# Latent-space Physics: Towards Learning the Temporal Evolution of Fluid Flow

Source: [Latent-space Physics: Towards Learning the Temporal Evolution of Fluid Flow](<https://www.sota2.com/research/paper/68fa65711e209131cea0a71a>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T21:27:45.299Z

Authors: Steffen Wiewel, Moritz Becher, Nils Thuerey

Published: 2018-02-27T19:18:43.000Z

## Abstract

We propose a method for the data-driven inference of temporal evolutions of physical functions with deep learning. More specifically, we target fluid flows, i.e. Navier-Stokes problems, and we propose a novel LSTM-based approach to predict the changes of pressure fields over time. The central challenge in this context is the high dimensionality of Eulerian space-time data sets. We demonstrate for the first time that dense 3D+time functions of physics system can be predicted within the latent spaces of neural networks, and we arrive at a neural-network based simulation algorithm with significant practical speed-ups. We highlight the capabilities of our method with a series of complex liquid simulations, and with a set of single-phase buoyancy simulations. With a set of trained networks, our method is more than two orders of magnitudes faster than a traditional pressure solver. Additionally, we present and discuss a series of detailed evaluations for the different components of our algorithm.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

- [Fluid dynamics simulation on Navier-Stokes periodic incompressible (test)](<https://www.sota2.com/research/sota/fluid-dynamics-simulation-on-navier-stokes-periodic-incompressible-test.md>): Fluid Dynamics Simulation; Navier-Stokes periodic incompressible (test); nRMSE: 5.5.

- [Navier-Stokes Rollout Simulation on Canonical incompressible Navier-Stokes (test)](<https://www.sota2.com/research/sota/navier-stokes-rollout-simulation-on-canonical-incompressible-navier-stokes-test.md>): Navier-Stokes Rollout Simulation; Canonical incompressible Navier-Stokes (test); nRMSE: 0.055.

- [Incompressible Navier-Stokes Rollout Simulation on Periodic Incompressible Navier-Stokes (test)](<https://www.sota2.com/research/sota/incompressible-navier-stokes-rollout-simulation-on-periodic-incompressible-navier-stokes-test.md>): Incompressible Navier-Stokes Rollout Simulation; Periodic Incompressible Navier-Stokes (test); Mean nRMSE: 0.076.

- [PDE Rollout Prediction on PDEBench Aggregate All time-dependent families](<https://www.sota2.com/research/sota/pde-rollout-prediction-on-pdebench-aggregate-all-time-dependent-families.md>): PDE Rollout Prediction; PDEBench Aggregate All time-dependent families; Mean nRMSE: 0.076.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1802.10123>)

[PDF](<https://arxiv.org/pdf/1802.10123.pdf>)