We propose an end-to-end trained neural networkarchitecture to robustly predict the complex dynamics of fluid flows with high temporal stability. We focus on single-phase smoke simulations in 2D and 3D based on the incompressible Navier-Stokes (NS) equations, which are relevant for a wide range of practical problems. To achieve stable predictions for long-term flow sequences, a convolutional neural network (CNN) is trained for spatial compression in combination with a temporal prediction network that consists of stacked Long Short-Term Memory (LSTM) layers. Our core contribution is a novel latent space subdivision (LSS) to separate the respective input quantities into individual parts of the encoded latent space domain. This allows to distinctively alter the encoded quantities without interfering with the remaining latent space values and hence maximizes external control. By selectively overwriting parts of the predicted latent space points, our proposed method is capable to robustly predict long-term sequences of complex physics problems. In addition, we highlight the benefits of a recurrent training on the latent space creation, which is performed by the spatial compression network.

本文提出了一种端到端训练神经网络体系结构，以具有高时态稳定性的方式强韧地预测流体流动的复杂动力学。该方法是基于卷积神经网络（CNN）的空间压缩与堆叠长期短期记忆（LSTM）层结构的时间预测网络，并采用新颖的潜在空间划分方法（LSS）。通过选择性地覆盖部分预测的潜在点空间，我们提出的方法能够强韧地预测复杂物理问题的长期序列，并突出空间压缩网络对潜在空间创建的循环训练的好处。

潜空间细分：流体流动的稳定可控时间预测