Augmenting Data Assimilation in CFD with Graph Neural Networks

In this article, we present a novel approach to enhance data-assimilation in computational fluid dynamics (CFD) using graph neural networks (GNNs). Data assimilation is the process of combining observations with a mathematical model to produce an improved estimate of the true state of a system. In CFD, this is particularly challenging due to the complex and nonlinear nature of fluid flow.
To address this challenge, we propose an augmented training process that combines the strengths of GNNs and traditional data-assimilation techniques. The proposed method consists of two main steps: (1) forward pass, where the GNN is used to predict the flow field based on the observations, and (2) backward pass, where the gradient of the cost function with respect to the model parameters is computed using the adjoint method.
In the forward pass, we use a GNN to approximate the nonlinear term in the RANS (Reynolds-Averaged Navier-Stokes) equations. This allows us to incorporate complex flow patterns and nonlinear interactions between different points in the system. In the backward pass, we compute the gradient of the cost function with respect to the model parameters using the adjoint method. This enables us to optimize the model parameters to minimize the cost function and improve the accuracy of the flow field prediction.
We demonstrate the effectiveness of our proposed method through several numerical experiments on a turbulent channel flow problem. Our results show that the proposed method can significantly improve the accuracy of the flow field prediction compared to traditional data-assimilation techniques. Additionally, we show that the GNN can learn to approximate complex nonlinear terms in the RANS equations, which cannot be easily captured by traditional numerical methods.
In summary, our proposed method combines the strengths of GNNs and traditional data-assimilation techniques to enhance the accuracy of flow field prediction in CFD. By leveraging the ability of GNNs to capture complex nonlinear patterns and optimize model parameters using adjoint methods, we can improve the efficiency and accuracy of CFD simulations.