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Smoothed Particle Hydrodynamics
Techniques for the Physics Based Simulation of Fluids and Solids
Part 4 Data-driven / ML Techniques
Dan Koschier Jan Bender Barbara Solenthaler Matthias Teschner
Smoothed Particle Hydrodynamics Techniques for the Physics Based - - PowerPoint PPT Presentation
Smoothed Particle Hydrodynamics Techniques for the Physics Based - - PowerPoint PPT Presentation
Smoothed Particle Hydrodynamics Techniques for the Physics Based Simulation of Fluids and Solids Part 4 Data-driven / ML Techniques Dan Jan Barbara Matthias Koschier Bender Solenthaler Teschner Mo Moti tivati tion Substantial
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SLIDE 3
Eurographics19 Tutorial - SPH
- Substantial improvements in speed, robustness, versatility…
3
Mo Moti tivati tion
Ihmsen et al. 2013 Horvath & Solenthaler 2013
Incompressibility Multi-scale simulations
- Potential of data-driven approaches?
– PhysicsForest: Real-time SPH simulations – Deep Learning & Fluids: Related work and Outlook
- Computation time
- Trial & error, parameters
- Data reuse
- Edit & control simulations
- …
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Eurographics19 Tutorial - SPH
Real-time prediction of fluids with Regression Forests
4
Ma Machine Learn rning based Simulati tions
Ladicky et al. 2015, Apagom AG
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Eurographics19 Tutorial - SPH 5
Ph Physics cs For
- rest
Current State Next State
Sn Sn+1
Regression Model
Training Simulation training data
Data size: 165 scenes x 6s x 30fps x 1-6M particles
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Eurographics19 Tutorial - SPH 6
Ph Physics cs For
- rest
Current State
Sn
Next State
Sn+1 Test
Regression Model
1) Regression method? 2) Input and output of regression? 3) Feature vector?
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Eurographics19 Tutorial - SPH 7
Ph Physics cs For
- rest
Current State
Sn
Next State
Sn+1 Test
Regression Model
1) Regression method? 2) Input and output of regression? 3) Feature vector?
Regression Forest
[Breiman 2001]
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Eurographics19 Tutorial - SPH 8
Ph Physics cs For
- rest
Current State
Sn
Next State
Sn+1 Test
Regression Model
1) Regression method? 2) Input and output of regression? 3) Feature vector?
Regression Forest
[Breiman 2001]
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Eurographics19 Tutorial - SPH 9
Le Lear arnin ing St Strat ategie ies
Naïve approach
Feature Vector Regression Advection Collision Detection
Standard Regression Pipeline Learn accelerations
- > mimics standard SPH (no incompressibility)
Sn Sn+1
Learn velocity or acceleration? Problem: no self-correction possible
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Eurographics19 Tutorial - SPH 10
Le Lear arnin ing St Strat ategie ies
Correction approach
Feature Vector Regression Apply Correction
Correction from Advected States Learn velocity corrections
- > mimics PBD (incompressibility)
Sn Sn+1 Advection External Forces Collision Detection Collision Detection
Learn acceleration corrections
- > mimics PCISPH (incompressibility)
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Eurographics19 Tutorial - SPH 11
Fea Featur ure Vec e Vector
F
= { FR0 FR1 FR2 … FRk}
Rk
Regression Forest
[Breiman 2001]
Integral features: Flat-kernel sums of rectangular regions around particle
- Regional forces and constraints
- ver the set of boxes
- Fast evaluation
- Robust to small input deviations
- Evaluation in constant time
(linear in number of particles)
1) Regression method? 2) Input and output of regression? 3) Feature vector?
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Eurographics19 Tutorial - SPH
- Data size: 165 scenes x 6s x 30fps x 1-6M particles
- Training: 4 days on 12 CPUs
- Size of trained model: 40MB
- Only use most discriminative features (pressure, compressibility)
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Tr Training Data and Performance
1-1.5M particles in real-time
Ladicky et al. 2015
RegFluid Ground Truth
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Eurographics19 Tutorial - SPH 13
Var Varying ing M Mat ater erial P ial Proper perties ies
Feature Vector Regression Apply Correction Sn
Sn+1
Advection External Forces Collision Detection Collision Detection
- Viscosity
- Surface Tension
- Static Friction
- Adhesion
- Drag
- Vorticity Confinement
Ladicky et al. 2015
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Eurographics19 Tutorial - SPH 14
Re Real-ti time Simulati tions wi with th Ph Physics csFor
- rests
Apagom AG
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Eurographics19 Tutorial - SPH
- RegressionFluid: fast, but hand-crafted features
- > Deep Learning (DL)
- Using DL for fluids (physics) is largely unexplored!
15
Re Relate ted Wo Work
bet- al- (IOU) se- percep- SP-
Schenk & Fox 2018 Wiewel et al. 2019 Kim et al. 2019 Xie et al. 2018 Kim et al. 2019
Talk tomorrow 9:30 Talk tomorrow 10:00 Panel discussion CreativeAI tomorrow 9:30
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Eurographics19 Tutorial - SPH
- PBF with a deep neural network
- > can compute full analytical gradients (differentiable solver)
- Two new layers: ConvSP for particle-particle interactions
ConvSDF for particle-object interaction
- Robots interacting with liquids (learning parameters, control)
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SPNe Nets - Smoothed Particle Ne Network for PBF
ApplyViscosity P V
X
+
t
ApplyForces
+
Gravity
X
t
SolveConstraints
SolvePressure SolveCohesion SolveSurfaceTension
+
SolveObjectCollisions
SolveConstraints
SolvePressure SolveCohesion SolveSurfaceTension
+
SolveObjectCollisions
SolveConstraints
SolvePressure SolveCohesion SolveSurfaceTension
+
SolveObjectCollisions
- X
1 t ConvSP
Positions FeaturesConvSP
Positions Features1
X
- (t)(λv)
ρ0
X
+
P’ V’
Schenk & Fox 2018
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Eurographics19 Tutorial - SPH 17
La Latent Sp Space Physics – Learning Te Temporal Evolution
- LSTM network to predict changes of pressure field over time (3D + time) within the
latent space
- Uses a history of 6 steps to infer next [1…x] steps, followed by a regular sim step
- 155x speed-up
Wiewel et al. 2019
Talk tomorrow 10:00
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Eurographics19 Tutorial - SPH 18
𝒗
𝐝
G†(𝐯)
G(𝒅) ෝ 𝒗𝒅
𝐝 = 𝐴 𝒒 Unsupervised Supervised
E G
De DeepFl Fluids: : Gen ener erati tive e Net Net for Paramet meter erized zed Si Simulation
Simulation Data
Input Parameters
source position inflow speed … time
- Input parameterizable data set
- Generative network with supervised training
- Latent space time integration network
- >1300x compression, >700x speed-up, trained model 30MB
Kim 2019
Talk tomorrow 9:30
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Eurographics19 Tutorial - SPH 19
Te TempoGAN - Su Superresolu
- lution
ion Fl Flui uids ds
training that the solutions. en a long- such details costs and time scales. simulations typically based the under- algorithm not require ver time.
- lumetric
that infer-
𝑦𝑏 𝑦𝑢−1 𝑦𝑢
𝑦𝑢+1 𝑧𝑢−1 𝑧𝑢 𝑧𝑢+1
𝐻(𝑦𝑢−1) 𝐻(𝑦𝑢) 𝐻(𝑦𝑢+1)
𝑧𝑏 𝐻(𝑦𝑏) Xie et al. 2018
- Infer high-resolution details
- Generator, guided during training by two discriminator networks (space and time)
- Training data: low- and high-res density pairs (density, velocity, vorticity)
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Eurographics19 Tutorial - SPH
- Transfer low- and high-level style features from images to 4D fluid data
- Structurally and temporally coherent
- Pre-trained networks on images, 3d reconstruction
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Fl FlowStyle – Ne Neural Stylization of Flows
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Eurographics19 Tutorial - SPH 21
Pot Potential and and Ch Challenges of
- f Da