Fast Neural Network Emulation and Control of Physics-Based ......Radek Grzeszczuk Demetri...

International Conference Graphicon 1998, Moscow, Russia, http://www.graphicon.ru/

Intel Corporation Microcomputer Research Lab

Intel Corporation Intel Corporation Microcomputer Research LabMicrocomputer Research Lab

Radek GrzeszczukDemetri Terzopoulos

Geoffrey Hinton

Radek GrzeszczukRadek GrzeszczukDemetri TerzopoulosDemetri Terzopoulos

Geoffrey HintonGeoffrey Hinton

Fast Neural Network Emulation and Control of Physics-Based Models

R

111

2,12,12,1

222

111 222 University of Toronto, Dept. of Computer ScienceUniversity of Toronto, University of Toronto, Dept. of Computer ScienceDept. of Computer Science


Physics-Based Animation

Animation through physical simulation• Inanimate objects:

– rigid models (Hahn88, Baraff89)

– articulated models (Barzel88)

– deformable models (Terzopoulos87, Platt88)

• Animate objects: – animal models (Miller88, Tu95)

– human models (Armstrong85, Wilhelms87, Hodgins95,)

Animation through physical simulationAnimation through physical simulation•• Inanimate objects: Inanimate objects:

–– rigid models rigid models (Hahn88, Baraff89)(Hahn88, Baraff89)

–– articulated models articulated models (Barzel88)(Barzel88)

–– deformable models deformable models (Terzopoulos87, Platt88)(Terzopoulos87, Platt88)

•• Animate objects: Animate objects: –– animal modelsanimal models (Miller88, Tu95)(Miller88, Tu95)

–– human models human models (Armstrong85, Wilhelms87, (Armstrong85, Wilhelms87, Hodgins95,)Hodgins95,)

• Pioneering work•• Pioneering workPioneering work


Physics-based Models

Simulate Newtonian mechanics• Benefits

– offer unsurpassed realism

– automate motion synthesis

• Drawbacks

– incur high computational costs

– difficult & expensive to control

• Moore’s Law is on our side!

Simulate Newtonian mechanicsSimulate Newtonian mechanics•• BenefitsBenefits

–– offer unsurpassed realismoffer unsurpassed realism

–– automate motion synthesisautomate motion synthesis

•• DrawbacksDrawbacks

–– incur high computational costsincur high computational costs

–– difficult & expensive to controldifficult & expensive to control

•• Moore’s Law is on our side!Moore’s Law is on our side!


NeuroAnimator

A neural network approach to physically realistic animation• Learns to approximate physical models by observing

their actions

• Yields outstanding efficiency

– fast synthesis of physically realistic motion

– fast synthesis of motion controllers for animation

A neural network approach to physically A neural network approach to physically realistic animationrealistic animation•• Learns to approximate physical models by observing Learns to approximate physical models by observing

their actionstheir actions

•• Yields outstanding efficiencyYields outstanding efficiency

–– fast synthesis of physically realistic motionfast synthesis of physically realistic motion

–– fast synthesis of motion controllers for animationfast synthesis of motion controllers for animation


Example NeuroAnimators


Motivation

Is there a more efficient alternative to animation by simulation?• Numerical simulation of a dynamical system evaluates

a high-dimensional map Φ at every timestep

• In principle (Cybenko89), neural networks can learn to approximate arbitrary, complex maps Φ

• NeuroAnimator: accurate and efficient neural network approximation of maps Φ associated with physics-based CG models

Is there a more efficient alternative to Is there a more efficient alternative to animation by simulation?animation by simulation?•• Numerical simulation of a dynamical system evaluates Numerical simulation of a dynamical system evaluates

a higha high--dimensional map dimensional map ΦΦ at everyat every timesteptimestep

•• In principle In principle (Cybenko89)(Cybenko89), neural networks can learn to , neural networks can learn to approximate arbitrary, complex maps approximate arbitrary, complex maps ΦΦ

•• NeuroAnimatorNeuroAnimator: accurate and efficient neural network : accurate and efficient neural network approximation of maps approximation of maps Φ Φ associated with physicsassociated with physics--based CG modelsbased CG models


⎩⎨⎧

+=+=

+

+

tttt

tttttt

t xvxfugvvA

δδδ ),(

⎩⎨⎧

+=+=

+

+

tttt

tttttt

t xvxfugvvA

δδδ ),(• Example:

Implicit Euler time-integration method

•• Example: Example: Implicit Euler timeImplicit Euler time--integration methodintegration method

Animation through numerical simulation• Discrete-time dynamical systems

Animation through numerical simulationAnimation through numerical simulation•• DiscreteDiscrete--time dynamical systemstime dynamical systems

),,( ttttt fuss

Motivation

Φ=+δ ),,( ttttt fuss Φ=+δControlsControlsControls

External ForcesExternal ForcesExternal Forces

[ ]vxs =[ ]vxs =StateStateState

MapMapMap

tt δ+s tt δ+s tsts


Initial State Final State

The NeuroAnimator learns dynamics by observing sample state transitionsTheThe NeuroAnimatorNeuroAnimator learns dynamics by learns dynamics by observing sample state transitionsobserving sample state transitions

Physical ModelPhysical ModelNeuroAnimatorNeuroAnimator

Learning Dynamics

Initial StateInitial State Final StateFinal StateInitial StateInitial State Final StateFinal State

Initial StateInitial State Final StateFinal State

tsts

tftf

tutu

tt Δ+s tt Δ+s


Emulation

Why is the NeuroAnimator efficient?• The emulation step is relatively cheap

• The NeuroAnimator can emulate super timesteps– up to 100 times faster than numerical simulation

• is analytically differentiable– dramatic efficiency for animation controller synthesis

Why is the Why is the NeuroAnimator NeuroAnimator efficient?efficient?•• The emulation step is relatively cheapThe emulation step is relatively cheap

•• TheThe NeuroAnimatorNeuroAnimator can emulate can emulate super super timestepstimesteps–– up to 100 times faster than numerical simulationup to 100 times faster than numerical simulation

•• is analytically differentiableis analytically differentiable–– dramatic efficiency for animation controller synthesisdramatic efficiency for animation controller synthesis

),,( ttttt fusNs ΦΔ+ = ),,( ttttt fusNs ΦΔ+ =NeuroAnimator approximation of ΦNeuroAnimator approximation of Φ

ΦNΦN

super timestepsuper timesteptnt δ=Δ tnt δ=Δ


Talk Overview• Introduction

• Artificial neural networks

• From physical models to NeuroAnimators

• NeuroAnimator based controller synthesis

• Conclusion and future work

•• IntroductionIntroduction

•• Artificial neural networksArtificial neural networks

•• From physical models to From physical models to NeuroAnimatorsNeuroAnimators

•• NeuroAnimatorNeuroAnimator based controller synthesisbased controller synthesis

•• Conclusion and future workConclusion and future work


Neural Networks

Seminal work in the field• Perceptrons

(Widrow60, Rosenblatt62, Minsky69)

• Backpropagation learning algorithm(Rumelhart86) (Bryson69, Werbos74, Parker85)

– backpropagation through time(Rumelhart86)

Seminal work in the fieldSeminal work in the field•• PerceptronsPerceptrons

(Widrow60, Rosenblatt62, Minsky69)(Widrow60, Rosenblatt62, Minsky69)

•• Backpropagation Backpropagation learning algorithmlearning algorithm(Rumelhart86) (Bryson69, Werbos74, Parker85)(Rumelhart86) (Bryson69, Werbos74, Parker85)

–– backpropagationbackpropagation through timethrough time(Rumelhart86)(Rumelhart86)


Artificial Neural Networks

NeuronNeuron Feedforward NetworkFeedforward Network

Networks of simple computing elementsNetworks of simple computing elementsNetworks of simple computing elements


Backpropagation

N ),(N wxτNeural Network

)(E wτ

∑

Adjusts the weights of a neural networkAdjusts the weights of a neural networkAdjusts the weights of a neural network

2),()()( wxNxw τττ Φ−Φ=E

2),()()( wxNxw τττ Φ−Φ=E

)(1 lwll E www w

τη ∇−=+ )(1 lwll E www w

τη ∇−=+• Approximation error:

• Weights update formula:

•• Approximation error:Approximation error:

•• Weights update formula:Weights update formula:

τx

Φ

)( τxΦDynamic System





– emulation results






–– emulation resultsemulation results




NeuroAnimator Structure

tsts

tftf

tutu

tt Δ+s tt Δ+s

Active dynamic,nondeterministic forcesActive dynamic,nondeterministic forces

tsts

tftftt Δ+s tt Δ+s

Passive dynamic, nondeterministic forces Passive dynamic, nondeterministic forces

tsts

tututt Δ+s tt Δ+s

Active dynamic, deterministic forcesActive dynamic, deterministic forces

tsts tt Δ+s tt Δ+s

Passive dynamic, deterministic forces Passive dynamic, deterministic forces


2s3s

2u

Emulation

),,( ttttt fusNs ΦΔ+ = ),,( ttttt fusNs ΦΔ+ =

1s

1u

1+Ms

Mu

Ms1−Ms

1−Mu

tt Δ+s

tu

tsSequence of network evaluationsSequence of network evaluationsSequence of network evaluations


Input & Output Transformations

ts

tf

tu

tt Δ+s

ΦN



• Predict state changes•• Predict state changesPredict state changes

ts

tf

tu

tt Δ+s

ΦN

ΔyTΔΦN


• Predict state changes

• Invariance to translation and rotation

•• Predict state changesPredict state changes

•• Invariance to translation and rotationInvariance to translation and rotation


ts

tf

tu

tt Δ+s

ΦN

ΔyTyT′xT′ Φ′N



• Predict state changes

• Invariance to translation and rotation

• Normalize inputs and outputs

•• Predict state changesPredict state changes

•• Invariance to translation and rotationInvariance to translation and rotation

•• Normalize inputs and outputsNormalize inputs and outputs

ts

tf

tu

tt Δ+s

ΦN

ΔyTyT′xT′ σxT

σyTσΦN


shoulderelbowwrist

shoulder

elbowwrist

tt Δ+

tt Δ+

tt Δ+

t

t

t

Hierarchical Emulators

Torso

Leg

Arm

torsoneckwaist

torso

neckwaist

tt Δ+

tt Δ+

tt Δ+

t

t

t

hipkneeankle

hip

kneeankle

tt Δ+

tt Δ+

tt Δ+

t

t

t

metatarsus t metatarsus tt Δ+

Human modelHuman modelHuman model

Neck 3dof

Shoulder 3dof

Elbow 1dof

Waist 3dof

Hip 3dof

Knee 1dof

Ankle 2dof

Metatarsus 1dof

Wrist 3dof


Hierarchical EmulatorsDolphin modelDolphin modelDolphin model

torsoneckwaist

torso

neckwaist

tt Δ+

tt Δ+

tt Δ+

t

t

t

torsoneckwaist

torso

neckwaist

tt Δ+

tt Δ+

tt Δ+

t

t

t


Training NeuroAnimators

Offline backpropagation training of networks• “Xerion” public domain neural network simulator

software from the University of Toronto

• Initialize networks with random weights

• Generate training examples with “short-time” physical model simulations from random initial conditions

– can reduce training times by sampling state, force, & control inputs that occur most often in practice

OfflineOffline backpropagationbackpropagation training of networkstraining of networks•• ““XerionXerion”” public domain neural network simulator public domain neural network simulator

software from the University of Torontosoftware from the University of Toronto

•• Initialize networks with random weightsInitialize networks with random weights

•• Generate training examples with “shortGenerate training examples with “short--time” physical time” physical model simulations from random initial conditionsmodel simulations from random initial conditions

–– can reduce training times by sampling state, force, can reduce training times by sampling state, force, & control inputs that occur most often in practice& control inputs that occur most often in practice


Example NeuroAnimatorsInputs: 12Outputs: 6Hidden Units: 20Training set: 3K

Inputs: 12Inputs: 12Outputs: 6Outputs: 6Hidden Units: 20Hidden Units: 20Training set: 3KTraining set: 3K

Inputs: 8Outputs: 6Hidden Units: 40Training set: 5K


Inputs: 17Outputs: 13Hidden Units: 50Training set: 13K


Inputs: 84 (76)Outputs: 78 (36) Hidden Units: 50 (40)Training set: 64K (32K)

Inputs: 84 (76)Inputs: 84 (76)Outputs: 78 (36) Outputs: 78 (36) Hidden Units: 50 (40)Hidden Units: 50 (40)Training set: 64K (32K)Training set: 64K (32K)


Emulation Examples


Emulation Performance

Speedups for a NeuroAnimator with super-timestep Δ t = 50 δ t• Passive pendulum 94.0x physical simulation

• Active pendulum 75.3x ”

• Truck 69.7x ”• Lunar lander 53.7x ”

• Dolphin 66.3x ”

– approximation error holds ~steady with Δ t

Speedups for a Speedups for a NeuroAnimatorNeuroAnimator with superwith super--timesteptimestep Δ Δ t = 50 t = 50 δ δ tt•• Passive pendulumPassive pendulum 94.0x physical simulation94.0x physical simulation

•• Active pendulumActive pendulum 75.3x75.3x ””

•• TruckTruck 69.7x69.7x ””

•• Lunar Lunar landerlander 53.7x53.7x ””

•• DolphinDolphin 66.3x66.3x ””

–– approximation error holds ~steady with approximation error holds ~steady with Δ Δ t t







– control learning results







–– control learning resultscontrol learning results



Control of Physical Models• Inverse dynamics

(Isaacs87,Barzel88)

• Constraint optimization (Brotman88)

• Hand-crafted controllers(Miller88, Lee95, Tu94, Wilhelms87, Hodgins95)

• Controller synthesis(Goh88, Pandy92, Panne93, Ngo93, Grzeszczuk95)

• Connectionist robotic control (Mendel70, Werbos74, Barto87, Jordan88, Nguyen89 - “truck backer-upper”)

•• Inverse dynamics Inverse dynamics (Isaacs87,Barzel88)(Isaacs87,Barzel88)

•• Constraint optimization Constraint optimization (Brotman88)(Brotman88)

•• HandHand--crafted controllerscrafted controllers(Miller88, Lee95, Tu94, Wilhelms87, Hodgins95)(Miller88, Lee95, Tu94, Wilhelms87, Hodgins95)

•• Controller synthesisController synthesis(Goh88, Pandy92, Panne93, Ngo93, Grzeszczuk95)(Goh88, Pandy92, Panne93, Ngo93, Grzeszczuk95)

•• Connectionist robotic control Connectionist robotic control (Mendel70, Werbos74, Barto87, Jordan88, (Mendel70, Werbos74, Barto87, Jordan88, Nguyen89 Nguyen89 -- “truck backer“truck backer--upper”)upper”)

Our approachOur approach


Controller Synthesis(Grzeszczuk & Terzopoulos 95)


Optimization of an objective function

• Objective function

• Controller adjustment rule

• Trained NeuroAnimator yields gradient analytically• Controller adjustment consists of two steps...

Optimization of an objective function Optimization of an objective function

•• Objective functionObjective function

•• Controller adjustment ruleController adjustment rule

•• Trained Trained NeuroAnimator NeuroAnimator yields yields gradientgradient analyticallyanalytically•• Controller adjustment consists of two steps...Controller adjustment consists of two steps...

)()()( suu ssuu JJJ

Controller Synthesis

μμ += )()()( suu ssuu JJJ μμ +=

)(1 lxll J uuu u∇−=

+ η )(1 lxll J uuu u∇−=

+ η

Controller quality Controller quality Motion quality Motion quality


1) Forward Step

Emulates the forward dynamicsEmulates the forward dynamicsEmulates the forward dynamics

Controller

2s3s

2u

1+Ms

Mu

Ms1−Ms

1−Mu

1s

1u


1−∂ Ms2s∂

3s∂

2u∂

1s∂

1u∂

Ms∂

1−∂ Mu

2) Backward Step

Computes gradient using backpropagation through timeComputes gradient using Computes gradient using backpropagation backpropagation through timethrough time

Controller

1+∂ Ms

Mu∂


Control Learning Results


Controller Learning Performance







– control learning results







–– control learning resultscontrol learning results



Conclusion

The NeuroAnimator can be a powerful complement to physics-based animation• NeuroAnimators accurately emulate various physical

models up to 2 orders of magnitude faster than numerical simulation

• NeuroAnimator based controller learning algorithm synthesizes motions satisfying prescribed animation goals with up to 2 orders of magnitude fewer iterations

TheThe NeuroAnimatorNeuroAnimator can be a powerful can be a powerful complement to physicscomplement to physics--based animationbased animation•• NeuroAnimatorsNeuroAnimators accurately emulate various physical accurately emulate various physical

models up to 2 orders of magnitude faster than models up to 2 orders of magnitude faster than numerical simulationnumerical simulation

•• NeuroAnimatorNeuroAnimator based controller learning algorithm based controller learning algorithm synthesizes motions satisfying prescribed animation synthesizes motions satisfying prescribed animation goals with up to 2 orders of magnitude fewer iterationsgoals with up to 2 orders of magnitude fewer iterations


Future Research• NeuroAnimators for Artificial Life graphical characters

– acquiring “mental models” of dynamic worlds

• NeuroAnimation by motion capture

– learning approximations of complex biomechanics

• Connectionist controller representation

• Hierarchical emulation and control

•• NeuroAnimatorsNeuroAnimators for Artificial Life graphical charactersfor Artificial Life graphical characters

–– acquiring “mental models” of dynamic worldsacquiring “mental models” of dynamic worlds

•• NeuroAnimationNeuroAnimation by motion captureby motion capture

–– learning approximations of complex biomechanicslearning approximations of complex biomechanics

•• Connectionist controller representationConnectionist controller representation

•• Hierarchical emulation and controlHierarchical emulation and control


One More Thing...

“The Eagle has Landed?”“The Eagle has Landed?”“The Eagle has Landed?”


AcknowledgementsIntel Corporation• Richard Wirt, Fellow & MRL Director• Edward Langlois• Steve Hunt• Sonja Jeter• Mike Gendimenico• Michael Shantz, Dave Sprague• Baining Guo• John Funge• Xiaoyuan Tu• Alexander Reshetov• Feng Xie• Bob Liang

Intel CorporationIntel Corporation•• Richard Wirt, Richard Wirt, Fellow & MRL DirectorFellow & MRL Director•• Edward Edward LangloisLanglois•• Steve HuntSteve Hunt•• Sonja JeterSonja Jeter•• Mike Mike GendimenicoGendimenico•• Michael Michael ShantzShantz, Dave Sprague, Dave Sprague•• Baining GuoBaining Guo•• John John FungeFunge•• Xiaoyuan Xiaoyuan TuTu•• Alexander Alexander ReshetovReshetov•• Feng XieFeng Xie•• Bob Bob LiangLiang

University of Toronto• Zoubin Ghahramani• Michiel van de Panne• Mike Revow• Drew van Camp

University of TorontoUniversity of Toronto•• Zoubin GhahramaniZoubin Ghahramani•• MichielMichiel van de van de PannePanne•• Mike Mike RevowRevow•• Drew van CampDrew van Camp

Natural Sciences & Engineering Research Council of CanadaSteacie Memorial Fellowship

Natural Sciences & Engineering Natural Sciences & Engineering Research Council of CanadaResearch Council of CanadaSteacieSteacie Memorial FellowshipMemorial Fellowship

R

Fast Neural Network Emulation and Control of Physics-Based ModelsPhysics-Based AnimationPhysics-based ModelsNeuroAnimatorExample NeuroAnimatorsMotivationMotivationLearning DynamicsEmulationTalk OverviewTalk OverviewNeural NetworksArtificial Neural NetworksBackpropagationTalk OverviewNeuroAnimator StructureEmulationInput & Output TransformationsInput & Output TransformationsInput & Output TransformationsInput & Output TransformationsHierarchical EmulatorsHierarchical EmulatorsTraining NeuroAnimatorsExample NeuroAnimatorsEmulation ExamplesEmulation Performance Talk OverviewControl of Physical ModelsController Synthesis�(Grzeszczuk & Terzopoulos 95)Controller Synthesis1) Forward Step2) Backward Step2) Backward StepControl Learning ResultsController Learning PerformanceTalk OverviewConclusionFuture ResearchOne More Thing...Acknowledgements

Fast Neural Network Emulation and Control of Physics-Based ......Radek Grzeszczuk Demetri...

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