Fast Data-Driven Grid-Based Fluid Simulation

Physically-based fluid simulation is one of the important topics in computer graphics.It needs to solve nonlinear partial differential equations,Navier-Stokes Equations(N-S equations),in the simulation process.Lagrangian methods and Eulerian methods have been proposed to solve N-S equations discretely.In high-resolution simulation field,Eulerian methods are widely used.However,it is inconvenient that Eulerian methods need to consume a lot of computing resource to solve Poisson equation in the projection step.In grid-based fluid simulation,the solving process of Poisson equation needs to iterate many times to obtain numerical solutions.Data-driven methods could effectively avoid the iteration steps.However,data-driven methods are not applicable to all solving steps.If the feature vector in the mapping relation between input data and output data includes too many dimensions,the computing process will become more time-consuming.The projection step is the most time-consuming step in the whole simulation process.More importantly,the solving method in the projection step and the relationship between input data and output data are both pretty stable.We propose a novel data-driven method and an adaptive data-driven framework in this paper to speed up the projection step and the whole process of grid-based simulation.Artificial neural network is a powerful machine learning tool,which is widely used in classification and numerical fitting problems.In this paper,the data-driven fluid simulation method and the data-driven framework based on artificial neural network both have the following features:1.Realistic visual effect.Data-driven methods could maintain the nonlinear mapping relation between input data and output data as accurately as possible.It makes data-driven simulation results visually acceptable.2.Fast simulation.Once the artificial neural network is trained completely,the computing time to solve Poisson equation in each grid is constant.It could effectively avoid the time-consuming iterations in traditional methods.3.Generality.The adaptive data-driven framework proposed in this paper only obviously changes the projection step in the grid-based fluid simulation process.Other grid-based fluid simulation methods are easy to integrate into our framework.4.Satisfactory extrapolation ability.The relationship between input data and output data in the Poisson equation is stable,so our data-driven method is applicable in various fluid scenes with some alterations.In addition,with well-designed incremental learning framework,the scope of the method could further expand.