“Neural Monte Carlo Fluid Simulation”
Conference:
Type(s):
Title:
- Neural Monte Carlo Fluid Simulation
Presenter(s)/Author(s):
Abstract:
We present a novel neural network representation for fluid simulation that augments neural fields with explicitly enforced boundary conditions and a Monte Carlo pressure solver to eliminate all weakly enforced boundary conditions. Our method is mesh-free and can accurately represent vorticity phenomena like the von K?rm?n vortex street.
References:
[1]
Ryoichi Ando, Nils Th?rey, and Chris Wojtan. 2013. Highly adaptive liquid simulations on tetrahedral meshes. ACM Transactions on Graphics (TOG) 32, 4 (2013), 1?10.
[2]
Adam W Bargteil, Tolga G Goktekin, James F O?brien, and John A Strain. 2006. A semi-Lagrangian contouring method for fluid simulation. ACM Transactions on Graphics (TOG) 25, 1 (2006), 19?38.
[3]
Christopher Batty, Florence Bertails, and Robert Bridson. 2007. A fast variational framework for accurate solid-fluid coupling. ACM Transactions on Graphics (TOG) 26, 3 (2007), 100?es.
[4]
Jan Bender and Dan Koschier. 2016. Divergence-free SPH for incompressible and viscous fluids. IEEE Transactions on Visualization and Computer Graphics 23, 3 (2016), 1193?1206.
[5]
Jens Berg and Kaj Nystr?m. 2018. A unified deep artificial neural network approach to partial differential equations in complex geometries. Neurocomputing 317 (2018), 28?41.
[6]
Robert Bridson. 2015. Fluid simulation for computer graphics. CRC press.
[7]
Mark Carlson, Peter J Mucha, and Greg Turk. 2004. Rigid fluid: animating the interplay between rigid bodies and fluid. ACM Transactions on Graphics (TOG) 23, 3 (2004), 377?384.
[8]
Yue Chang, Peter Yichen Chen, Zhecheng Wang, Maurizio M Chiaramonte, Kevin Carlberg, and Eitan Grinspun. 2023. LiCROM: Linear-Subspace Continuous Reduced Order Modeling with Neural Fields. In SIGGRAPH Asia 2023 Conference Papers. 1?12.
[9]
Honglin Chen, Rundi Wu, Eitan Grinspun, Changxi Zheng, and Peter Yichen Chen. 2023b. Implicit neural spatial representations for time-dependent PDEs. In Proceedings of the 40th International Conference on Machine Learning(ICML?23). Article 202, 16 pages.
[10]
Peter Yichen Chen, Maurizio M Chiaramonte, Eitan Grinspun, and Kevin Carlberg. 2023a. Model reduction for the material point method via an implicit neural representation of the deformation map. J. Comput. Phys. 478 (2023), 111908.
[11]
Peter Yichen Chen, Jinxu Xiang, Dong Heon Cho, Yue Chang, GA Pershing, Henrique Teles Maia, Maurizio M Chiaramonte, Kevin Carlberg, and Eitan Grinspun. 2022. CROM: Continuous reduced-order modeling of PDEs using implicit neural representations. arXiv preprint arXiv:2206.02607 (2022).
[12]
Simin Chen, Zhixiang Liu, Wenbo Zhang, and Jinkun Yang. 2024. A Hard-Constraint Wide-Body Physics-Informed Neural Network Model for Solving Multiple Cases in Forward Problems for Partial Differential Equations. Applied Sciences 14, 1 (2024).
[13]
Zhiqin Chen and Hao Zhang. 2019. Learning implicit fields for generative shape modeling. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 5939?5948.
[14]
Aditya Chetan, Guandao Yang, Zichen Wang, Steve Marschner, and Bharath Hariharan. 2023. Accurate Differential Operators for Hybrid Neural Fields. arXiv preprint arXiv:2312.05984 (2023).
[15]
Alexandre Joel Chorin. 1968. Numerical Solution of the Navier-Stokes Equations. Math. Comp. 22, 104 (1968), 745?762.
[16]
Pi-Yueh Chuang and Lorena A Barba. 2022. Experience report of physics-informed neural networks in fluid simulations: pitfalls and frustration. arXiv preprint arXiv:2205.14249 (2022).
[17]
Fernando De Goes, Corentin Wallez, Jin Huang, Dmitry Pavlov, and Mathieu Desbrun. 2015. Power particles: an incompressible fluid solver based on power diagrams.ACM Trans. Graph. 34, 4 (2015), 50?1.
[18]
Tyler De Witt, Christian Lessig, and Eugene Fiume. 2012. Fluid simulation using laplacian eigenfunctions. ACM Transactions on Graphics (TOG) 31, 1 (2012), 1?11.
[19]
Yitong Deng, Hong-Xing Yu, Diyang Zhang, Jiajun Wu, and Bo Zhu. 2023. Fluid Simulation on Neural Flow Maps. ACM Trans. Graph. 42, 6, Article 248 (2023).
[20]
Ana Dodik, Oded Stein, Vincent Sitzmann, and Justin Solomon. 2023. Variational Barycentric Coordinates. ACM Transactions on Graphics (2023). https://doi.org/10.1145/3618403
[21]
Tao Du. 2023. Deep Learning for Physics Simulation. In ACM SIGGRAPH 2023 Courses. Article 6, 25 pages.
[22]
Emilien Dupont, Hyunjik Kim, SM Eslami, Danilo Rezende, and Dan Rosenbaum. 2022. From data to functa: Your data point is a function and you can treat it like one. arXiv preprint arXiv:2201.12204 (2022).
[23]
Ronald Fedkiw, Jos Stam, and Henrik Wann Jensen. 2001. Visual simulation of smoke. In Proceedings of the 28th annual conference on Computer graphics and interactive techniques. 15?22.
[24]
Yun Fei, Henrique Teles Maia, Christopher Batty, Changxi Zheng, and Eitan Grinspun. 2017. A multi-scale model for simulating liquid-hair interactions. ACM Transactions on Graphics (TOG) 36, 4 (2017), 1?17.
[25]
Marc Anton Finzi, Andres Potapczynski, Matthew Choptuik, and Andrew Gordon Wilson. 2023. A Stable and Scalable Method for Solving Initial Value PDEs with Neural Networks. In The Eleventh International Conference on Learning Representations.
[26]
Sergei K Godunov and I Bohachevsky. 1959. Finite difference method for numerical computation of discontinuous solutions of the equations of fluid dynamics. Matemati?eskij sbornik 47, 3 (1959), 271?306.
[27]
Tamara G. Grossmann, Urszula Julia Komorowska, Jonas Latz, and Carola-Bibiane Sch?nlieb. 2023. Can Physics-Informed Neural Networks beat the Finite Element Method?arxiv:2302.04107 [math.NA]
[28]
David AB Hyde and Ronald Fedkiw. 2019. A unified approach to monolithic solid-fluid coupling of sub-grid and more resolved solids. J. Comput. Phys. 390 (2019), 490?526.
[29]
Chenfanfu Jiang, Craig Schroeder, Andrew Selle, Joseph Teran, and Alexey Stomakhin. 2015. The affine particle-in-cell method. ACM Transactions on Graphics (TOG) 34, 4 (2015), 1?10.
[30]
Navami Kairanda, Marc Habermann, Christian Theobalt, and Vladislav Golyanik. 2023. Neuralclothsim: Neural deformation fields meet the kirchhoff-love thin shell theory. arXiv preprint arXiv:2308.12970 (2023).
[31]
Byungsoo Kim, Vinicius C Azevedo, Nils Thuerey, Theodore Kim, Markus Gross, and Barbara Solenthaler. 2019. Deep fluids: A generative network for parameterized fluid simulations. In Computer graphics forum, Vol. 38. Wiley Online Library, 59?70.
[32]
Theodore Kim, Nils Th?rey, Doug James, and Markus Gross. 2008. Wavelet turbulence for fluid simulation. ACM Transactions on Graphics (TOG) 27, 3 (2008), 1?6.
[33]
Nikola Kovachki, Zongyi Li, Burigede Liu, Kamyar Azizzadenesheli, Kaushik Bhattacharya, Andrew Stuart, and Anima Anandkumar. 2023. Neural Operator: Learning Maps Between Function Spaces With Applications to PDEs. Journal of Machine Learning Research 24, 89 (2023), 1?97.
[34]
Wei Li, Yixin Chen, Mathieu Desbrun, Changxi Zheng, and Xiaopei Liu. 2020. Fast and scalable turbulent flow simulation with two-way coupling. ACM Transactions on Graphics 39, 4 (2020), Art?No.
[35]
Zilu Li, Guandao Yang, Xi Deng, Christopher De Sa, Bharath Hariharan, and Steve Marschner. 2023. Neural Caches for Monte Carlo Partial Differential Equation Solvers. In SIGGRAPH Asia 2023 Conference Papers. 1?10.
[36]
Songming Liu, Hao Zhongkai, Chengyang Ying, Hang Su, Jun Zhu, and Ze Cheng. 2022. A Unified Hard-Constraint Framework for Solving Geometrically Complex PDEs. In Advances in Neural Information Processing Systems, Vol. 35. 20287?20299.
[37]
Aleka McAdams, Eftychios Sifakis, and Joseph Teran. 2010. A Parallel Multigrid Poisson Solver for Fluids Simulation on Large Grids. In Symposium on Computer Animation, Vol. 65. 74.
[38]
Lars Mescheder, Michael Oechsle, Michael Niemeyer, Sebastian Nowozin, and Andreas Geiger. 2019. Occupancy networks: Learning 3d reconstruction in function space. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 4460?4470.
[39]
Nicholas Metropolis and Stanis?aw Ulam. 1949. The Monte Carlo Method. J. Amer. Statist. Assoc. 44, 247 (1949), 335?341.
[40]
Bailey Miller, Rohan Sawhney, Keenan Crane, and Ioannis Gkioulekas. 2023. Boundary Value Caching for Walk on Spheres. ACM Trans. Graph. 42, 4, Article 82 (2023).
[41]
Fadl Moukalled, Luca Mangani, Marwan Darwish, F Moukalled, L Mangani, and M Darwish. 2016. The finite volume method. Springer.
[42]
Matthias M?ller, David Charypar, and Markus Gross. 2003. Particle-based fluid simulation for interactive applications. In Proceedings of the 2003 ACM SIGGRAPH/Eurographics symposium on Computer animation. 154?159.
[43]
Ken Museth. 2013. VDB: High-resolution sparse volumes with dynamic topology. ACM transactions on graphics (TOG) 32, 3 (2013), 1?22.
[44]
Mohammad Sina Nabizadeh, Stephanie Wang, Ravi Ramamoorthi, and Albert Chern. 2022. Covector fluids. ACM Transactions on Graphics (TOG) 41, 4 (2022), 1?16.
[45]
Jeong Joon Park, Peter Florence, Julian Straub, Richard Newcombe, and Steven Lovegrove. 2019. Deepsdf: Learning continuous signed distance functions for shape representation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 165?174.
[46]
Ziyin Qu, Xinxin Zhang, Ming Gao, Chenfanfu Jiang, and Baoquan Chen. 2019. Efficient and conservative fluids using bidirectional mapping. ACM Transactions on Graphics (TOG) 38, 4 (2019), 1?12.
[47]
Maziar Raissi, Paris Perdikaris, and George E Karniadakis. 2019. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J. Comput. Phys. 378 (2019), 686?707.
[48]
Bo Ren, Chenfeng Li, Xiao Yan, Ming C Lin, Javier Bonet, and Shi-Min Hu. 2014. Multiple-fluid SPH simulation using a mixture model. ACM Transactions on Graphics (TOG) 33, 5 (2014), 1?11.
[49]
Damien Rioux-Lavoie, Ryusuke Sugimoto, T?may ?zdemir, Naoharu H. Shimada, Christopher Batty, Derek Nowrouzezahrai, and Toshiya Hachisuka. 2022. A Monte Carlo Method for Fluid Simulation. ACM Trans. Graph. 41, 6, Article 240 (2022).
[50]
Liangwang Ruan, Jinyuan Liu, Bo Zhu, Shinjiro Sueda, Bin Wang, and Baoquan Chen. 2021. Solid-fluid interaction with surface-tension-dominant contact. ACM Transactions on Graphics (TOG) 40, 4 (2021), 1?12.
[51]
Igor Santesteban, Miguel A. Otaduy, Nils Thuerey, and Dan Casas. 2022. ULNeF: Untangled Layered Neural Fields for Mix-and-Match Virtual Try-On. In Advances in Neural Information Processing Systems, (NeurIPS).
[52]
Rohan Sawhney and Keenan Crane. 2020. Monte Carlo geometry processing: a grid-free approach to PDE-based methods on volumetric domains. ACM Trans. Graph. 39, 4, Article 123 (2020).
[53]
Rohan Sawhney and Bailey Miller. 2023. Zombie: A Grid-Free Monte Carlo Solver for PDEs.
[54]
Rohan Sawhney, Dario Seyb, Wojciech Jarosz, and Keenan Crane. 2022. Grid-free Monte Carlo for PDEs with spatially varying coefficients. ACM Trans. Graph. 41, 4, Article 53 (2022).
[55]
Rohan Sawhney, Dario Seyb, Wojciech Jarosz, and Keenan Crane. 2023. Walk on Stars: A Grid-Free Monte Carlo Method for PDEs with Neumann Boundary Conditions. ACM Trans. Graph. (2023).
[56]
Andrew Selle, Ronald Fedkiw, Byungmoon Kim, Yingjie Liu, and Jarek Rossignac. 2008. An unconditionally stable MacCormack method. Journal of Scientific Computing 35, 2 (2008), 350?371.
[57]
Rajsekhar Setaluri, Mridul Aanjaneya, Sean Bauer, and Eftychios Sifakis. 2014. SPGrid: A sparse paged grid structure applied to adaptive smoke simulation. ACM Transactions on Graphics (TOG) 33, 6 (2014), 1?12.
[58]
Vincent Sitzmann, Julien N.P. Martel, Alexander W. Bergman, David B. Lindell, and Gordon Wetzstein. 2020. Implicit Neural Representations with Periodic Activation Functions. In Proc. NeurIPS.
[59]
Barbara Solenthaler and Renato Pajarola. 2009. Predictive-corrective incompressible SPH. In ACM SIGGRAPH 2009 papers. 1?6.
[60]
Jos Stam. 1999. Stable fluids. In Proceedings of the 26th Annual Conference on Computer Graphics and Interactive Techniques(SIGGRAPH ?99). 121??128.
[61]
N. Sukumar and Ankit Srivastava. 2022. Exact imposition of boundary conditions with distance functions in physics-informed deep neural networks. Computer Methods in Applied Mechanics and Engineering 389 (2022).
[62]
Geoffrey I. Taylor and Albert E. Green. 1936. Mechanism of the Production of Small Eddies from Large Ones. Proceedings of the Royal Society of London 158, 895 (1936), 499?521.
[63]
Sifan Wang, Shyam Sankaran, Hanwen Wang, and Paris Perdikaris. 2023. An Expert?s Guide to Training Physics-informed Neural Networks. arXiv preprint arXiv:2308.08468 (2023).
[64]
Sifan Wang, Hanwen Wang, and Paris Perdikaris. 2021. Learning the solution operator of parametric partial differential equations with physics-informed DeepONets. Science advances 7, 40 (2021), eabi8605.
[65]
Guandao Yang, Serge Belongie, Bharath Hariharan, and Vladlen Koltun. 2021. Geometry Processing with Neural Fields. Advances in Neural Information Processing Systems 34 (2021).
[66]
Cem Yuksel, Donald H House, and John Keyser. 2007. Wave particles. ACM Transactions on Graphics (TOG) 26, 3 (2007), 99?es.
[67]
Jonas Zehnder, Yue Li, Stelian Coros, and Bernhard Thomaszewski. 2021. Ntopo: Mesh-free topology optimization using implicit neural representations. Advances in Neural Information Processing Systems 34 (2021), 10368?10381.
[68]
Jonas Zehnder, Rahul Narain, and Bernhard Thomaszewski. 2018. An advection-reflection solver for detail-preserving fluid simulation. ACM Transactions on Graphics (TOG) 37, 4 (2018), 1?8.
[69]
Ryan S Zesch, Vismay Modi, Shinjiro Sueda, and David IW Levin. 2023. Neural Collision Fields for Triangle Primitives. In SIGGRAPH Asia 2023 Conference Papers. 1?10.
[70]
Fangcheng Zhong, Kyle Fogarty, Param Hanji, Tianhao Wu, Alejandro Sztrajman, Andrew Spielberg, Andrea Tagliasacchi, Petra Bosilj, and Cengiz Oztireli. 2023. Neural Fields with Hard Constraints of Arbitrary Differential Order. arxiv:2306.08943 [cs.LG]
[71]
Bo Zhu, Wenlong Lu, Matthew Cong, Byungmoon Kim, and Ronald Fedkiw. 2013. A new grid structure for domain extension. ACM Transactions on Graphics (TOG) 32, 4 (2013), 1?12.
[72]
Yongning Zhu and Robert Bridson. 2005. Animating sand as a fluid. ACM Transactions on Graphics (TOG) 24, 3 (2005), 965?972.
[73]
Zeshun Zong, Xuan Li, Minchen Li, Maurizio M Chiaramonte, Wojciech Matusik, Eitan Grinspun, Kevin Carlberg, Chenfanfu Jiang, and Peter Yichen Chen. 2023. Neural Stress Fields for Reduced-order Elastoplasticity and Fracture. In SIGGRAPH Asia 2023 Conference Papers. 1?11.
