Combining Differentiable PDE Solvers and Graph Neural Networks for Fluid Flow Prediction
This work addresses the computational expense and generalization issues in CFD simulations for fluid dynamics applications, representing an incremental improvement over existing methods.
The authors tackled the problem of poor generalization in deep learning approaches for computational fluid dynamics (CFD) by developing a hybrid graph neural network that integrates a differentiable fluid dynamics simulator. They achieved improved generalization to new scenarios and substantial speedup, outperforming coarse CFD simulations alone.
Solving large complex partial differential equations (PDEs), such as those that arise in computational fluid dynamics (CFD), is a computationally expensive process. This has motivated the use of deep learning approaches to approximate the PDE solutions, yet the simulation results predicted from these approaches typically do not generalize well to truly novel scenarios. In this work, we develop a hybrid (graph) neural network that combines a traditional graph convolutional network with an embedded differentiable fluid dynamics simulator inside the network itself. By combining an actual CFD simulator (run on a much coarser resolution representation of the problem) with the graph network, we show that we can both generalize well to new situations and benefit from the substantial speedup of neural network CFD predictions, while also substantially outperforming the coarse CFD simulation alone.