We propose an end‐to‐end trained neural network architecture 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 with linear execution times, 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. As a result, 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, like the flow of fluids. In addition, we highlight the benefits of a recurrent training on the latent space creation, which is performed by the spatial compression network. Furthermore, we thoroughly evaluate and discuss several different components of our method.

中文翻译：

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潜在空间细分：流体流动的稳定可控时间预测

我们提出了一种端到端训练的神经网络架构，以稳健地预测具有高时间稳定性的流体流动的复杂动力学。我们专注于基于不可压缩 Navier-Stokes (NS) 方程的 2D 和 3D 单相烟雾模拟，这与广泛的实际问题相关。为了实现对具有线性执行时间的长期流序列的稳定预测，卷积神经网络 (CNN) 结合由堆叠的长短期记忆 (LSTM) 层组成的时间预测网络进行空间压缩训练。我们的核心贡献是一种新颖的潜在空间细分（LSS），用于将各个输入量分成编码的潜在空间域的各个部分。因此，这允许在不干扰剩余潜在空间值的情况下明显地改变编码量，从而最大化外部控制。通过选择性地覆盖部分预测的潜在空间点，我们提出的方法能够稳健地预测复杂物理问题的长期序列，例如流体的流动。此外，我们强调了由空间压缩网络执行的潜在空间创建的循环训练的好处。此外，我们彻底评估和讨论了我们方法的几个不同组成部分。此外，我们强调了由空间压缩网络执行的潜在空间创建的循环训练的好处。此外，我们彻底评估和讨论了我们方法的几个不同组成部分。此外，我们强调了由空间压缩网络执行的潜在空间创建的循环训练的好处。此外，我们彻底评估和讨论了我们方法的几个不同组成部分。