# Enhancing Data-Assimilation in CFD using Graph Neural Networks

arXiv: https://arxiv.org/abs/2311.18027 · HTML: https://mlsanity.com/paper/2311.18027/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 11 references that are in the map.
- First posted on arXiv 29 Nov 2023.

## Builds on (most cited first, 3 of 3)

- [Machine Learning for Fluid Mechanics](https://mlsanity.com/paper/1905.11075/) (2019)
- [Combining Differentiable PDE Solvers and Graph Neural Networks for Fluid Flow Prediction](https://mlsanity.com/paper/2007.04439/) (2020)
- [A Continuous Convolutional Trainable Filter for Modelling Unstructured Data](https://mlsanity.com/paper/2210.13416/) (2022)

## Abstract (arXiv)

We present a novel machine learning approach for data assimilation applied in fluid mechanics, based on adjoint-optimization augmented by Graph Neural Networks (GNNs) models. We consider as baseline the Reynolds-Averaged Navier-Stokes (RANS) equations, where the unknown is the meanflow and a closure model based on the Reynolds-stress tensor is required for correctly computing the solution. An end-to-end process is cast; first, we train a GNN model for the closure term. Second, the GNN model is introduced in the training process of data assimilation, where the RANS equations act as a physics constraint for a consistent prediction. We obtain our results using direct numerical simulations based on a Finite Element Method (FEM) solver; a two-fold interface between the GNN model and the solver allows the GNN's predictions to be incorporated into post-processing steps of the FEM analysis. The proposed scheme provides an excellent reconstruction of the meanflow without any features selection; preliminary results show promising generalization properties over unseen flow configurations.