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 improvements in speed, robustness, versatility… Incompressibility Multi-scale simulations Ihmsen et al. 2013 Horvath & Solenthaler 2013 Computation time • • Potential of data-driven approaches? Trial & error, parameters • Data reuse – PhysicsForest: Real-time SPH simulations • Edit & control simulations • – Deep Learning & Fluids: Related work and Outlook … • Eurographics19 Tutorial - SPH 3

Ma Machine Learn rning based Simulati tions Real-time prediction of fluids with Regression Forests Ladicky et al. 2015, Apagom AG Eurographics19 Tutorial - SPH 4

Training Simulation training data Ph Physics cs For orest Next State Current State S n S n+1 Regression Model Data size: 165 scenes x 6s x 30fps x 1-6M particles Eurographics19 Tutorial - SPH 5

Test Ph Physics cs For orest 1) Regression method? 2) Input and output of regression? 3) Feature vector? Regression S n Model Current State S n+1 Next State Eurographics19 Tutorial - SPH 6

Test Ph Physics cs For orest 1) Regression method? 2) Input and output of regression? 3) Feature vector? Regression S n Model Regression Current State Forest [Breiman 2001] S n+1 Next State Eurographics19 Tutorial - SPH 7

Test Ph Physics cs For orest 1) Regression method? 2) Input and output of regression? 3) Feature vector? Regression S n Model Regression Current State Forest [Breiman 2001] S n+1 Next State Eurographics19 Tutorial - SPH 8

Le Lear arnin ing St Strat ategie ies Learn velocity or acceleration? Problem: no self-correction possible Standard Regression Pipeline Naïve approach Feature Collision S n Regression Advection S n+1 Vector Detection Learn accelerations -> mimics standard SPH (no incompressibility) Eurographics19 Tutorial - SPH 9

Le Lear arnin ing St Strat ategie ies Correction from Advected States Collision External Advection S n Correction Detection Forces approach Feature Apply Collision Regression S n+1 Vector Correction Detection Learn acceleration corrections -> mimics PCISPH (incompressibility) Learn velocity corrections -> mimics PBD (incompressibility) Eurographics19 Tutorial - SPH 10

Fea Featur ure Vec e Vector 1) Regression method? 2) Input and output of regression? Integral features: 3) Feature vector? R k Flat-kernel sums of rectangular regions around particle F • Regional forces and constraints over the set of boxes • Fast evaluation Regression • Robust to small input deviations Forest • Evaluation in constant time [Breiman 2001] = { F R 0 F R 1 F R 2 … F R k } (linear in number of particles) Eurographics19 Tutorial - SPH 11

Tr Training Data and Performance • 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) 1-1.5M particles in real-time Ground Truth RegFluid Ladicky et al. 2015 Eurographics19 Tutorial - SPH 12

Var Varying ing M Mat ater erial P ial Proper perties ies External Collision Advection S n Forces Detection Feature Apply Collision Regression S n+1 Vector Correction Detection Viscosity • Surface Tension • Static Friction • Adhesion • Drag • Vorticity Confinement • Ladicky et al. 2015 Eurographics19 Tutorial - SPH 13

Re Real-ti time Simulati tions wi with th Ph Physics csFor orests Apagom AG Eurographics19 Tutorial - SPH 14

Relate Re ted Wo Work • RegressionFluid: fast, but hand-crafted features -> Deep Learning (DL) • Using DL for fluids (physics) is largely unexplored! Talk tomorrow 9:30 Talk tomorrow 10:00 bet- al- (IOU) se- percep- SP- Wiewel et al. 2019 Kim et al. 2019 Schenk & Fox 2018 Panel discussion CreativeAI tomorrow 9:30 Xie et al. 2018 Kim et al. 2019 Eurographics19 Tutorial - SPH 15

SPNe Nets - Smoothed Particle Ne Network for PBF • PBF with a deep neural network V P � t Gravity + + -> can compute full analytical gradients (differentiable solver) X X � t ApplyForces • Two new layers: ConvSP for particle-particle interactions SolveCohesion SolvePressure SolveSurfaceTension ConvSDF for particle-object interaction + SolveObjectCollisions SolveConstraints • Robots interacting with liquids (learning parameters, control) SolvePressure SolveCohesion SolveSurfaceTension + SolveObjectCollisions SolveConstraints SolvePressure SolveCohesion SolveSurfaceTension + SolveObjectCollisions SolveConstraints - 1 X � t 1 Positions Features Positions Features ConvSP ConvSP ( � t)( λ v ) X ρ 0 - + X ApplyViscosity P’ V’ Schenk & Fox 2018 Eurographics19 Tutorial - SPH 16

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 Talk tomorrow 10:00 Wiewel et al. 2019 Eurographics19 Tutorial - SPH 17

DeepFl De Fluids: : Gen ener erati tive e Net Net for Paramet meter erized zed Si Simulation • Input parameterizable data set • Generative network with supervised training • Latent space time integration network • >1300x compression, >700x speed-up, trained model 30MB Simulation Data G G † (𝐯) 𝐝 G(𝒅) Input Parameters E 𝒗 𝒗 𝒅 ෝ 𝐝 = 𝐴 𝒒 source position Unsupervised Supervised inflow speed … time Talk tomorrow 9:30 Kim 2019 Eurographics19 Tutorial - SPH 18

Te TempoGAN - Su Superresolu olution ion Fl Flui uids ds • 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) 𝑧 𝑏 training that the 𝑦 𝑏 solutions. en a long- 𝐻(𝑦 𝑏 ) such details costs and time scales. 𝑦 𝑢−1 simulations typically based the under- 𝐻(𝑦 𝑢−1 ) 𝐻(𝑦 𝑢 ) 𝐻(𝑦 𝑢+1 ) 𝑦 𝑢 algorithm not require ver time. 𝑧 𝑢−1 𝑧 𝑢 𝑧 𝑢+1 𝑦 𝑢+1 olumetric that infer- Xie et al. 2018 Eurographics19 Tutorial - SPH 19

FlowStyle – Ne Fl Neural Stylization of Flows • Transfer low- and high-level style features from images to 4D fluid data • Structurally and temporally coherent • Pre-trained networks on images, 3d reconstruction Eurographics19 Tutorial - SPH 20

Pot Potential and and Ch Challenges of of Da Data-dr driv iven en Fl Flui uids ds Unexplored area Exciting research, triggers research and collaborations across disciplines What is the potential of data-driven simulations? Computational speed, data compression, novel applications: quick simulation previews, interpolation of simulations, image-based modeling and control... Use DL as a black box? No; synergistic combination of mathematical models and data What are the challenges? Loads of data (expensive, lack of data sets), training time / re-training, visual quality (memory limitations), 4D data, network architecture and parameters Eurographics19 Tutorial - SPH 21