Combining Differentiable PDE Solvers and Graph Neural Networks for Fluid Flow Prediction
Filipe De Avila Belbute-Peres, Thomas Economon, Zico Kolter
Abstract
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.
BibTeX
@InProceedings{pmlr-v119-de-avila-belbute-peres20a,
title = {Combining Differentiable {PDE} Solvers and Graph Neural Networks for Fluid Flow Prediction},
author = {De Avila Belbute-Peres, Filipe and Economon, Thomas and Kolter, Zico},
booktitle = {Proceedings of the 37th International Conference on Machine Learning},
pages = {2402--2411},
year = {2020},
editor = {III, Hal Daumé and Singh, Aarti},
volume = {119},
series = {Proceedings of Machine Learning Research},
month = {13--18 Jul},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v119/de-avila-belbute-peres20a/de-avila-belbute-peres20a.pdf},
url = {https://proceedings.mlr.press/v119/de-avila-belbute-peres20a.html},
abstract = {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.}
}