FREQUENCY-AWARE INTERFACE DYNAMICS WITH GENERATIVE ADVERSARIAL NETWORKS

Abstract

We present a new method for reconstructing and refining complex surfaces based on physical simulations. Taking a roughly approximated simulation as input, our method infers corresponding spatial details while taking into account how they evolve over time. We consider this problem in terms of spatial and temporal frequencies, and leverage generative adversarial networks to learn the desired spatiotemporal signal for the surface dynamics. Furthermore, we investigate the possibility to train our network in an unsupervised manner, i.e. without predefined training pairs. We highlight the capabilities of our method with a set of synthetic wave function tests and complex 3D dynamics of elasto-plastic materials.

1. INTRODUCTION

Complex and chaotic physical phenomena such as liquids, gels and goo are still very challenging when it comes to representing them as detailed and realistically as possible. A variety of numerical methods have been proposed to simulate such materials, from purely Eulerian methods (Harlow & Welch, 1965; Stam, 1999) , over particle based methods (Gingold & Monaghan, 1977; Ihmsen et al., 2014) , to hybrids (Zhu & Bridson, 2005; Stomakhin et al., 2013) . Such simulations have also been targeted with deep learning methods (Tompson et al., 2017; Mrowca et al., 2018; Li et al., 2019) , but despite significant advances, they remain very time-consuming and highly challenging to solve. One approach to speed up the necessary calculations and to allow for more control is to employ super-sampling. This can be seen as a form of post-processing where one simulates only a lowresolution simulation and uses an up-sampling technique to approximate the behavior of a highresolution simulation. Neural networks are of special interest here because of their capability to efficiently approximate the strongly nonlinear behavior of physical simulations. Applying neural networks to space-time data sets of physical simulations has seen strongly growing interest in recent years (Ladicky et al., 2015; Kim et al., 2020) , and is particularly interesting in this context to incorporate additional constraints, e.g., for temporal coherence (Xie et al., 2018) , or for physical plausibility (Tompson et al., 2017; Kim et al., 2019) . An important aspect here is that methods based on simple distance losses, such as mean square errors, quickly reach their limits. The generated data tends to be smooth without the necessary small-scale features. Generative adversarial networks (GANs) have been proposed to overcome this issue (Goodfellow, 2016) . They are characterized by the fact that, apart from a generative network, they also make use of a discriminator that classifies the results of the generator with respect to the ground-truth data. Via a joint training, the distribution of solutions of the generator is guided to approximate the ground-truth data distribution. As the quality of the results is primarily determined by the discriminator network, it remains an open problem to accurately evaluate the quality of the inferred results. In our work we propose to evaluate the problem in the Fourier space. In this way, we are able to evaluate the given methods reliably, and it allows us to design improved learning algorithms that more faithfully recover the small scale details of the reference data. For the core of our method, we build on an existing GAN-based architecture that employs two discriminator networks, one for the spatial and one for the temporal behaviour (Xie et al., 2018) . In terms of ground truth data, we focus on multi-phase (solid-fluid-air) interactions with a sharp fluid-air interface. Unlike single-phase flow whose details are visible and relevant solely due to transparency throughout the volume, the details of our data are in most cases only visible on the surface. Of course, the internal dynamics in the volume also play a role, but they are mostly hidden 1

