Objective

2

Physics-based smoke simulation is an important topic in computer graphics. Realistically simulating turbulent smoke flows is generally computationally expensive due to intrinsic small-scale structures that require sophisticated nondissipative solvers with a relatively high resolution. To effectively preserve small-scale structures

neural networks have been recently proposed and applied. However

the common problem in previous models for upsampling fluid flow fields with added small-scale structures is that the upsampled fluid field may not be sufficiently close to the corresponding high-resolution simulations. This problem may produce visual artifacts as important features

e.g.

vortex rings that require high-resolution samples to capture can be overlooked. The difficulty behind such upsampling

which considerably differs from image upsampling

is that the flow structures between high- and low-resolution simulations can substantially differ. This structure inconsistency becomes increasingly evident when high and low resolutions differ significantly from local nonlinear vortex structures to the global shape of turbulent flow distributions. To enable upsampling with close similarity to its high-resolution simulation counterpart

local and global information should be acquired and encoded. In this study

we propose a novel dictionary-based neural network for synthesizing the high-frequency components of a turbulent smoke flow from a very low-resolution simulation. By learning a local generative scheme from a large set of patches that exist in high-resolution simulations

our network can faithfully synthesize a high-resolution smoke flow that closely resembles the corresponding high-resolution simulations

with well-preserved important features and considerably improved computing efficiency.

Method

2

First

high- and low-resolution turbulent smoke data are simulated using a high-precision numerical method. We propose a feature vector that encodes the local velocity information of each 3D patch

global position

and time. This vector can help accurately predict local high-frequency components. Then

we construct a novel neural network based on the dictionary learning framework; this network simultaneously learns the dictionary and the associated coefficients. High-resolution smoke data have more details than low-resolution smoke data; thus

the former has a more complex spatial structure. Accordingly

we add gradient loss to maintain the spatial structure

with a regularization term to prevent overfitting. The advantage of our model is that it jointly optimizes all the layer parameters from end to end. After the training process

our neural network can learn a complex mapping function to efficiently synthesize high-resolution turbulent smoke patch data. During online synthesis given a low-resolution simulation

the trained neural network is used to predict overlapping local patches in parallel

with convolution in overlapping regions to ensure smooth transition.

Result

2

On the basis of the experimental results

we propose a novel dictionary-based neural network as a small-scale structure predictor to address such upsampling problem. The proposed neural network can produce spatially and temporally consistent high-resolution flow fields from very low-resolution simulations that closely approximate the direct high-resolution simulation results

with considerably improved computational efficiency. Our method faithfully preserves small-scale structures by comparing low- and high-resolution simulations. With our learning-based fast smoke simulation method

efficiency is improved by one order of magnitude compared with direct simulations at a resolution of 200×400×200 with highly similar results.

Conclusion

2

In this study

we address the crucial problem of synthesizing a high-resolution flow field from a very low-resolution simulation to achieve efficient smoke animation. The synthesized high-resolution flows can closely approximate their simulation counterparts. To produce a high-resolution flow field

we design a novel neural network that is motivated by dictionary learning and a new feature descriptor that encodes local and global information. The neural network can be used for efficient synthesis to quickly predict flow details in high resolutions. Parallel implementations of such mechanisms are realized on a GPU

with comparisons with numerical simulations to highlight the advantages of our method.