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. Learning physical functions is an area of growing interest within the research community, with applications ranging from physical priors for computer vision problems BID20 , over robotic control BID35 , to fast approximations for numerical solvers Tompson et al. (2017) . While the underlying model equations for many physics problems are known, finding solutions is often prohibitively expensive for phenomena on human scales. At the same time, the availability of model equations allows for the creation of reliable ground truth data for training, if enough computational resources can be allocated.Water, and liquids in general, are ubiquitous in our world. At the same time, they represent an especially tough class of physics problems, as the constantly changing boundary conditions at the liquid-gas interface result in a complex space of surface motions and configurations. In this work we present a novel approach to capture parametrized spaces of liquid behavior that is based on space-time deformations. We represent a single 3D input surface over time as a four-dimensional signed-distance function (SDF), which we deform in both space and time with learned deformations to recover the desired physical behavior. To calculate and represent these deformations efficiently, we take a two-stage approach: First, we span the sides of the original parameter region with precomputed deformations, and infer a suitable weighting function. In a second step, we synthesize a dense deformation field for refinement. As both the parameter weighting problem and the deformation synthesis are highly non-linear problems, we demonstrate that neural networks are a particularly suitable solver to robustly find solutions.We will demonstrate that it is possible to incorporate the non-linear effects of weighted deformations into the loss functions of neural networks. In particular, we put emphasis on incorporating the influence of deformation alignment into the loss gradients. This alignment step is necessary to ensure the correct application of multiple consecutive deformations fields. The second stage of our algorithm is a generative model for deformation fields, for which we rely on a known parametrization of the inputs. Thus, in contrast to other generative models which learn to represent unknown parametrization of data sets BID31 , our models are trained with a known range and dimensionality to parameter range, which serves as input.Once trained, the models can be evaluated very efficiently to synthesize new implicit surface configurations. To demonstrate its performance, we have implemented a proof-of-concept version for mobile devices, and a demo app is available for Android devices in the Google Play store. Our approach generates liquid animations several orders of magnitude faster than a traditional simulator, and achieves effective speed up factors of more than 2000, as we will outline in Sec. 5. The central contributions of our work are:• A novel deformation-aware neural network approach to very efficiently represent large collections of space-time surfaces with complex behavior.• We show how to compute suitable loss gradient approximations for the sub-problems of parameter and deformation inference.• In addition we showcase the high performance of our approach with a mobile device implementation that generates liquid simulations interactively. We have presented a novel method to generate space-time surfaces with deformation-aware neural networks. In particular, we have demonstrated the successful inference of weighting sequences of aligned deformations, and the generation of dense deformation fields across a range of varied inputs. Our method exhibits significant improvements in terms surface reconstruction accuracy across the full parameter range. In this way, our networks can capture spaces of complex surface behavior, and Beyond liquid surfaces, our deformation networks could also find application for other types of surface data, such as those from object collections or potentially also moving characters. Likewise, it could be interesting to extend our method in order to infer deformations for input sets without an existing parametrization.
Learning weighting and deformations of space-time data sets for highly efficient approximations of liquid behavior. A neural-network based model is used to interpolate simulations for novel scene conditions from densely registered 4D implicit surfaces for a structured scene. This paper presents a coupled deep learning approach for generating realistic liquid simulation data that can be useful for real-time decision support applications. This paper introduces a deep learning approach for physical simulation that combines two networks for synthesizing 4D data that represents 3D physical simulations