Unsteady cylinder wakes from arbitrary bodies with differentiable physics-assisted neural network.

This work describes a hybrid predictive framework configured as a coarse-grained surrogate for reconstructing unsteady fluid flows around multiple cylinders of diverse configurations. The presence of cylinders of arbitrary nature causes abrupt changes in the local flow profile while globally exhibiting a wide spectrum of dynamical wakes fluctuating in either a periodic or chaotic manner. Consequently, the focal point of the present study is to establish predictive frameworks that accurately reconstruct the overall fluid velocity flowfield such that the local boundary layer profile, as well as the wake dynamics, are both preserved for long time horizons. The hybrid framework is realized using a base differentiable flow solver combined with a neural network, yielding a differentiable physics-assisted neural network (DPNN). The framework is trained using bodies with arbitrary shapes, and then it is tested and further assessed on out-of-distribution samples. Our results indicate that the neural network acts as a forcing function to correct the local boundary layer profile while also remarkably improving the dissipative nature of the flowfields. It is found that the DPNN framework clearly outperforms the supervised learning approach while respecting the reduced feature space dynamics. The model predictions for arbitrary bodies indicate that the Strouhal number distribution with respect to spacing ratio exhibits similar patterns with existing literature. In addition, our model predictions also enable us to discover similar wake categories for flow past arbitrary bodies. For the chaotic wakes, the present approach predicts the chaotic switch in gap flows up to the mid-time range.

Volumetric Isosurface Rendering with Deep Learning-Based Super-Resolution.

Rendering an accurate image of an isosurface in a volumetric field typically requires large numbers of data samples. Reducing this number lies at the core of research in volume rendering. With the advent of deep learning networks, a number of architectures have been proposed recently to infer missing samples in multidimensional fields, for applications such as image super-resolution. In this article, we investigate the use of such architectures for learning the upscaling of a low resolution sampling of an isosurface to a higher resolution, with reconstruction of spatial detail and shading. We introduce a fully convolutional neural network, to learn a latent representation generating smooth, edge-aware depth and normal fields as well as ambient occlusions from a low resolution depth and normal field. By adding a frame-to-frame motion loss into the learning stage, upscaling can consider temporal variations and achieves improved frame-to-frame coherence. We assess the quality of inferred results and compare it to bi-linear and cubic upscaling. We do this for isosurfaces which were never seen during training, and investigate the improvements when the network can train on the same or similar isosurfaces. We discuss remote visualization and foveated rendering as potential applications.

Implicit Density Projection for Volume Conserving Liquids.

We propose a novel implicit density projection approach for hybrid Eulerian/Lagrangian methods like FLIP and APIC to enforce volume conservation of incompressible liquids. Our approach is able to robustly recover from highly degenerate configurations and incorporates volume-conserving boundary handling. A problem of the standard divergence-free pressure solver is that it only has a differential view on density changes. Numerical volume errors, which occur due to large time steps and the limited accuracy of pressure projections, are invisible to the solver and cannot be corrected. Moreover, these errors accumulate over time and can lead to drastic volume changes, especially in long-running simulations or interactive scenarios. Therefore, we introduce a novel method that enforces constant density throughout the fluid. The density itself is tracked via the particles of the hybrid Eulerian/Lagrangian simulation algorithm. To achieve constant density, we use the continuous mass conservation law to derive a pressure Poisson equation which also takes density deviations into account. It can be discretized with standard approaches and easily implemented into existing code by extending the regular pressure solver. Our method enables us to relax the strict time step and solver accuracy requirements of a regular solver, leading to significantly higher performance. Moreover, our approach is able to push fluid particles out of solid obstacles without losing volume and generates more uniform particle distributions, which makes frequent particle resampling unnecessary. We compare the proposed method to standard FLIP and APIC and to previous volume correction approaches in several simulations and demonstrate significant improvements in terms of incompressibility, visual realism, and computational performance.

Simulating Liquids on Dynamically Warping Grids.

We introduce dynamically warping grids for adaptive liquid simulation. Our primary contributions are a strategy for dynamically deforming regular grids over the course of a simulation and a method for efficiently utilizing these deforming grids for liquid simulation. Prior work has shown that unstructured grids are very effective for adaptive fluid simulations. However, unstructured grids often lead to complicated implementations and a poor cache hit rate due to inconsistent memory access. Regular grids, on the other hand, provide a fast, fixed memory access pattern and straightforward implementation. Our method combines the advantages of both: we leverage the simplicity of regular grids while still achieving practical and controllable spatial adaptivity. We demonstrate that our method enables adaptive simulations that are fast, flexible, and robust to null-space issues. At the same time, our method is simple to implement and takes advantage of existing highly-tuned algorithms.