Abstract
In this chapter, we consider perspectives in deep learning for fluid animation. Firstly, the input data generation for neural network training depends on simulating fluid dynamics using traditional methods to produce the training data, which is time-consuming. To address this issue, we describe the basic model for physics-informed neural networks (PINNs) applied to the Navier–Stokes simulation. In this case, the fluid equations and the initial and boundary conditions are included in the model as new terms in the loss function, which can reduce the necessity for large training databases. Secondly, the success of deep architectures happens with the increase in the difficulties of understanding how deep neural networks come to decisions. This fact motivates the development of explainable artificial intelligence (XAI) techniques, like Shapley additive explanations (SHAP), to quantify the importance of hidden layers for model outcomes. From the rendering perspective, machine learning is a new approach that brings many exciting possibilities to improve visual results for the entertainment industry. But at the same time, it still has drawbacks to scientific applications, where visual accuracy is a vital requirement. We end the material by discussing how machine learning techniques improve the rendering algorithms.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Tianqi Chen and Carlos Guestrin. Xgboost: A scalable tree boosting system. Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2016.
Chen Cheng and Guang-Tao Zhang. Deep learning method based on physics informed neural network with resnet block for solving fluid flow problems. Water, 13, 02 2021.
Fabienne Christen, Byungsoo Kim, Vinicius C. Azevedo, and Barbara Solenthaler. Neural Smoke Stylization with Color Transfer. arXiv preprint arXiv:1912.08757, pages 2–5, 2019.
Mengyu Chu, Lingjie Liu, Quan Zheng, Erik Franz, Hans-Peter Seidel, Christian Theobalt, and Rhaleb Zayer. Physics informed neural fields for smoke reconstruction with sparse data. ACM Trans. Graph., 41(4), Jul 2022.
SM Ali Eslami, Danilo Jimenez Rezende, Frederic Besse, Fabio Viola, Ari S Morcos, Marta Garnelo, Avraham Ruderman, Andrei A Rusu, Ivo Danihelka, Karol Gregor, et al. Neural scene representation and rendering. Science, 360(6394):1204–1210, 2018.
Xiaowei Jin, Shengze Cai, Hui Li, and George Em Karniadakis. Nsfnets (navier-stokes flow nets): Physics-informed neural networks for the incompressible navier-stokes equations. J. Comput. Phys., 426:109951, 2021.
Simon Kallweit, Thomas Müller, Brian Mcwilliams, Markus Gross, and Jan Novák. Deep scattering: Rendering atmospheric clouds with radiance-predicting neural networks. ACM Transactions on Graphics (TOG), 36(6):1–11, 2017.
Ali Kamali, Mohammad Sarabian, and Kaveh Laksari. Elasticity imaging using physics-informed neural networks: Spatial discovery of elastic modulus and poisson’s ratio. Acta biomaterialia, 2022.
George Karniadakis, Yannis Kevrekidis, Lu Lu, Paris Perdikaris, Sifan Wang, and Liu Yang. Physics-informed machine learning. Nature Reviews, pages 1–19, 05 2021.
Karthik Kashinath, M Mustafa, Adrian Albert, Jinlong Wu, C Jiang, Soheil Esmaeilzadeh, Kamyar Azizzadenesheli, R Wang, Ashesh Chattopadhyay, A Singh, A Manepalli, D Chirila, R Yu, R Walters, B White, Heng Xiao, Hamdi Tchelepi, P Marcus, Animashree Anandkumar, and Mr Prabhat. Physics-informed machine learning: Case studies for weather and climate modelling. Philosophical transactions. Series A, Mathematical, physical, and engineering sciences, 379:20200093, 04 2021.
Hiroharu Kato, Deniz Beker, Mihai Morariu, Takahiro Ando, Toru Matsuoka, Wadim Kehl, and Adrien Gaidon. Differentiable Rendering: A Survey. arXiv preprint arXiv:2006.12057, 14(8):1–20, 2020.
Byungsoo Kim, Vinicius C. Azevedo, Markus Gross, and Barbara Solenthaler. Transport-based neural style transfer for smoke simulations. ACM Transactions on Graphics, 38(6):1–11, 2019.
Byungsoo Kim, Vinicius C. Azevedo, Markus Gross, and Barbara Solenthaler. Lagrangian neural style transfer for fluids. ACM Trans. Graph., 39(4), Jul 2020.
Byungsoo Kim, Xingchang Huang, Laura Wuelfroth, Jingwei Tang, Guillaume Cordonnier, Markus Gross, and Barbara Solenthaler. Deep reconstruction of 3d smoke densities from artist sketches. Computer Graphics Forum, 41(2):97–110, 2022.
Martin Lellep, Jonathan Prexl, Bruno Eckhardt, and Moritz Linkmann. Interpreted machine learning in fluid dynamics: Explaining relaminarisation events in wall-bounded shear flows. Journal of Fluid Mechanics, 2021.
Pantelis Linardatos, Vasilis Papastefanopoulos, and Sotiris Kotsiantis. Explainable ai: A review of machine learning interpretability methods. Entropy, 23(1):1–45, 2021.
Scott M. Lundberg and Su-In Lee. A unified approach to interpreting model predictions. ArXiv, abs/1705.07874, 2017.
Charles C Margossian. A review of automatic differentiation and its efficient implementation. Wiley interdisciplinary reviews: data mining and knowledge discovery, 9(4):e1305, 2019.
Pasindu Meddage, Imesh Udara Ekanayake, Udara Sachinthana Perera, Hazi Md. Azamathulla, Md. Azlin Md. Said, and Upaka S. Rathnayake. Interpretation of machine-learning-based (black-box) wind pressure predictions for low-rise gable-roofed buildings using shapley additive explanations (shap). Buildings, 2022.
Ben Mildenhall, Pratul P. Srinivasan, Matthew Tancik, Jonathan T. Barron, Ravi Ramamoorthi, and Ren Ng. Nerf: Representing scenes as neural radiance fields for view synthesis. ArXiv, abs/2003.08934, 2020.
Grégoire Montavon, Wojciech Samek, and Klaus-Robert Müller. Methods for interpreting and understanding deep neural networks. Digital Signal Processing, 73:1–15, 2018.
Keunhong Park, Utkarsh Sinha, Jonathan T Barron, Sofien Bouaziz, Dan B Goldman, Steven M Seitz, and Ricardo Martin-Brualla. Nerfies: Deformable neural radiance fields. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 5865–5874, 2021.
Rahul Rai and Chandan K. Sahu. Driven by data or derived through physics? a review of hybrid physics guided machine learning techniques with cyber-physical system (cps) focus. IEEE Access, 8:71050–71073, 2020.
Ribana Roscher, Bastian Bohn, Marco F. Duarte, and Jochen Garcke. Explainable Machine Learning for Scientific Insights and Discoveries. IEEE Access, 8:42200–42216, 2020.
Bruno Roy, Pierre Poulin, and Eric Paquette. Neural UpFlow: A Scene Flow Learning Approach to Increase the Apparent Resolution of Particle-Based Liquids. ACM Transactions on Graphics, 1(1):1–14, 2021.
Farnood Salehi, Marco Manzi, Gerhard Roethlin, Romann Weber, Christopher Schroers, and Marios Papas. Deep adaptive sampling and reconstruction using analytic distributions. ACM Transactions on Graphics (TOG), 41(6):1–16, 2022.
Wojciech Samek, Thomas Wiegand, and Klaus-Robert Müller. Explainable artificial intelligence: Understanding, visualizing and interpreting deep learning models. ArXiv, abs/1708.08296, 2017.
Anju Tewari, Otto Fried, Justus Thies, Vincent Sitzmann, S. Lombardi, Z Xu, Tanaba Simon, Matthias Nießner, Edgar Tretschk, L. Liu, Ben Mildenhall, Pranatharthi Srinivasan, R. Pandey, Sergio Orts-Escolano, S. Fanello, M. Guang Guo, Gordon Wetzstein, J y Zhu, Christian Theobalt, Manju Agrawala, Donald B. Goldman, and Michael Zollhöfer. Advances in neural rendering. Computer Graphics Forum, 41, 2021.
Marcelo Bernardes Vieira, Gilson Antonio Giraldi, Allan Carlos Amaral Ribeiro, Marcelo Caniato Renhe, and Claudio Esperança. Anisotropic helmholtz decomposition for controlled fluid simulation. Appl. Math. Comput., 411:126501, 2021.
Laura von Rueden, Sebastian Mayer, Jochen Garcke, Christian Bauckhage, and Jannis Schücker. Informed machine learning - towards a taxonomy of explicit integration of knowledge into machine learning. ArXiv, abs/1903.12394, 2019.
Jiří Vorba, Ondřej Karlík, Martin Šik, Tobias Ritschel, and Jaroslav Křivánek. On-line learning of parametric mixture models for light transport simulation. ACM Transactions on Graphics (TOG), 33(4):1–11, 2014.
Daniel S. Weld and Gagan Bansal. The challenge of crafting intelligible intelligence. Communications of the ACM, 62:70–79, 2019.
Jared D. Willard, Xiaowei Jia, Shaoming Xu, Michael S. Steinbach, and Vipin Kumar. Integrating physics-based modeling with machine learning: A survey. ArXiv, abs/2003.04919, 2020.
Jin-Long Wu, Heng Xiao, and Eric Paterson. Physics-informed machine learning approach for augmenting turbulence models: A comprehensive framework. Phys. Rev. Fluids, 3:074602, Jul 2018.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Antonio Giraldi, G., Almeida, L.R.d., Lopes Apolinário Jr., A., Silva, L.T.d. (2023). Perspectives and Final Remarks. In: Deep Learning for Fluid Simulation and Animation. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-031-42333-8_9
Download citation
DOI: https://doi.org/10.1007/978-3-031-42333-8_9
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-42332-1
Online ISBN: 978-3-031-42333-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)