We propose a novel approach for deformation-aware neural networks that learn
the weighting and synthesis of dense volumetric deformation fields. Our method
specifically targets the space-time representation of physical surfaces from
liquid simulations. Liquids exhibit highly complex, non-linear behavior under
changing simulation conditions such as different initial conditions. Our
algorithm captures these complex phenomena in two stages: a first neural
network computes a weighting function for a set of pre-computed deformations,
while a second network directly generates a deformation field for refining the
surface. Key for successful training runs in this setting is a suitable loss
function that encodes the effect of the deformations, and a robust calculation
of the corresponding gradients. To demonstrate the effectiveness of our
approach, we showcase our method with several complex examples of flowing
liquids with topology changes. Our representation makes it possible to rapidly
generate the desired implicit surfaces. We have implemented a mobile
application to demonstrate that real-time interactions with complex liquid
effects are possible with our approach.

提出了一种新颖的变形感知神经网络方法，用于学习密集体积变形场的加权合成，特别针对液体模拟的时空表征，成功地实现了实时流体效果的移动端交互。

利用变形感知神经网络生成液体模拟

Generating Liquid Simulations with Deformation-aware Neural Networks

We present a novel method to interpolate smoke and liquid simulations in
order to perform data-driven fluid simulations. Our approach calculates a dense
space-time deformation using grid-based signed-distance functions of the
inputs. A key advantage of this implicit Eulerian representation is that it
allows us to use powerful techniques from the optical flow area. We employ a
five-dimensional optical flow solve. In combination with a projection
algorithm, and residual iterations, we achieve a robust matching of the inputs.
Once the match is computed, arbitrary in between variants can be created very
efficiently. To concatenate multiple long-range deformations, we propose a
novel alignment technique. Our approach has numerous advantages, including
automatic matches without user input, volumetric deformations that can be
applied to details around the surface, and the inherent handling of topology
changes. As a result, we can interpolate swirling smoke clouds, and splashing
liquid simulations. We can even match and interpolate phenomena with
fundamentally different physics: a drop of liquid, and a blob of heavy smoke.

介绍了一种将烟雾和液体模拟进行数据驱动流体模拟的新方法，该方法使用基于格网的有符号距离函数计算密集的时空变形，并结合光流求解、投影算法和残差迭代实现了输入匹配。此外还提出了对齐技术，它可以连接多个长距离形变，从而实现旋转烟云或飞溅液体等现象。