Data‐driven projection method in fluid simulation

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.

[1]  Milton S. Boyd,et al.  Designing a neural network for forecasting financial and economic time series , 1996, Neurocomputing.

[2]  Claudio Moraga,et al.  The Influence of the Sigmoid Function Parameters on the Speed of Backpropagation Learning , 1995, IWANN.

[3]  Marina Fruehauf,et al.  Nonlinear Programming Analysis And Methods , 2016 .

[4]  Christopher Wojtan,et al.  A Dimension‐reduced Pressure Solver for Liquid Simulations , 2015, Comput. Graph. Forum.

[5]  Ming C. Lin,et al.  Fast animation of turbulence using energy transport and procedural synthesis , 2008, SIGGRAPH Asia '08.

[6]  Doug L. James,et al.  Wavelet turbulence for fluid simulation , 2008, SIGGRAPH 2008.

[7]  Ronald Fedkiw,et al.  Practical animation of liquids , 2001, SIGGRAPH.

[8]  Martin T. Hagan,et al.  Neural network design , 1995 .

[9]  Barbara Solenthaler,et al.  Data-driven fluid simulations using regression forests , 2015, ACM Trans. Graph..

[10]  Ronald Fedkiw,et al.  A new grid structure for domain extension , 2013, ACM Trans. Graph..

[11]  Ronald Fedkiw,et al.  Simulating water and smoke with an octree data structure , 2004, ACM Trans. Graph..

[12]  J. Stam Real-Time Fluid Dynamics for Games , 2003 .

[13]  Eftychios Sifakis,et al.  A parallel multigrid Poisson solver for fluids simulation on large grids , 2010, SCA '10.

[14]  Russell J. Athay,et al.  Proceedings of the 13th annual conference on Computer graphics and interactive techniques , 1986, International Conference on Computer Graphics and Interactive Techniques.

[15]  Adrien Treuille,et al.  Model reduction for real-time fluids , 2006, ACM Trans. Graph..

[16]  Jos Stam,et al.  Stable fluids , 1999, SIGGRAPH.

[17]  Takeo Kanade,et al.  Neural Network-Based Face Detection , 1998, IEEE Trans. Pattern Anal. Mach. Intell..

[18]  Greg Turk,et al.  Blending liquids , 2014, ACM Trans. Graph..

[19]  Geoffrey E. Hinton,et al.  ImageNet classification with deep convolutional neural networks , 2012, Commun. ACM.

[20]  F. Harlow,et al.  Numerical Calculation of Time‐Dependent Viscous Incompressible Flow of Fluid with Free Surface , 1965 .

[21]  Markus H. Gross,et al.  Particle-based fluid simulation for interactive applications , 2003, SCA '03.

[22]  Ronald Fedkiw,et al.  Visual simulation of smoke , 2001, SIGGRAPH.

[23]  Eitan Grinspun,et al.  Sparse matrix solvers on the GPU: conjugate gradients and multigrid , 2003, ACM Trans. Graph..