Survey on Deep Learning for Scientific Visualization](https://mlsanity.com/paper/2204.06504/) (2022)
- [Latent Space Data Assimilation by using Deep Learning](https://mlsanity.com/paper/2104.00430/) (2021)
- [Guaranteed Conservation of Momentum for Learning Particle-based Fluid Dynamics](https://mlsanity.com/paper/2210.06036/) (2022)
- [Fluid Simulation on Neural Flow Maps](https://mlsanity.com/paper/2312.14635/) (2023)
- [A composable machine-learning approach for steady-state simulations on high-resolution grids](https://mlsanity.com/paper/2210.05837/) (2022)
- [IDLat: An Importance-Driven Latent Generation Method for Scientific Data](https://mlsanity.com/paper/2208.03345/) (2022)
- [A Latent space solver for PDE generalization](https://mlsanity.com/paper/2104.02452/) (2021)
- [A composable autoencoder-based iterative algorithm for accelerating numerical simulations](https://mlsanity.com/paper/2110.03780/) (2021)
- [Exploring Physical Latent Spaces for High-Resolution Flow Restoration](https://mlsanity.com/paper/2211.11298/) (2022)
- [Resistance-Time Co-Modulated PointNet for Temporal Super-Resolution Simulation of Blood Vessel Flows](https://mlsanity.com/paper/2111.10372/) (2021)
- [LatentFlow: Cross-Frequency Experimental Flow Reconstruction from Sparse Pressure via Latent Mapping](https://mlsanity.com/paper/2508.16648/) (2025)

## Abstract (arXiv)

We propose an end-to-end trained neural networkarchitecture to robustly predict the complex dynamics of fluid flows with high temporal stability. We focus on single-phase smoke simulations in 2D and 3D based on the incompressible Navier-Stokes (NS) equations, which are relevant for a wide range of practical problems. To achieve stable predictions for long-term flow sequences, a convolutional neural network (CNN) is trained for spatial compression in combination with a temporal prediction network that consists of stacked Long Short-Term Memory (LSTM) layers. Our core contribution is a novel latent space subdivision (LSS) to separate the respective input quantities into individual parts of the encoded latent space domain. This allows to distinctively alter the encoded quantities without interfering with the remaining latent space values and hence maximizes external control. By selectively overwriting parts of the predicted latent space points, our proposed method is capable to robustly predict long-term sequences of complex physics problems. In addition, we highlight the benefits of a recurrent training on the latent space creation, which is performed by the spatial compression network.