Pre-computed Liquid Spaces with Generative Neural Networks and Optical Flow

Liquids exhibit highly complex, non-linear behavior under changing simulation conditions such as user interactions. We propose a method to map this complex behavior over a parameter range onto a reduced representation based on space-time deformations. In order to represent the complexity of the full space of inputs, we use aligned deformations from optical flow solves, and we leverage the power of generative neural networks to synthesize additional deformations for refinement. We introduce a novel deformation-aware loss function, which enables optimization in the highly non-linear space of multiple deformations. To demonstrate the effectiveness of our approach, we showcase the method with several complex examples in two and four dimensions. Our representation makes it possible to generate implicit surfaces of liquids very efficiently, which allows us to very efficiently display the scene from any angle, and to add secondary effects such as particle systems. We have implemented a mobile application with our full pipeline to demonstrate that real-time interaction is possible with our approach.