Mesh-based numerical solvers are an important part in many design tool
chains. However, accurate simulations like computational fluid dynamics are
time and resource consuming which is why surrogate models are employed to
speed-up the solution process. Machine Learning based surrogate models on the
other hand are fast in predicting approximate solutions but often lack
accuracy. Thus, the development of the predictor in a predictor-corrector
approach is the focus here, where the surrogate model predicts a flow field and
the numerical solver corrects it. This paper scales a state-of-the-art
surrogate model from the domain of graph-based machine learning to
industry-relevant mesh sizes of a numerical flow simulation. The approach
partitions and distributes the flow domain to multiple GPUs and provides halo
exchange between these partitions during training. The utilized graph neural
network operates directly on the numerical mesh and is able to preserve complex
geometries as well as all other properties of the mesh. The proposed surrogate
model is evaluated with an application on a three dimensional turbomachinery
setup and compared to a traditionally trained distributed model. The results
show that the traditional approach produces superior predictions and
outperforms the proposed surrogate model. Possible explanations, improvements
and future directions are outlined.

基于网格的数值求解器，代理模型，预测 - 校正方法，基于图机器学习，分布式模型。

大型 CFD 网格上图机学习模型的多 GPU 训练方法

Multi-GPU Approach for Training of Graph ML Models on large CFD Meshes

We provide a novel accelerated first-order method that achieves the
asymptotically optimal convergence rate for smooth functions in the first-order
oracle model. To this day, Nesterov's Accelerated Gradient Descent (AGD) and
variations thereof were the only methods achieving acceleration in this
standard blackbox model. In contrast, our algorithm is significantly different
from AGD, as it relies on a predictor-corrector approach similar to that used
by Mirror-Prox [Nemirovski, 2004] and Extra-Gradient Descent [Korpelevich,
1977] in the solution of convex-concave saddle point problems. For this reason,
we dub our algorithm Accelerated Extra-Gradient Descent (AXGD). Its
construction is motivated by the discretization of an accelerated
continuous-time dynamics [Krichene et al., 2015] using the classical method of
implicit Euler discretization. Our analysis explicitly shows the effects of
discretization through a conceptually novel primal-dual viewpoint. Moreover, we
show that the method is quite general: it attains optimal convergence rates for
other classes of objectives (e.g., those with generalized smoothness properties
or that are non-smooth and Lipschitz-continuous) using the appropriate choices
of step lengths. Finally, we present experiments showing that our algorithm
matches the performance of Nesterov's method, while appearing more robust to
noise in some cases.

提出了一种新的加速一阶方法 (AXGD)，采用了预测 - 校正方法，解决了凸 - 凹鞍点问题，通过隐式欧拉离散化构建了加速连续时间动态模型，并通过原始 - 对偶视角进行了分析，对于其他类别的目标也能够达到最佳收敛速度。