Research On Deep Neural Network Based Fluid Simulation

Physically-based fluid simulation is one of the most important research directions in computer graphics,and fluid animation can be widely used in visual effects production applications,game design,disaster accident simulation.Therefore,how to simulate large-scale,highresolution,high-quality fluid,e.g.,smoke,liquid,and many other natural fluid phenomena,in a more effective way has become a hot research direction in computer graphics.However,with the increasing demand for visual effects of movies,games,as well as the continuous deepening and growth of industrial needs and practical applications,various traditional fluid simulation methods are facing unprecedented challenges.In many traditional fluid simulation frameworks based on Eulerian grid methods,the most time-consuming and computing resources consumption sub-process is the projection step,especially for high-resolution fluid simulations.Most simulation algorithms have their shortcomings in terms of calculation speed or computational efficiency.For example,many fluid simulation methods lack effective projection step calculation acceleration schemes,which may suffer from high computation time,complicated programming or unacceptable computational memory consumption.Those methods cannot balance calculation accuracy and computational efficiency,and there are deficiencies in algorithm design and applications.Furthermore,many numerical acceleration algorithms have been proposed to solve the Poisson equation in the projection step,which leads to a large sparse linear system.In order to obtain the convergent solution,most numerical methods,such as preconditioned conjugate gradient method(PCG),need to solve the equation iteratively,which makes the entire fluid simulation process timeconsuming,and unable to achieve the real-time calculation mode.In addition,due to the numerical viscosity and computational error of those traditional numerical algorithms,the simulation process would produce simulation results with different flow shapes at different resolutions,while the parameter settings are all the same.In other words,the low-resolution simulation results would have huge differences with the corresponding high-resolution fluid simulation results in the overall flow shapes,which makes the cost of preview increased greatly and reduce the interaction efficiency of those fluid simulation algorithms.Many fluid simulation algorithms based on deep learning are limited by the high dimensionality of data of fluid variables in discrete space,which affects the study of the simulation acceleration and the essential characteristics of fluid and even affects the practical application and popularization of this kind of simulation and acceleration algorithms.To solve those problems above and consider the requirements of fluid simulation methods in calculation accuracy and simulation efficiency in real-time,high interactivity and high physically-accuracy applications,we propose solution schemes based on deep neural network methods.With the in-depth development of artificial intelligence technologies,deep learning algorithms have been widely used in image classification,speech recognition,fluid detail synthesis and many other scientific research domains with their powerful data learning capability.The robust and efficient calculation mode provides a new solving direction for the problem of fluid animation problem.Therefore,this thesis employs deep neural network methods and focuses on the following aspects in physically-based fluid simulation:· We propose a projection solver using a deep neural network(DNN).In many traditional Eulerian grid-based fluid simulation frameworks,the computational bottleneck is the projection process,which is the most computationally expensive,memory demanding and time-consuming sub-process.In this part,we propose a deep neural network model to accelerate the projection solving process.We also introduce a patch-based grid structure to construct the corresponding input and output feature vectors,and reduce the dimension of the training data,which can improve the training and prediction efficiency of our deep learning algorithm.Then,we incorporate the divergence items in the loss function to ensure the incompressibility of the prediction fluid results.Compared with the traditional projection methods,our method can speed up more than 17 times in the projection process.At the same time,we propose an adaptive learning based projection solver based on incremental learning technique,which aims at improving the stability and robustness of the deep neural network based projection solver.We introduce two modes: "fast mode" and "normal mode" as the basic projection solving modes,which combines the preconditioned conjugate gradient method(PCG)with the deep neural network based projection solver.In this framework,we use the incremental learning method to quickly update the deep neural model in the “fast mode”by self-learning from the target simulation scene,and improve the prediction accuracy in scenes that far away from the training scenes as well as much more complex fluid scenes.· We propose a novel convolutional neural network(CNN)based Poisson solver for fast fluid simulation.Through the analysis of the large-scale sparse linear system generated by the discretization process of the fluid Poisson equation,we introduce a globalbased feature matrix/vector with a hierarchical geometric structure,which can efficiently represent the large sparse matrix-vector and reduce the dimension of the input/output matrices/vectors for the pressure Poisson equation.Moreover,we build a training data generation system,which combines the manually designed training scenes and the randomly synthesized scenes,we can generate rich training samples for our CNN model.This model aims at solving the essential problem of the Poisson equation,i.e.,solving the large sparse linear equations Ap = d,to improve the computational efficiency of the projection calculation.We also compare our method with many traditional iterative methods,such as ICPCG,MIC-CG(0),and MG-PCG methods,which can show the computational efficiency of our method.Through the test scenes of smoke and liquid,we can prove that our method can be applied in many complex fluid scenes.We also consider the incompressibility of the prediction results of the deep learning model in the loss function.In the liquid simulation scenes,we also propose a special free surface neural network to further improve the prediction results.· We propose a novel convolutional neural network based flow correction method for fast smoke preview and details enhancement.Due to the different numerical dissipation on grid resolutions and the nonlinearity of the fluid equations,the differences in simulation resolutions will result in different flow shapes.This makes it challenging for artists to preview the animation results based on low-resolution simulations.we propose a deep neural network based flow correction method for fast flow 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.· We propose a novel fluid system analysis method based on phase space.Most fluid simulation algorithms can not avoid the computational difficulties caused by the high dimensional data in the Euclidean space,thus,these algorithms can not effectively analyze the nature and the features of non-linear systems such as fluid.In this section,we attempt to map the variables of non-linear physical systems such as fluids into phase space and construct features with low-dimensional manifold characteristics,and further transform the related problems into typical geometric problems.At the same time,we also combine the classical deep learning algorithms in geometric space,such as Point Net,based on those variables in fluid phase space,and carried out a series of exploratory applications.In detail,the geometric manifold characteristics of single pendulum,double pendulum and fluid system in the corresponding phase space are preliminarily studied,we also show the properties of different phase spaces formed by different bases.For single pendulum and double pendulum systems,we complete the extended applications such as classification and recognition.For fluid simulation,we introduce the Strain Tensor and Rotate Tensor to construct the corresponding fluid phase space,and further complete the fluid recognition based on this space.