Data-driven simulation in fluids animation: A survey

The field of fluid simulation is developing rapidly, and data-driven methods provide many frameworks and techniques for fluid simulation. This paper presents a survey of data-driven methods used in fluid simulation in computer graphics in recent years. First, we provide a brief introduction of physicalbased fluid simulation methods based on their spatial discretization, including Lagrangian, Eulerian, and hybrid methods. The characteristics of these underlying structures and their inherent connection with datadriven methodologies are then analyzed. Subsequently, we review studies pertaining to a wide range of applications, including data-driven solvers, detail enhancement, animation synthesis, fluid control, and differentiable simulation. Finally, we discuss some related issues and potential directions in data-driven fluid simulation. We conclude that the fluid simulation combined with data-driven methods has some advantages, such as higher simulation efficiency, rich details and different pattern styles, compared with traditional methods under the same parameters. It can be seen that the data-driven fluid simulation is feasible and has broad prospects.

[1]  D. Wen,et al.  Particle-based hybrid and multiscale methods for nonequilibrium gas flows , 2019, Advances in Aerodynamics.

[2]  Barbara Solenthaler,et al.  Latent Space Subdivision: Stable and Controllable Time Predictions for Fluid Flow , 2020, Comput. Graph. Forum.

[3]  Nils Thuerey,et al.  Learning Similarity Metrics for Numerical Simulations , 2020, ICML.

[4]  Jinchao Xu,et al.  Relu Deep Neural Networks and Linear Finite Elements , 2018, Journal of Computational Mathematics.

[5]  Jan Bender,et al.  Divergence-free smoothed particle hydrodynamics , 2015, Symposium on Computer Animation.

[6]  Jinchao Xu,et al.  MgNet: A unified framework of multigrid and convolutional neural network , 2019, Science China Mathematics.

[7]  Jinlong Wu,et al.  A Physics-Informed Machine Learning Approach of Improving RANS Predicted Reynolds Stresses , 2017 .

[8]  Leon A. Gatys,et al.  A Neural Algorithm of Artistic Style , 2015, ArXiv.

[9]  Nils Thuerey,et al.  A Multi-Pass GAN for Fluid Flow Super-Resolution , 2019, PACMCGIT.

[10]  J. Brackbill,et al.  FLIP: A method for adaptively zoned, particle-in-cell calculations of fluid flows in two dimensions , 1986 .

[11]  Arnulf Jentzen,et al.  Solving high-dimensional partial differential equations using deep learning , 2017, Proceedings of the National Academy of Sciences.

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

[13]  Xi Chen,et al.  Real‐time fluid simulation with adaptive SPH , 2009, Comput. Animat. Virtual Worlds.

[14]  James F. O'Brien,et al.  Self-refining games using player analytics , 2014, ACM Trans. Graph..

[15]  Yi Li,et al.  A public turbulence database cluster and applications to study Lagrangian evolution of velocity increments in turbulence , 2008, 0804.1703.

[16]  Ronald Fedkiw,et al.  A novel algorithm for incompressible flow using only a coarse grid projection , 2010, SIGGRAPH 2010.

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

[18]  Nam Dinh,et al.  Computationally Efficient CFD Prediction of Bubbly Flow using Physics-Guided Deep Learning , 2019, International Journal of Multiphase Flow.

[19]  Ken Perlin,et al.  Accelerating Eulerian Fluid Simulation With Convolutional Networks , 2016, ICML.

[20]  Chenfanfu Jiang,et al.  The affine particle-in-cell method , 2015, ACM Trans. Graph..

[21]  Xingzhe He,et al.  Learning Physical Constraints with Neural Projections , 2020, NeurIPS.

[22]  Stefano Ermon,et al.  Learning Neural PDE Solvers with Convergence Guarantees , 2019, ICLR.

[23]  Dinesh Manocha,et al.  Efficient Solver for Spacetime Control of Smoke , 2017, ACM Trans. Graph..

[24]  Jure Leskovec,et al.  Learning to Simulate Complex Physics with Graph Networks , 2020, ICML.

[25]  P. Marais.  Ieee Transactions on Visualization and Computer Graphics 1 Warp Sculpting , 2022 .

[26]  Wolfgang Heidrich,et al.  TomoFluid: Reconstructing Dynamic Fluid From Sparse View Videos , 2020, 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR).

[27]  Tae-Yong Kim,et al.  Unified particle physics for real-time applications , 2014, ACM Trans. Graph..

[28]  Nils Thürey,et al.  Latent Space Physics: Towards Learning the Temporal Evolution of Fluid Flow , 2018, Comput. Graph. Forum.

[29]  Raia Hadsell,et al.  Graph networks as learnable physics engines for inference and control , 2018, ICML.

[30]  Talgat Daulbaev,et al.  Deep Multigrid: learning prolongation and restriction matrices , 2017, 1711.03825.

[31]  Huamin Wang,et al.  NeuralDrop: DNN-based Simulation of Small-Scale Liquid Flows on Solids , 2018, ArXiv.

[32]  Jun Zhang,et al.  Data-driven discovery of governing equations for fluid dynamics based on molecular simulation , 2020, Journal of Fluid Mechanics.

[33]  Bo Ren,et al.  Fluid directed rigid body control using deep reinforcement learning , 2018, ACM Trans. Graph..

[34]  Jing Li,et al.  A unified stochastic particle Bhatnagar-Gross-Krook method for multiscale gas flows , 2018, J. Comput. Phys..

[35]  Razvan Pascanu,et al.  Interaction Networks for Learning about Objects, Relations and Physics , 2016, NIPS.

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

[37]  Markus H. Gross,et al.  Lagrangian vortex sheets for animating fluids , 2012, ACM Trans. Graph..

[38]  T. Belytschko,et al.  Element‐free Galerkin methods , 1994 .

[39]  Raquel Urtasun,et al.  Deep Parametric Continuous Convolutional Neural Networks , 2018, 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition.

[40]  Francis H Harlow,et al.  The particle-in-cell method for numerical solution of problems in fluid dynamics , 1962 .

[41]  Wing Kam Liu,et al.  Reproducing kernel particle methods , 1995 .

[42]  Theodore Kim,et al.  Example-based turbulence style transfer , 2018, ACM Trans. Graph..

[43]  Petros Koumoutsakos,et al.  Machine Learning for Fluid Mechanics , 2019, Annual Review of Fluid Mechanics.

[44]  Rüdiger Westermann,et al.  Narrow Band FLIP for Liquid Simulations , 2016, Comput. Graph. Forum.

[45]  Afwarman Manaf,et al.  Material point method based fluid simulation on GPU using compute shader , 2017, 2017 International Conference on Advanced Informatics, Concepts, Theory, and Applications (ICAICTA).

[46]  Miles Macklin,et al.  Position based fluids , 2013, ACM Trans. Graph..

[47]  Cheng Yang,et al.  Adaptive learning‐based projection method for smoke simulation , 2018, Comput. Animat. Virtual Worlds.

[48]  Seth Holladay,et al.  Fluid carving , 2019, ACM Trans. Graph..

[49]  Robert Bridson,et al.  Animating sand as a fluid , 2005, ACM Trans. Graph..

[50]  Ronen Basri,et al.  Learning to Optimize Multigrid PDE Solvers , 2019, ICML.

[51]  Robert Youngblood,et al.  Using Deep Learning to Explore Local Physical Similarity for Global-scale Bridging in Thermal-hydraulic Simulation , 2020, Annals of Nuclear Energy.

[52]  Yoshinori Dobashi,et al.  A data-driven approach for synthesizing high-resolution animation of fire , 2012, DigiPro '12.

[53]  Nils Thürey,et al.  Data-driven synthesis of smoke flows with CNN-based feature descriptors , 2017, ACM Trans. Graph..

[54]  Justin A. Sirignano,et al.  DGM: A deep learning algorithm for solving partial differential equations , 2017, J. Comput. Phys..

[55]  Jiajun Wu,et al.  Learning Particle Dynamics for Manipulating Rigid Bodies, Deformable Objects, and Fluids , 2018, ICLR.

[56]  T. Teichmann,et al.  Mathematical Theory of Compressible Fluid Flow , 1958 .

[57]  Robert Bridson,et al.  Guide shapes for high resolution naturalistic liquid simulation , 2011, ACM Trans. Graph..

[58]  Kenneth Moreland,et al.  The FFT on a GPU , 2003, HWWS '03.

[59]  Chenfanfu Jiang,et al.  A polynomial particle-in-cell method , 2017, ACM Trans. Graph..

[60]  Jan Bender,et al.  Divergence-Free SPH for Incompressible and Viscous Fluids , 2017, IEEE Transactions on Visualization and Computer Graphics.

[61]  Vladlen Koltun,et al.  Lagrangian Fluid Simulation with Continuous Convolutions , 2020, ICLR.

[62]  Markus H. Gross,et al.  Deep Fluids: A Generative Network for Parameterized Fluid Simulations , 2018, Comput. Graph. Forum.

[63]  Leon A. Gatys,et al.  Image Style Transfer Using Convolutional Neural Networks , 2016, 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[64]  Eftychios Sifakis,et al.  A scalable schur-complement fluids solver for heterogeneous compute platforms , 2016, ACM Trans. Graph..

[65]  Nobuhide Kasagi,et al.  A New Approach to the Improvement of k-ε Turbulence Model for Wall-Bounded Shear Flows , 1990 .

[66]  Matthias Teschner,et al.  IISPH‐FLIP for incompressible fluids , 2014, Comput. Graph. Forum.

[67]  M. Gross,et al.  A multiscale approach to mesh-based surface tension flows , 2010, SIGGRAPH 2010.

[68]  Nils Thuerey,et al.  Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solvers , 2020, NeurIPS.

[69]  Nils Thuerey,et al.  Deep Learning Methods for Reynolds-Averaged Navier–Stokes Simulations of Airfoil Flows , 2018, AIAA Journal.

[70]  Z. Popovic,et al.  Model reduction for real-time fluids , 2006, SIGGRAPH 2006.

[71]  Hui Wang,et al.  A CNN‐based Flow Correction Method for Fast Preview , 2019, Comput. Graph. Forum.

[72]  Jieyu Chu,et al.  A schur complement preconditioner for scalable parallel fluid simulation , 2017, TOGS.

[73]  Yoshinori Dobashi,et al.  Editing Fluid Animation Using Flow Interpolation , 2018, ACM Trans. Graph..

[74]  Xiangyu Hu,et al.  Liquid Splash Modeling with Neural Networks , 2017, Comput. Graph. Forum.

[75]  Juncai He sci.  Relu Deep Neural Networks and Linear Finite Elements , 2020 .

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

[77]  Zachary Chase Lipton.  The mythos of model interpretability , 2016, ACM Queue.

[78]  Dimitris N. Metaxas,et al.  Controlling fluid animation , 1997, Proceedings Computer Graphics International.

[79]  Nils Thuerey,et al.  ScalarFlow , 2019, ACM Trans. Graph..

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

[81]  Thomas Brox,et al.  Artistic Style Transfer for Videos , 2016, GCPR.

[82]  Leif Kobbelt,et al.  A survey of point-based techniques in computer graphics , 2004, Comput. Graph..

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

[84]  Multiscale investigation of Kolmogorov flow: From microscopic molecular motions to macroscopic coherent structures , 2019, Physics of Fluids.

[85]  Karthik Duraisamy,et al.  Turbulence Modeling in the Age of Data , 2018, Annual Review of Fluid Mechanics.

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

[87]  Nils Thürey.  Interpolations of smoke and liquid simulations , 2017, ACM Trans. Graph..

[88]  Dimitrios I. Fotiadis,et al.  Artificial neural networks for solving ordinary and partial differential equations , 1997, IEEE Trans. Neural Networks.

[89]  Barbara Solenthaler,et al.  Lagrangian neural style transfer for fluids , 2020, ACM Trans. Graph..

[90]  Jun-yong Noh,et al.  A heterogeneous CPU–GPU parallel approach to a multigrid Poisson solver for incompressible fluid simulation , 2013, Comput. Animat. Virtual Worlds.

[91]  Andre Pradhana,et al.  GPU optimization of material point methods , 2018, ACM Trans. Graph..

[92]  Vipin Kumar,et al.  Integrating Physics-Based Modeling with Machine Learning: A Survey , 2020, ArXiv.

[93]  Bin Dong,et al.  PDE-Net 2.0: Learning PDEs from Data with A Numeric-Symbolic Hybrid Deep Network , 2018, J. Comput. Phys..

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

[95]  P. Colella,et al.  Local adaptive mesh refinement for shock hydrodynamics , 1989 .

[96]  Achmad Imam Kistijantoro,et al.  Fluid Simulation Based on Material Point Method with Neural Network , 2019, 2019 International Conference of Artificial Intelligence and Information Technology (ICAIIT).

[97]  Eric P. Xing,et al.  GeePS: scalable deep learning on distributed GPUs with a GPU-specialized parameter server , 2016, EuroSys.

[98]  Andre Pradhana,et al.  A moving least squares material point method with displacement discontinuity and two-way rigid body coupling , 2018, ACM Trans. Graph..

[99]  Sarah Tariq,et al.  Scalable fluid simulation using anisotropic turbulence particles , 2010, ACM Trans. Graph..

[100]  Byungsoo Kim,et al.  Transport-based neural style transfer for smoke simulations , 2019, ACM Trans. Graph..

[101]  Yuan Yu,et al.  TensorFlow: A system for large-scale machine learning , 2016, OSDI.

[102]  J. Templeton,et al.  Reynolds averaged turbulence modelling using deep neural networks with embedded invariance , 2016, Journal of Fluid Mechanics.

[103]  Jiancheng Liu,et al.  ChainQueen: A Real-Time Differentiable Physical Simulator for Soft Robotics , 2018, 2019 International Conference on Robotics and Automation (ICRA).

[104]  Wolfgang Heidrich,et al.  Stereo Event-Based Particle Tracking Velocimetry for 3D Fluid Flow Reconstruction , 2020, ECCV.

[105]  Pedro M. Milani,et al.  Physical Interpretation of Machine Learning Models Applied to Film Cooling Flows , 2018, Journal of Turbomachinery.

[106]  V. Avsarkisov,et al.  Turbulent plane Couette flow at moderately high Reynolds number , 2014, Journal of Fluid Mechanics.

[107]  J. Monaghan.  Smoothed particle hydrodynamics , 2005 .

[108]  Ramis Örlü,et al.  Assessment of direct numerical simulation data of turbulent boundary layers , 2010, Journal of Fluid Mechanics.

[109]  Cheng Yang,et al.  Data‐driven projection method in fluid simulation , 2016, Comput. Animat. Virtual Worlds.

[110]  N. Dinh,et al.  Classification of machine learning frameworks for data-driven thermal fluid models , 2018, International Journal of Thermal Sciences.

[111]  J. Monaghan.  Smoothed particle hydrodynamics , 2005 .

[112]  Matthias Müller,et al.  Real-time Eulerian water simulation using a restricted tall cell grid , 2011, ACM Trans. Graph..

[113]  Bo Zhu,et al.  Neural Vortex Method: from Finite Lagrangian Particles to Infinite Dimensional Eulerian Dynamics , 2020, Computers & Fluids.

[114]  Xubo Yang,et al.  An adaptive staggered-tilted grid for incompressible flow simulation , 2020, ACM Trans. Graph..

[115]  Julia Ling,et al.  Physical Interpretation of Machine Learning Models Applied to Film Cooling Flows , 2018, Volume 5A: Heat Transfer.

[116]  Yongning Zhu,et al.  Animating sand as a fluid , 2005, SIGGRAPH 2005.

[117]  Mykel J. Kochenderfer,et al.  Deep Dynamical Modeling and Control of Unsteady Fluid Flows , 2018, NeurIPS.

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

[119]  Natalia Gimelshein,et al.  PyTorch: An Imperative Style, High-Performance Deep Learning Library , 2019, NeurIPS.