Turbulence modeling requires space and time combined analysis
Let's Do Turbulence Right: In Space and Time!
Machine Learning
Summary
Turbulence in fluids is complicated because it changes constantly in both space and time. The authors studied very large computer simulations that track these changes in detail to understand how numerical methods affect what gets captured. They found that looking at space and time separately can give conflicting insights, especially when using machine learning to represent turbulence. They recommend treating turbulence as a four-dimensional problem, including time, to better capture its true behavior.
What this means in practice
- •For computer simulation engineers: Improve fluid simulation accuracy by integrating spatial and temporal data handling for turbulence modeling.
- •For machine learning developers: Develop neural networks that learn from combined space-time turbulence data to better represent fluid flows.
Authors
Maximilian Plattner, Fabian Paischer, Johannes Brandstetter
Abstract
The three-dimensional Navier-Stokes equations govern fluid turbulence, a chaotic and non-linear physical phenomenon characterized by complex eddies interacting across vast spatial and temporal scales. A numerically accurate modeling of this multi-scale energy cascade requires fully resolving both the fine spatial structures and the continuous temporal evolution of the flow field. In this paper, we leverage massive, time-resolved direct numerical simulations, which exceed 28 TB per run, to assess how numerical choices govern the resolved (3+1)-dimensional physics of turbulent flows. Building on this analysis, we study how neural networks represent the recorded turbulent motion. Our results highlight that spatial and temporal assessments can disagree for both numerical records and learned representations. We therefore call on the machine learning community to treat (3+1)-dimensional turbulence as a four-dimensional phenomenon.