The resolution of the Poisson equation is usually one of the most computationally intensive steps for incompressible fluid solvers. Lately, Deep Learning, and especially Convolutional Neural Networks (CNN), has been introduced to solve this equation, leading to significant inference time reduction at the cost of a lack of guarantee on the accuracy of the solution. This drawback might lead to inaccuracies and potentially unstable simulations. It also makes impossible a fair assessment of the CNN speedup, for instance, when changing the network architecture, since evaluated at different error levels. To circumvent this issue, a hybrid strategy is developed, which couples a CNN with a traditional iterative solver to ensure a user-defined accuracy level. The CNN hybrid method is tested on two flow cases, consisting of a variable-density plume with and without obstacles, demostrating remarkable generalization capabilities, ensuring both the accuracy and stability of the simulations. The error distribution of the predictions using several network architectures is further investigated. Results show that the threshold of the hybrid strategy defined as the mean divergence of the velocity field is ensuring a consistent physical behavior of the CNN-based hybrid computational strategy. This strategy allows a systematic evaluation of the CNN performance at the same accuracy level for various network architectures. In particular, the importance of incorporating multiple scales in the network architecture is demonstrated, since improving both the accuracy and the inference performance compared with feedforward CNN architectures, as these networks can provide solutions 1 10-25 faster than traditional iterative solvers.
翻译:Poisson 方程式的解析通常是无法压缩的流体溶液的计算最密集的步骤之一。 最近,深度学习,特别是进化神经网络网络(CNN)被引入解决这个方程式,导致大量推论时间减少,其代价是无法保证解决方案的准确性。这种退步可能导致模拟的不准确性和可能不稳定的模拟。这也使得无法对CNN的快速化进行公平的评估,例如,在改变网络结构时,由于在不同的错误级别上进行了评估,因此无法对网络结构进行更快速化的评估。为了绕过这一问题,制定了一种混合战略,将CNN与传统的迭代解剂连接起来,以确保用户定义的准确性水平。CNN混合法方法在两个流程中进行了测试,由不设障碍和不设障碍的可变密度流来进行测试,能够淡化一般化的超常化能力,确保模拟的准确性能。 使用若干网络结构的预测的错误分布可以进一步调查。结果显示,作为平均速度差异的混合战略的阈值,即将CNNCN的网络的物理行为行为动作行为规范性行为在1号网络的精确度战略中可以使CNNCMS- 的系统结构的系统化结构在10级结构中进行。