Solving a large-scale Poisson system is computationally expensive for most of the Eulerian fluid simulation applications. We propose a novel machine learning-based approach to accelerate this process. At the heart of our approach is a deep convolutional neural network (CNN), with the capability of predicting the solution (pressure) of a Poisson system given the discretization structure and the intermediate velocities as input. Our system consists of four main components, namely, a deep neural network to solve the large linear equations, a geometric structure to describe the spatial hierarchies of the input vector, a Principal Component Analysis (PCA) process to reduce the dimension of input in training, and a novel loss function to control the incompressibility constraint. We have demonstrated the efficacy of our approach by simulating a variety of high-resolution smoke and liquid phenomena. In particular, we have shown that our approach accelerates the projection step in a conventional Eulerian fluid simulator by two orders of magnitude. In addition, we have also demonstrated the generality of our approach by producing a diversity of animations deviating from the original datasets.

Abstract Eulerian‐based smoke simulations are sensitive to the initial parameters and grid resolutions. Due to the numerical dissipation on different levels of the grid and the nonlinearity of the governing equations, the differences in simulation resolutions will result in different results. This makes it challenging for artists to preview the animation results based on low‐resolution simulations. In this paper, we propose a learning‐based flow correction method for fast previewing based on low‐resolution smoke simulations. The main components of our approach lie in a deep convolutional neural network, a grid‐layer feature vector and a special loss function. We provide a novel matching model to represent the relationship between low‐resolution and high‐resolution smoke simulations and correct the overall shape of a low‐resolution simulation to closely follow the shape of a high‐resolution down‐sampled version. We introduce the grid‐layer concept to effectively represent the 3D fluid shape, which can also reduce the input and output dimensions. We design a special loss function for the fluid divergence‐free constraint in the neural network training process. We have demonstrated the efficacy and the generality of our approach by simulating a diversity of animations deviating from the original training set. In addition, we have integrated our approach into an existing fluid simulation framework to showcase its wide applications.

Abstract Traditional Eulerian‐based fluid simulations require much time and computational resources to solve the projection step, especially the large linear system produced by the Poisson equation. In this paper, we propose an adaptive machine‐learning‐based projection method combining deep neural network and incremental learning technique. We provide two modes: Fast Mode and Normal Mode to solve the most time‐consuming projection step and deal with various simulation scenes largely different from the training data set. We introduce patch‐based feature vectors to represent the whole velocity field and a loss function to keep the divergence‐free constraint. We have demonstrated the acceleration and extrapolation ability of our method by testing various smoke scenes far different from our training data set.

Particle-based methods like Smoothed Particle Hydrodynamics (SPH) are increasingly adopted for large scale fluid simulation in interactive computer graphics. However, surface rendering for such dynamic particle sets is challenging: current methods either produce coarse results, or time consuming. We introduce a novel approach to render high-quality fluid surface in screen space by an efficient combination of particle splatting, ray-casting and surface normal estimation techniques. We apply particle splatting to accelerate ray-casting process, and estimate surface normal using Principal Component Analysis (PCA). We adopt GPU technique to further accelerate our method. Our method can produce high-quality smooth surface while preserving thin and sharp details of large scale fluids. The computation and memory cost of our rendering step only depend on the image resolution. These advantages make our method very suitable for previewing or rendering hundreds of millions particles interactively. We demonstrate the efficiency and effectiveness of our method by rendering various fluid scenarios with different-sized particle sets.

Abstract Physically based fluid simulation requires much time in numerical calculation to solve Navier–Stokes equations. Especially in grid‐based fluid simulation, because of iterative computation, the projection step is much more time‐consuming than other steps. In this paper, we propose a novel data‐driven projection method using an artificial neural network to avoid iterative computation. Once the grid resolution is decided, our data‐driven method could obtain projection results in relatively constant time per grid cell, which is independent of scene complexity. Experimental results demonstrated that our data‐driven method drastically speeded up the computation in the projection step. With the growth of grid resolution, the speed‐up would increase strikingly. In addition, our method is still applicable in different fluid scenes with some alterations, when computational cost is more important than physical accuracy. Copyright © 2016 John Wiley & Sons, Ltd.