DNN#Assisted*Parameter*Space*Exploration*and*Visualization*for*Large*Scale*Simulations

HAN#WEI *SHEN

DEPARTMENT*OF*COMPUTER*SCIENCE*AND*ENGINEERING

THE*OHIO*STATE*UNIVERSITY

1

Traditional**Visualization*Pipeline*

DiskI/O

SupercomputerSimulator Raw*data

Post9analysisMemory

I/O

• Data*are*often*very*large*•Mainly*batch*mode*processing;**Interactive*exploration*is*not*possible• Limited*parameters*to*explore

Parameter'Space'Exploration• Running&large&scale&simulations&is&very&time&and&storage&consuming&• A&physical&simulation&typically&have&a&huge&parameter&space• Ensemble&simulations&are&needed&for&analyzing&the&model&quality&and&also&identify&the&uncertainty&of&the&simulation&• It&is&not&possible&to&exhaust&all&possible&input&parameters&– time&and&space&prohibitive&

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DNN#Assisted#Parameter#Space#Exploration• Can$we$create$visualization$of$the$simulation$outputs$without$saving$the$data?Or

• Can$we$predict$the$simulation$results$without$running$the$simulation?• Why?$: Identify$important$simulation$parameters$: Identify$simulation$parameter$sensitivity$: Quantify$the$uncertainty$of$the$simulation$models

• Methods:: InSituNet (IEEE$SciVis’19$Best$Paper): NNVA (IEEE$VAST’19$Best$Paper$Honorable$Mention)

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InSituNet:*Deep*Image*Synthesis*for*Parameter*Space*Exploration*of*Ensemble*Simulations

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Introduction• Ensemble(data(analysis(workflow• Issues5 I/O(bottleneck(and(storage(overhead

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ensemblesimulations

simulationparameters

disk

I/O

raw data

post-hocanalysis

I/O

Introduction• In#situ#visualization- Generating#visualizations#at#simulation#time- Storing#images#for#post-hoc#analysis

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ensemblesimulations

simulationparameters

disk

I/O

post-hocanalysis

I/O

viewparameters

visual mappingparameters

in situ visvisualization

images

image data

• Challenges) Limiting.the.flexibility.of.post)hoc.exploration.and.analysis) Raw.data.are.no.longer.available

) Incapable.of.exploring.the.simulation.parameters) Expensive.simulations.need.to.be.conducted.for.new.parameter.settings

• Our.Approach) Studying.how.the.parameters.influence.the.visualization.results) Predicting.visualization.results.for.new.parameter.settings

Introduction

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Approach(Overview

9

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InSituNetA#deep#neural#network#that#models#the#function#ℱ

Design'of'InSituNet

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• Three'subnetworks'and'two'losses3 Regressor (mapping'parameters'to'prediction'images)3 Feature+comparator+(computing'feature+reconstruction+loss)3 Discriminator (computing'adversarial+loss)

inputparameters

Regressor

ground truth

prediction

featurereconstruction

loss

Discriminator adversarial loss

FeatureComparator

Design'of'InSituNet

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• Three&subnetworks&and&two&losses2 Regressor (mapping(parameters(to(prediction(images)2 Feature'comparator'(computing&feature'reconstruction'loss)2 Discriminator (computing&adversarial'loss)

inputparameters

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ground truth

prediction

featurereconstruction

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FeatureComparator

• A"convolutional"neural"network"(CNN)4 Input:"parameters"!"#$,"!%#","and"!%#&'4 Output:"prediction"image" ()4 Weights:"*,"updated"during"training

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• A$convolutional$neural$network$(CNN)• Input:$simulation,$visual$mapping,$view$parameters

• Output:$prediction$image

• Weights$#:$weights$collected$from$all$layers

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• Fully'connected'layer• Input:'1D'vector'# ∈ ℝ&• Output:'1D'vector'' ∈ ℝ(• Weights:'matrix') ∈ ℝ&×(

• Activation'function• Rectified'Linear'Units'(ReLU)

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• 2D%Convolutional%Layer• Input:%tensor%# ∈ ℝ&×(×)• Output:%tensor%* ∈ ℝ&×(×)+• Weights:%kernel%, ∈ℝ-_(×-_&×)×)+

• Residual%block1• Adding%input%to%the%output%of%convolutional%layers

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1K.%He,%X.%Zhang,%S.%Ren,%and%J.%Sun.%Deep%residual%learning%for%image%recognition.%In%Proceedings%of%2016%IEEE%Conference%on%Computer%Vision%and%Pattern%Recognition,%pp.%770–778,%2016.

Loss$Function

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inputparameters Regressor

prediction

• Difference*between*the*prediction*and*the*ground*truth• Used*to*update*the*weights*!

ground truth

Loss

Backpropagation

• Pixel&wise&loss&functions/ Example:&mean&squared&error&loss&(MSE&loss&ℒ"#$)/ Issue:&blurry&prediction&images

Loss$Function$+ Straightforward$Approach

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inputparameters Regressor

prediction

ground truth

MSE&Loss

Blurry&image&generated&by&aregressor&trained&with&the&MSE&loss

• Combining(two(loss(functions(defined(by(two(subnetworks5 Feature(comparator(5>(feature(reconstruction(loss(ℒ"#$%5 Discriminator(5>(adversarial(loss(ℒ$&'

Loss$Function$+ Our$Approach

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inputparameters Regressor

prediction

ground truth

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loss

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FeatureComparator

Design'of'InSituNet

19

• Three'subnetworks'and'two'losses3 Regressor (mapping'parameters'to'prediction'images)3 Feature'comparator'(computing+feature'reconstruction'loss)3 Discriminator (computing'adversarial1loss)

inputparameters

Regressor

ground truth

prediction

featurereconstruction

loss

Discriminator adversarial loss

FeatureComparator

Feature'Comparator'!• A"pretrained"CNN"(e.g.,"VGG3191)3 Input:"image""3 Output:"feature"map"!#(") ∈ ℝ(×*×+of"an"intermedia"layer",

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1K."Simonyan and"A."Zisserman."Very"deep"convolutional"networks"for"large3scale"image"recognition."In"Proceedings"of"International"Conference"on"Learning"Representations,"2015.

• Definition( MSE,loss between,the,feature'maps of,the,prediction,and,the,ground,truth( Given,a,batch,of,ground,truth,images,!":$%& and,predictions, '!":$%&

• Benefits( Making,the,regressor,to,generate,images,sharing,similar,features,with,the,ground,truth,,which,leads,to,images,with,sharper,features

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ℒ)*+,-,/ = 1ℎ345678"

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Feature'Reconstruction'Loss'ℒ)*+,

ground,truth ℒ)*+,ℒ<=*

Design'of'InSituNet

22

• Three&subnetworks&and&two&losses2 Regressor (mapping&parameters&to&prediction&images)2 Feature+comparator+(computing&feature+reconstruction+loss)2 Discriminator (computing+adversarial/loss)

inputparameters

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FeatureComparator

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• A$binary$classifier$(CNN)$with$weights$#• Trained$to$differentiate$prediction$(fake)$and$ground$truth$(real)$images• Input:$real/fake$image$$ and$the$input$parameters$%

• Output:$likelihood$value$!" $, % ∈ [0,1]• 1$means$real• 0$means$fake

• Regressor'and'discriminator'are'trained'in'an'adversarialmanner1

• Given'a'batch'of'real'images'!":$%&,'fake'images' '!":$%&,'and'parameter'settings'(":$%&9 Regressor'is'trying'to'fool'discriminator'by'minimizing

9 Discriminator'is'trying'to'differentiate'real'and'fake'images'by'minimizing

Adversarial*Loss*ℒ*+,

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1I.'J.'Goodfellow,'J.'Pouget9Abadie,'M.'Mirza,'B.'Xu,'D.'Warde9Farley,'S.'Ozair,'A.'Courville,'and'Y.'Bengio.'Generative'adversarial'nets.'In'Proceedings'of'Advances'in'Neural'Information'Processing'Systems,'pp.'2672–2680,'2014.

ℒ*+,_. = −12345"

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Total&Loss• A"weighted"combination"of"ℒ"#$% and"ℒ$&'

• ℒ"#$% and"ℒ$&' are"complimentary"with"each"other5 ℒ"#$%:"overall"feature"level"difference"between"image"pairs5 ℒ$&':"local"details"that"the"real"and"fake"images"differ"the"most

ℒ = ℒ"#$% + λℒ$&'

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ground"truth ℒ"#$%ℒ+,# ℒ$&' ℒ"#$% + λℒ$&'

Training• Updating)!" and)#$ w.r.t. the)loss)functions)iteratively

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Parameter'Space'Exploration'with'InSituNet• Forward'prediction. Predicting'image'for'new'parameter'settings

• Backward'sensitivity'analysis. Computing'the'sensitivity'of'the'parameters

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Subregion Sensitivity of: BwsA Visualization ViewCompute Overall Sensitivity Curve

Simulation Parameters

BwsA

1 1.5 2 2.5 3 3.5 3.8

Visual Mapping Parameters

Isovalue of temperature:15 20 25

View Parameters

theta

0 60 120 240 300 360160

phi

-90 -30 0 30 60 90-54

Parameters View

sens

itivi

ty

300350400450500550600

sensitivity0 80

salinity30 40

forward'prediction

backward'sensitivity'analysis

• Three%simulations:%SmallPoolFire,%Nyx,%and%MPAS:Ocean

• Comparing%the%prediction%with%the%ground%truth

Results

28

Nyx

Smal

lPoo

lFire

MPA

S-O

cean

Lmse LfeatGround Truth Ladv_R Lfeat +10-2Ladv_R

log

dens

ity9

12.5

salin

ity30

40te

mpe

ratu

re30

018

50

Results• Nyx$(cosmological$simulation) •MPAS6Ocean$(ocean$simulation)

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Results

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Datasets(and(timings:(tsim,(tvis,(and(ttr are(timings(for(running(ensemble(simulations,(visualizing(data(in(situ,and(training(InSituNet,(respectively;(tfp and(tbp are(timings(for(a(forward(and(backward(propagation(ofthe(trained(InSituNet,(respectively.

•We#propose#InSituNet,#a#deep#learning4based#image#synthesis#model#for#parameter#space#exploration#of#large4scale#ensemble#simulations

•We#evaluate#the#effectiveness#of#InSituNet in#analyzing#ensemble#simulations#that#model#different#physical#phenomena

Conclusion

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Neural'Network'Assisted'Visual'Analysis'of'Yeast'Cell'Polarization'Simulation

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Experimental Biologist Computational Biologist

Mathematical Simulation Model

Simulation Domain

Computational Biologist

Mathematical Simulation Model

• Protein species of interest : Cdc42

• Identify parameters configurations that can simulate high Cdc42 polarization

• Polarization: Asymmetric localization of protein concentration in a small region of the cell membrane

Simulation Background

Microscopic Image Simulation

Domain

Computational Biologist

• High-dimensional input/output spaces! 35 uncalibrated simulation input parameters! 400-dimensional output

• Computationally expensive! ~2.3 hrs/execution

• Challenging to perform interactive exploratory analysis of the parameter space

Challenges

Mathematical Simulation Model

Simulation Domain

Computational Biologist

• Neural network-based surrogate model

• Mimics the expensive simulation during analysis

• Facilitates interactive visual analytics

• Quick preview of predicted results for new parameters configurations

Proposed Approach

Mathematical Simulation Model

Data Scientist Surrogate Model

≈Simulation

Domain

• Quickly preview results for new parameters

• Perform parameter sensitivity analysis

• Discover interesting parameter configurations

• Validate the surrogate model

• Extract insights from trained surrogate

VA System Requirements

≈Surrogate Simulation

Computational Biologist

Visual'Analysis'Workflow

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Neural Network Surrogate Model

NNVA: Visual Analysis System

Yeast Cell Polarization Simulation

training data new parameters

uncertainty visualization

parameter sensitivity

parameter optimizatio

nmodel

diagnosis

dropout

Act.Max-Min

Weight Matrix

visual queries, new input parameter configurations, etc.

Network Structure and Training

35 1024

ReLU

Drop

out1(0.3)

800

500

400

ReLU

ReLU

Drop

out1(0.3)

InputLayer

Hidden Layer (H0)

Hidden Layer (H1)

Hidden Layer (H2)

OutputLayer

( p1,

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p35

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Simulation Domain

Network Structure and Training

35 1024

ReLU

Drop

out1(0.3)

800

500

400

ReLU

ReLU

Drop

out1(0.3)

InputLayer

Hidden Layer (H0)

Hidden Layer (H1)

Hidden Layer (H2)

OutputLayer

( p1,

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Visualization: Predicted protein concentration is color-mapped and laid-out radially

Cdc42 concentration

0 200 400

Network Structure and Training

35 1024

ReLU

Drop

out1(0.3)

800

500

400

ReLU

ReLU

Drop

out1(0.3)

• Loss Function: MSE

• Training data size: 3000

• Uniformly sampled parameter space

• Validation data size: 500

• Final Accuracy: 87.6%

InputLayer

Hidden Layer (H0)

Hidden Layer (H1)

Hidden Layer (H2)

OutputLayer

Uncertainty in Neural Networks using Dropout

• Important to visualize the prediction uncertainty in the exploration process

• Dropout: Randomly ignoring the output of neurons in a layer

• Training phase: ! Acts as regularizer to avoid overfitting

• Prediction phase[1]:! Uncertainty quantification of predicted result

[1] Gal et al. : Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning. ICML 2016

Uncertainty in Neural Networks using Dropout

• Important to visualize the prediction uncertainty in the exploration process

• Dropout: Randomly ignoring the output of neurons in a layer

• Training phase: ! Acts as regularizer to avoid overfitting

• Prediction phase[1]:! Uncertainty quantification of predicted result

• Visualized using standard deviation bands

[1] Gal et al. : Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning. ICML 2016

Uncertainty

bands

Parameter Sensitivity Analysis• Influence of individual parameters on different areas of output domain! Measure of how much the output changes for a small change in the input! Useful for parameter tuning

• Partial derivative of output w.r.t input:

• Computed using backpropagation

!"#!$#

"#$#

Parameter Sensitivity Analysis• Influence of individual parameters on different areas of output domain! Measure of how much the output changes for a small change in the input! Useful for parameter tuning

• Visualize detail parameter sensitivity across the cell membrane400

35

Parameter Sensitivity Analysis• Influence of individual parameters on different areas of output domain! Measure of how much the output changes for a small change in the input! Useful for parameter tuning

• Visualize detail parameter sensitivity across the cell membrane

• Interactive sensitivity brush to select area of interest

Parameter Optimization• Recommend parameter configurations which maximizes/minimizes the predicted protein

concentration values at different regions

• Activation Maximization:! Keeping the weights fixed, update the input (via gradient ascent) such that it maximize the model output

i,e.

• Activation Minimization: !"#

max#

'( # − * # − #+ ,

L2 -regularizer

m-.#'( # + * # − #+ ,

Parameter Optimization• Recommend parameter configurations which maximizes/minimizes the predicted protein

concentration values at different regions

• Interactive brushes to select specific areas of the cell membrane

Act. Max

Act. Min

Act. Max-Min

Visual'Analysis'System

50

• Instance View: ! Detail analysis of the predicted result for a specific

parameter configuration of interest

• Instance View: ! Detail analysis of the predicted result for a specific

parameter configuration of interest

• Parameter Control Board:! Interactively calibrate the 35 simulation parameters

• Instance View: ! Detail analysis of the predicted result for a specific

parameter configuration of interest

• Parameter Control Board:! Interactively calibrate the 35 simulation parameters

• Quick View ! Visualize predicted protein concentration

• Instance View: ! Detail analysis of the predicted result for a specific

parameter configuration of interest

• Parameter Control Board:! Interactively calibrate the 35 simulation parameters

• Quick View ! Visualize predicted protein concentration

• Parameter List View:! Progressively store newly discovered sets of parameters

• Instance View: ! Detail analysis of the predicted result for a specific

parameter configuration of interest

• Parameter Control Board:! Interactively calibrate the 35 simulation parameters

• Quick View ! Visualize predicted protein concentration

• Parameter List View:! Progressively store newly discovered sets of parameters

• Model Analysis View:! Analysis the weight matrices of the trained network

Use Case 1: Discover New Parameter Configurations

• Identify parameters configurations that can simulate high Cdc42 polarization

• Polarization Factor (PF): Measure of the extent of polarization [0.0, 1.0]

• Found several parameter configurations that simulated high PF (>0.8)! Highest PF = 0.82

• Compared with previous analysis efforts (using polynomial surrogate models)

Angles in degrees

Cdc

42 c

onc.

Raw$image$data$(PF$=$0.87)

NNVA$discovered$(PF$=$0.82)

MCMC$(PF$=$0.57)Simulated$Annealing$(PF$=$0.64)

Use Case 2: Analyzing the trained surrogate• To extract and validate the knowledge learned by the trained network

• Visualize and analyze the weight matrices35 1024 800

500

400

InputLayer

H0 H1

H2OutputLayer

Use Case 2: Analyzing the trained surrogate• First Weight Matrix

w1

w1024

102435

• k_24cm0, k_24cm1• k_42a, k_42d

• q, h

• k_24cm0, k_24cm1, k_42a, k_42d, q, h, C42_t

Correlated Parameters

Insufficient parameter ranges

Row-wise Sorted

H0

Input

Case Study 2: Analyzing the trained surrogate• Final Weight Matrix

w1

w400

400

50035

H2Output

Input

neuron indices in H2 layer• Patterns with high weights to the

center neurons• Avg. Parameter sensitivity to such

patterns• Top 15 aligns with the domain

knowledge

Sorted Avg. Sensitivity

400

Conclusion and Future Work

• Neural network-assisted analysis backend for interactive visual analytics

• Utilized post-hoc analysis operation on trained model to facilitate scientific enquires

• [Future] Investigate more effective model interpretation techniques. Currently, weight matrix analyses require ML knowledge

• [Future] Explore additional post-hoc analysis techniques for neural networks to interpret abstract domain level scientific concepts from the model