Simulating turbulent smoke flows with fine details is computationally intensive. For iterative editing or simply faster generation, efficiently upsampling a low-resolution numerical simulation is an attractive alternative. We propose a novel learning approach to the dynamic upsampling of smoke flows based on a training set of flows at coarse and fine resolutions. Our multiscale neural network turns an input coarse animation into a sparse linear combination of small velocity patches present in a precomputed over-complete dictionary. These sparse coefficients are then used to generate a high-resolution smoke animation sequence by blending the fine counterparts of the coarse patches. Our network is initially trained from a sequence of example simulations to both construct the dictionary of corresponding coarse and fine patches and allow for the fast evaluation of a sparse patch encoding of any coarse input. The resulting network provides an accurate upsampling when the coarse input simulation is well approximated by patches present in the training set (e.g., for re-simulation), or simply visually plausible upsampling when input and training sets differ significantly. We show a variety of examples to ascertain the strengths and limitations of our approach and offer comparisons to existing approaches to demonstrate its quality and effectiveness.

中文翻译：

---

通过基于字典的学习对烟雾进行动态上采样

模拟具有精细细节的湍流烟雾流是计算密集型的。对于迭代编辑或简单的快速生成，有效地对低分辨率数值模拟进行上采样是一种有吸引力的选择。我们提出了一种基于粗略和精细分辨率的训练集的烟流动态上采样的新学习方法。我们的多尺度神经网络将输入粗略动画转换为预先计算的过完备字典中存在的小速度块的稀疏线性组合。然后，这些稀疏系数用于通过混合粗糙补丁的精细对应物来生成高分辨率烟雾动画序列。我们的网络最初是从一系列示例模拟中训练出来的，以构建相应的粗和细补丁的字典，并允许快速评估任何粗输入的稀疏补丁编码。当粗略的输入模拟通过训练集中存在的补丁（例如，用于重新模拟）很好地近似时，所得网络提供准确的上采样，或者当输入和训练集显着不同时提供简单的视觉上合理的上采样。我们展示了各种示例来确定我们方法的优势和局限性，并提供与现有方法的比较以证明其质量和有效性。当粗略的输入模拟通过训练集中存在的补丁（例如，用于重新模拟）很好地近似时，所得网络提供准确的上采样，或者当输入和训练集显着不同时提供简单的视觉上合理的上采样。我们展示了各种示例来确定我们方法的优势和局限性，并与现有方法进行比较以证明其质量和有效性。当粗略的输入模拟通过训练集中存在的补丁（例如，用于重新模拟）很好地近似时，所得网络提供准确的上采样，或者当输入和训练集显着不同时提供简单的视觉上合理的上采样。我们展示了各种示例来确定我们方法的优势和局限性，并提供与现有方法的比较以证明其质量和有效性。