论文标题
结合了可区分的PDE求解器和图形神经网络以进行流体流动预测
Combining Differentiable PDE Solvers and Graph Neural Networks for Fluid Flow Prediction
论文作者
论文摘要
求解大型复杂的部分微分方程（PDE），例如计算流体动力学（CFD）中出现的大型偏微分方程，是一个计算昂贵的过程。这促使使用深度学习方法来近似PDE解决方案，但是从这些方法预测的仿真结果通常并不能很好地概括到真正的新颖场景。在这项工作中，我们开发了一个混合（图）神经网络，该神经网络将传统的图形卷积网络与网络本身内部的嵌入式不同流体动力学模拟器结合在一起。通过将实际的CFD模拟器（以问题的更粗糙的分辨率表示）与图形网络相结合，我们表明，我们既可以很好地概括到新情况下，又可以从神经网络CFD预测的大幅加速中受益，同时基本上比仅仅超过了粗糙的CFD模拟。
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.
