Deep Learning for Fluid Simulation and Animation: Fundamentals, Modeling, and Case Studies

Preface
Contents
Acronyms
1 Introductory Material to Animation and Learning
	1.1 Introduction
2 Fluids and Deep Learning: A Brief Review
	2.1 Introduction
	2.2 Fluid Modeling and Neural Networks
	2.3 Fluid Rendering
3 Fluid Modeling Through Navier–Stokes Equations and Numerical Methods
	3.1 Introduction
	3.2 Navier–Stokes Equations
		3.2.1 Conservation of Mass
		3.2.2 Conservation of Linear Momentum
	3.3 Smoothed Particle Hydrodynamics (SPH)
		3.3.1 Standard Approach
			3.3.1.1 Gaussian Function
			3.3.1.2 Spline Function
		3.3.2 Volume Maps
		3.3.3 Divergence-Free Smoothed Particle Hydrodynamics
		3.3.4 Versatile Rigid-Fluid Coupling for Incompressible SPH
			3.3.4.1 Boundary-Fluid Pressure Force
			3.3.4.2 Boundary-Fluid Friction Force
	3.4 Stable Fluids
4 Neural Networks Universality, Geometric, and Dynamical System Elements for Fluid Animation
	4.1 Introduction
	4.2 Neural Networks and Universality
		4.2.1 Boolean Expressions
		4.2.2 Circuit Theory
		4.2.3 Multilayer Perceptron Model
	4.3 Activation Functions
	4.4 Neural Networks as Universal Computing Model
	4.5 Regular Surfaces and Differentiable Manifolds
	4.6 Data Model and Learning
	4.7 Hamiltonian Systems and Fluids
5 Data and Learning Theory
	5.1 Introduction
	5.2 Learning From Examples: Mathematical Perspective
	5.3 Optimizing the Loss Function
	5.4 Train, Validation, and Test Stages
6 Modeling Fluids Through Neural Networks
	6.1 Introduction
	6.2 Deep Architectures and Fluid Simulation
		6.2.1 Convolutional Neural Networks: CNNs
		6.2.2 Generative Adversarial Network: GAN
7 Fluid Rendering
	7.1 Introduction
		7.1.1 The Rendering Process in Fluid Simulation
	7.2 Traditional Techniques
		7.2.1 Surface Extraction
		7.2.2 Screen-Space Approaches
		7.2.3 Volume Rendering
	7.3 Advanced Techniques
		7.3.1 Optical Effects
		7.3.2 Bubble, Spray, Foam, and Droplets
		7.3.3 Optimizations
	7.4 Machine Learning in Rendering
		7.4.1 Neural Rendering
		7.4.2 Differentiable Rendering
	7.5 Machine Learning in Fluid Rendering
8 Case Studies
	8.1 Introduction
	8.2 Lagrangian Fluid Simulation with Continuous Convolutions
		8.2.1 Comparison with SPlisHSPlasH Simulation
		8.2.2 Rendering Liquids
	8.3 TempoGAN: GAN for Super-resolution Fluid Flow
		8.3.1 TempoGAN Results
9 Perspectives and Final Remarks
	9.1 Introduction
	9.2 Physics-Informed Neural Networks for Fluid Animation
	9.3 Explainable Artificial Intelligence for Fluid Simulation
	9.4 Machine Learning and Fluid Rendering
	9.5 Final Remarks
References
Index