Kiwon Um

Chloe Paliard, Nils Thuerey, Kiwon Um

We explore training deep neural network models in conjunction with physics simulations via partial differential equations (PDEs), using the simulated degrees of freedom as latent space for a neural network. In contrast to previous work, this paper treats the degrees of freedom of the simulated space purely as tools to be used by the neural network. We demonstrate this concept for learning reduced representations, as it is extremely challenging to faithfully preserve correct solutions over long time-spans with traditional reduced representations, particularly for solutions with large amounts of small scale features. This work focuses on the use of such physical, reduced latent space for the restoration of fine simulations, by training models that can modify the content of the reduced physical states as much as needed to best satisfy the learning objective. This autonomy allows the neural networks to discover alternate dynamics that significantly improve the performance in the given tasks. We demonstrate this concept for various fluid flows ranging from different turbulence scenarios to rising smoke plumes.

Marie-Lena Eckert, Kiwon Um, Nils Thuerey

In this paper, we present ScalarFlow, a first large-scale data set of reconstructions of real-world smoke plumes. We additionally propose a framework for accurate physics-based reconstructions from a small number of video streams. Central components of our algorithm are a novel estimation of unseen inflow regions and an efficient regularization scheme. Our data set includes a large number of complex and natural buoyancy-driven flows. The flows transition to turbulent flows and contain observable scalar transport processes. As such, the ScalarFlow data set is tailored towards computer graphics, vision, and learning applications. The published data set will contain volumetric reconstructions of velocity and density, input image sequences, together with calibration data, code, and instructions how to recreate the commodity hardware capture setup. We further demonstrate one of the many potential application areas: a first perceptual evaluation study, which reveals that the complexity of the captured flows requires a huge simulation resolution for regular solvers in order to recreate at least parts of the natural complexity contained in the captured data.

Kiwon Um, Robert Brand, Yun et al.

Finding accurate solutions to partial differential equations (PDEs) is a crucial task in all scientific and engineering disciplines. It has recently been shown that machine learning methods can improve the solution accuracy by correcting for effects not captured by the discretized PDE. We target the problem of reducing numerical errors of iterative PDE solvers and compare different learning approaches for finding complex correction functions. We find that previously used learning approaches are significantly outperformed by methods that integrate the solver into the training loop and thereby allow the model to interact with the PDE during training. This provides the model with realistic input distributions that take previous corrections into account, yielding improvements in accuracy with stable rollouts of several hundred recurrent evaluation steps and surpassing even tailored supervised variants. We highlight the performance of the differentiable physics networks for a wide variety of PDEs, from non-linear advection-diffusion systems to three-dimensional Navier-Stokes flows.

Georg Kohl, Kiwon Um, Nils Thuerey

We propose a neural network-based approach that computes a stable and generalizing metric (LSiM) to compare data from a variety of numerical simulation sources. We focus on scalar time-dependent 2D data that commonly arises from motion and transport-based partial differential equations (PDEs). Our method employs a Siamese network architecture that is motivated by the mathematical properties of a metric. We leverage a controllable data generation setup with PDE solvers to create increasingly different outputs from a reference simulation in a controlled environment. A central component of our learned metric is a specialized loss function that introduces knowledge about the correlation between single data samples into the training process. To demonstrate that the proposed approach outperforms existing metrics for vector spaces and other learned, image-based metrics, we evaluate the different methods on a large range of test data. Additionally, we analyze generalization benefits of an adjustable training data difficulty and demonstrate the robustness of LSiM via an evaluation on three real-world data sets.

Kiwon Um, Xiangyu Hu, Nils Thuerey

This paper proposes a new data-driven approach to model detailed splashes for liquid simulations with neural networks. Our model learns to generate small-scale splash detail for the fluid-implicit-particle method using training data acquired from physically parametrized, high resolution simulations. We use neural networks to model the regression of splash formation using a classifier together with a velocity modifier. For the velocity modification, we employ a heteroscedastic model. We evaluate our method for different spatial scales, simulation setups, and solvers. Our simulation results demonstrate that our model significantly improves visual fidelity with a large amount of realistic droplet formation and yields splash detail much more efficiently than finer discretizations.