# A note on the error analysis of data-driven closure models for large eddy simulations of turbulence

arXiv: https://arxiv.org/abs/2405.17612 · HTML: https://mlsanity.com/paper/2405.17612/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 9 references that are in the map.
- First posted on arXiv 27 May 2024.

## Builds on (most cited first, 4 of 4)

- [Input Convex Neural Networks](https://mlsanity.com/paper/1609.07152/) (2016)
- [Learned Turbulence Modelling with Differentiable Fluid Solvers: Physics-based Loss-functions and Optimisation Horizons](https://mlsanity.com/paper/2202.06988/) (2022)
- [Generalizable data-driven turbulence closure modeling on unstructured grids with differentiable physics](https://mlsanity.com/paper/2307.13533/) (2023)
- [Neural PDE Solvers for Irregular Domains](https://mlsanity.com/paper/2211.03241/) (2022)

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

- [Adaptive Diffusion Posterior Sampling for Data and Model Fusion of Complex Nonlinear Dynamical Systems](https://mlsanity.com/paper/2603.12635/) (2026)
- [Deep Learning of Solver-Aware Turbulence Closures from Nudged LES Dynamics](https://mlsanity.com/paper/2604.23874/) (2026)

## Abstract (arXiv)

In this work, we provide a mathematical formulation for error propagation in flow trajectory prediction using data-driven turbulence closure modeling. Under the assumption that the predicted state of a large eddy simulation prediction must be close to that of a subsampled direct numerical simulation, we retrieve an upper bound for the prediction error when utilizing a data-driven closure model. We also demonstrate that this error is significantly affected by the time step size and the Jacobian which play a role in amplifying the initial one-step error made by using the closure. Our analysis also shows that the error propagates exponentially with rollout time and the upper bound of the system Jacobian which is itself influenced by the Jacobian of the closure formulation. These findings could enable the development of new regularization techniques for ML models based on the identified error-bound terms, improving their robustness and reducing error propagation.