1223 Research system Subhashis Hazarika, Haoyu Li, Ko-Chih Wang, Han-Wei Shen
are with Department of Computer Science, Ohio State University. E-mail:
hazarika.3, li.8460, wang.3182<EMAIL_ADDRESS>Ching-Shan Chou is with
Department of Mathematics, Ohio State University. E-mail<EMAIL_ADDRESS>Biv et al.: Global Illumination for Fun and Profit

# NNVA: Neural Network Assisted Visual Analysis of Yeast Cell Polarization
Simulation

Subhashis Hazarika  Haoyu Li  Ko-Chih Wang  Han-Wei Shen and Ching-Shan Chou

###### Abstract

Complex computational models are often designed to simulate real-world
physical phenomena in many scientific disciplines. However, these simulation
models tend to be computationally very expensive and involve a large number of
simulation input parameters which need to be analyzed and properly calibrated
before the models can be applied for real scientific studies. We propose a
visual analysis system to facilitate interactive exploratory analysis of high-
dimensional input parameter space for a complex yeast cell polarization
simulation. The proposed system can assist the computational biologists, who
designed the simulation model, to visually calibrate the input parameters by
modifying the parameter values and immediately visualizing the predicted
simulation outcome without having the need to run the original expensive
simulation for every instance. Our proposed visual analysis system is driven
by a trained neural network-based surrogate model as the backend analysis
framework. Surrogate models are widely used in the field of simulation
sciences to efficiently analyze computationally expensive simulation models.
In this work, we demonstrate the advantage of using neural networks as
surrogate models for visual analysis by incorporating some of the recent
advances in the field of uncertainty quantification, interpretability and
explainability of neural network-based models. We utilize the trained network
to perform interactive parameter sensitivity analysis of the original
simulation at multiple levels-of-detail as well as recommend optimal parameter
configurations using the activation maximization framework of neural networks.
We also facilitate detail analysis of the trained network to extract useful
insights about the simulation model, learned by the network, during the
training process. We perform two case studies and evaluate our results by
comparing with the original simulation model outcomes as well as the findings
from previous parameter analysis performed by our experts.

###### keywords:

Surrogate modeling, Neural networks, Computational biology, Visual analysis,
Parameter analysis

K.6.1Management of Computing and Information SystemsProject and People
ManagementLife Cycle; K.7.mThe Computing ProfessionMiscellaneousEthics
Approach Overview: A trained neural network-based surrogate model acts as the
backend analysis framework, driving our interactive visual analysis system for
analyzing a computationally expensive yeast simulation model.

Introduction

In the field of computational biology, scientists often design mathematical
simulation models to offer quantitative descriptions of complex biological
processes. These simulations are subsequently used to perform in-depth
analyses of the real biological phenomenon. However, designing an optimal
simulation model can be challenging. Scientists need to have a clear picture
of how the different simulation input parameters are affecting the simulation
output. For compute-intensive simulation models with high-dimensional input
and output spaces, this can become a computationally prohibitive and non-
trivial analysis task.

We collaborated with computational biologists to design an interactive visual
analysis framework which can assist them in analyzing and visualizing a
complex yeast cell polarization simulation model. The model simulates the
concentration of important protein molecules along the membrane of a yeast
cell (single-cell microorganism) during its mating process. Cell polarization
refers to asymmetric localization of protein concentration in a small region
of the cell membrane and is a fundamental stage in the life-cycle of many
microorganisms. Our experts are interested in exploring and analyzing the
simulation input parameters which can simulate varying levels of cell
polarization results, particularly, the ones with high polarization. However,
there are 35 different unknown/uncalibrated input parameters for the
simulation. Besides the high-dimensional nature of the problem, the simulation
model itself is computationally expensive. It takes hours on a supercomputing
cluster to complete a single execution of the model. This seriously hampers
the possibility of performing any exploratory analysis task that requires
frequent execution of the simulation on new and unseen parameter
configurations to study its properties in detail. In the field of simulation
sciences, a popular and effective strategy to address this issue has been to
create a simpler statistical/mathematical surrogate model, mimicking the
original expensive simulation model [43, 13, 16, 44, 22]. The surrogate is
then utilized to perform detailed analysis tasks instead of the expensive
simulation model. A well-trained surrogate model can greatly facilitate the
analysis workflow of complex simulation models.

Compared to popular surrogate model options like polynomial fitting or
gaussian processes, neural networks are particularly well-suited for designing
interactive visual analysis systems. This is primarily because, besides
accurately predicting the output of high-dimensional non-linear functions,
they can also be utilized to extract and analyze interesting properties about
the original simulation by opening up the black-box of the trained neural
networks. Recent advances in the field of interpretability and explainability
of neural network-based models [38] have resulted in many useful post-hoc
analysis techniques, making them more transparent in the process. This has led
to a surge in their usage as proper analysis tools in many application domains
[4, 25, 51, 47]. In this work, we propose a neural network-assisted visual
analysis system (NNVA) which utilizes a neural network-based surrogate model
to perform exploratory analysis and visualization of the aforementioned yeast
simulation model. The surrogate model acts as the backend analysis framework,
facilitating various visual interactions and analysis activities in the
system. Of late, there is a growing interest in the usage of different neural
network-based models to solve complex real-world problems. Our work,
therefore, exemplifies how to build an interactive visual analysis system
around these powerful models, i.e, ML4VA.

Our proposed system facilitates interactive exploratory analysis by allowing
the experts to modify the input parameter values and immediately visualize the
predicted simulation outcome. This helps them discover new parameter
configurations without having the need to execute the original expensive
simulation for every instance. Using different interactive selection brushes,
experts can perform parameter sensitivity analysis at multiple levels-of-
detail as well as get optimal parameter recommendations to produce desired
simulation outcomes for selected regions of the membrane. To further assist
the experts in analyzing the dynamics of their simulation model, interactive
hierarchical cluster trees are provided for the parameter sensitivity values
as well as the predicted simulation output. For easy integration of our system
with the simulation workflow of the experts, we allow them to export the newly
discovered parameter configurations into a file format which can be used to
directly execute the original simulation model. To establish the
trustworthiness of any visual analysis system, it is important to convey the
underlying uncertainty associated with the predictions of the surrogate model.
Therefore, to incorporated uncertainty visualization in our system, we apply a
recently proposed uncertainty quantification technique for neural networks
using dropout layers [14]. We also allow the experts to validate the surrogate
model itself, by analyzing the various weight matrices and extracting the
knowledge learned by the surrogate during the training process. We performed
extensive evaluations of the proposed framework by comparing with the original
simulation model and the results of a previous analysis effort using
polynomial surrogate models [45].

To summarize, the major contributions of our work are as follows:

  * •

We demonstrate how a trained neural network can act as an analysis backend to
drive an interactive visual analysis system.

  * •

We discovered multiple previously unknown parameter configurations, which
generated strong cell polarization results in the original simulation model.

  * •

We provide easy integration of our visual analysis workflow with the
simulation modeling workflow of the experts.

##  1 Related Work

In this section, we focus on previous research works from the field of visual
analysis, which are relevant to our proposed approach.

Visual Exploration of Parameter Space: Over the years, multiple visual
analysis systems have been proposed to facilitate interactive visual
exploration of the input parameter space for simulation models. Each of them
are application specific, and caters to the requirements of their domain
experts. Orban et al. [41] projected input parameters and output data in
material science to 2D spaces, and allowed users to manipulate in the input
space and observe the change in the output space. Wang et al. [57] developed a
nested parallel coordinate plot for parameter analysis of multi-resolution
climate ensemble datasets. Biswas et al. [7] used a gaussian process based
surrogate model to perform interactive exploration in a shock physic
application. Coffey et al. [9] designed an interface which uses a mapping
between model features and simulation inputs to enable direct simulation input
parameter manipulations. Piringer et al. [42] proposed an approach called
HyperMoVal, which can evaluate the bad fit of surrogate models and provide
visual validation for their physical plausibility. Berger et al. [5] proposed
an uncertainty-aware statistical approach to predict results of given
parameters for real-time analysis. Sedlmair et al. [48] provided an extensive
survey and proposed a conceptual framework to categorize the various analysis
tasks and navigation strategies used in such visual analysis systems.

Our proposed visual analysis system encompasses three of the six analysis
tasks formalized by Sedlmair et al., namely, optimization, uncertainty, and
sensitivity. Among the four navigation strategies that they identified, our
system covers two of them, namely informed trial and error and local-to-
global. One main advantage of our proposed neural network-assisted visual
analysis system is that, all of these analysis and navigation tasks are
carried out using a single analysis framework in the backend, i.e, the trained
neural network-based surrogate model. Simulation parameter analysis is also a
popular topic in scientific visualization community. Parameter sensitivity
analysis techniques [39, 27, 12] have been widely used to perform various
uncertainty-aware scientific analysis and visualization [8, 17, 61]. The
recent survey on ensemble simulation data visualization by Wang et al. [56]
also covers the sub-category of simulation parameter analysis in visualization
community.

Machine Learning Models for Visual Analysis: Visualization community often
uses machine learning techniques to enhance their visual analytics tools. Xie
et al. [60] develop a visual analytics tool to visualize huge amount of images
by using CNN (Convolutional Neural Network) to extract semantic information.
Using Word2Vec with skip-gram model, Zhou et al. [63] developed a tool to
analyze and visualize the correlation between origin-destination (OD) movement
data. Xie et al. [59] used One-Class Support Vector Machine to build a
visualization tool for detecting anomalies in high performance computing
systems. Latent Dirichlet Allocation (LDA) was used by Lee et al. [30] to
develop an interactive document clustering tool, and also by Liu et al. [34]
to build a visual tool which summarizes large collection of text data for
analysis. Marai et al. [36] used KNN (K Nearest Neighbor) algorithm to develop
a tool to analyze the survival chance under certain conditions from historical
data. An abnormal network behavior analytics tool was proposed by Goodal et
al. [15]. When new observations are given, they used Bayes rule to update the
abnormality score of an event and summarize the information on the interface
for domain expert to judge. Liu et al. [33] developed an interactive system
which integrates results from learning-from-crowds model into visualization
system to assist experts to improve data labels. Liang et al. [31] proposed a
photo composition systems which uses an online metric learning based on earth
mover’s distance to find similar photos of an user given example. Based on
Word2Vec model, a visualization system with pen and touch was proposed by Lu
et al. [35] to assist the writers in the process of creating their idea before
writing a draft.

Visual Analysis for Machine Learning Models: Since the past few years, the
visualization community has played a significant role in explaining the inner
workings of complicated machine learning models. Multiple visual analytic
tools have been developed to visualize different machine learning algorithms,
such as Adaboost, SVM, decision tree and random forest [21, 19, 10, 46, 52].
Recently, Hohman et al. [20] published a comprehensive survey on the various
visual analytic approaches to explain deep neural network models, which are
gaining significant popularity in the machine learning community. At a high-
level, we can categorize these approaches into three categories. The goal of
one category of visualization tools is to open the black box by interpreting
the trained model [58, 32, 37, 54, 50, 24]. While, another category of
visualization tools not only interpret, but also diagnose the trained model
[23, 62, 49, 55]. Recently, a third category of visualization tools, focusing
more on assisting the machine learning experts to improve their models is
gaining popularity[53, 6].

Besides the visualization community, the machine learning community is also
working in parallel to create various post-hoc analysis techniques to
interpret and explain complicated models. Unlike most of the visualization
tools, these post-hoc analysis functions are intended to be more generic and
applicable for different network architectures. Montavon et al. [38] covers in
great details the various post-hoc analysis techniques that can be performed
on trained neural networks to make them more interpretable and explainable.
These analysis techniques for trained neural networks have seen wide-spread
application in scientific domains, ranging from cancer diagnosis to quantum
physics [4, 25, 51, 47]. In our proposed visual analysis system, we use
different post-hoc analysis functions on the trained neural network-based
surrogate model to study and analyze the original yeast simulation. We also
visualize the network structure (weight matrices) to extract and validate the
knowledge learned by the surrogate model during the training process.

##  2 Simulation Model Background

Traditional laboratory-based approach for studying yeast cell polarization
consists of a laborious workflow. The cells are first cultured/grown in a
growth media and then treated with various straining agents. They are then
visualized using high-resolution microscopes. Fig. 1(a) shows the microscopic
image of a highly polarized yeast cell. A mathematical simulation model,
therefore, can significantly accelerate the study of such biological
phenomena.

To capture the spatio-temporal dynamics of yeast cell polarization during the
mating cycle, scientists created a mechanistic spatial model to simulate the
concentration of important protein species along the cell membrane. In this
work, we focus only on one important protein species called Cdc42. Protein
concentration is measured as the number of molecules per unit area of the
membrane. The model simulates the cell membrane as a circle, centered at the
origin with radius $2\mu m$. Fig. 1(b) shows a pedagogical diagram of the
yeast cell structure with the peripheral cell membrane, while, Fig. 1(c) shows
the corresponding computational domain of the simulation model used by the
scientists. The computational domain (circle) have spatial resolution of 400,
parameterized by angles in the range $[0\degree,360\degree]$. Scientists are
interested in simulating results with high degree of polarization, in
particular of Cdc42 protein. To quantify the extent of Cdc42 polarization,
they constructed a scalar function of active Cdc42 (C42a) values called
polarization factor (PF), denoted as;

$PF=\Big{(}1-2\frac{S_{p}(C42a)}{SA}\Big{)}\times\frac{(ax)^{5}}{1+(ax)^{5}}$
(1)

where, $SA$ is the surface area of the membrane simulated by the model,
$S_{p}(C42a)$ is the surface area at the front of the cell that encompasses
half of the polarized component C42a, $x$ is the maximum C42a concentration
value and $a$ is an experiment constant dependent on simulation parameter. An
unpolarized cell would have a PF value of 0 and an infinitely polarized cell
would have a PF value of 1.

However, the simulation model comprises of 35 different input parameters. For
the model to be useful to study the biological process of yeast cell
polarization, scientists need to have a clear understanding of how the
simulation input parameters effect the simulation results. More specifically,
they want to figure out the parameter configurations which can generate high
cell polarization results in the model. Studying this high-dimensional
parameter space is not trivial, especially when the individual simulation
execution itself takes few hours to execute. Any analysis task that requires
frequent execution of the model on new parameter configurations is effected by
the long execution time of the simulation model.

Previous Simulation Model Analysis: Previous efforts into analyzing this
simulation model involved creating a polynomial surrogate model [45]. The
surrogate model was created by uniformly sampling the parameter space and
fitting a polynomial function to the polarization factor (PF) values (Equation
1). The surrogate model facilitated in analyzing the parameter sensitivity of
the model and helped estimate parameter configurations using a Markov Chain
Monte-Carlo (MCMC) approach. However, the approach was not able to identify
satisfactory parameter configurations with which the simulation can generate
significantly high polarization results. Moreover, given a parameter
configuration, the polynomial surrogate model only predicts the final PF value
and not the Cdc42 protein concentration values across the membrane, which is
the final output of the simulation. As a result, parameter sensitivity
analysis performed with the polynomial surrogate model was not able to study
the influence of the parameters on different regions of the membrane in finer
details. Such analysis is important to get a better understanding of how the
simulation parameters actually affect the protein concentration across the
membrane and not just the final PF value. In this work, we train a neural
network-based surrogate model to predict Cdc42 concentration values for the
400 spatial locations across the membrane as modeled by the computational
domain (fig. 1(c)). We use this neural network-based surrogate model to create
a visual analysis system for the simulation model. We utilize some of the
important findings in the previous work [45] to extensively evaluate and
validate the results produced by our proposed system.

Figure 1: (a) Microscopic image of a highly polarization yeast cell. (b)
Pedagogical illustration of the yeast cell structure. (c) The computational
domain used in the simulation to model the cell membrane.

##  3 Requirement Analysis and Approach Overview

Requirements: Throughout the course of this project, we had multiple
interactions with the scientists from computational biology to understand the
various aspects of their simulation model and get a clear picture of their
needs and requirements from a visual analysis system. Based on these
discussions, the most important requirements are as follows:

  * R1

Discover new parameter configurations which can generated high Cdc42
polarization results in the simulation model. The system should have the
ability to visually guide the users in the process of finding desired
parameter configurations for the simulation.

  * R2

Ability to get a quick preview of the predicted simulation output for a
particular parameter configuration to facilitate model calibration. This helps
them decide whether to execute the expensive simulation model with certain
parameter configurations or not.

  * R3

Perform detail sensitivity analysis of the input parameters with respect to
Cdc42 concentration for different regions of the cell membrane.

  * R4

Analyze the distribution of protein concentration values across the
computational domain of the model. This is required to decide on an ideal
partitioning scheme for the computational domain.

  * R5

Ability to extract and validate the knowledge learned by the surrogate during
its training process. This is required to make sure that the trained network
is not making any random predictions.

Overview: Based on these requirements, we have proposed an interactive visual
analysis system, which is driven by a neural network-based surrogate model. We
first train a fully connected neural network on a finite set of training data,
obtained by running the simulation on random parameter configurations. The
neural network learns to predict the concentration of the Cdc42 protein along
the cell membrane for a given input parameter configurations. We then design a
visual analysis framework which allows the users to visually query for
different properties about the simulation model to address the aforementioned
user requirements. These queries are executed in the backend by the trained
surrogate model to provided prompt feedback via the visual interface. The
system visually guides the users to discover new parameter configurations,
which can be later used to execute the original simulation model. Fig. NNVA:
Neural Network Assisted Visual Analysis of Yeast Cell Polarization Simulation
shows the high-level overview of the proposed system.

##  4 Neural Network-based Surrogate Model

Surrogate models are widely used in many areas of engineering and simulation
science as cost effective alternatives to expensive simulation models for
various analyses [43, 13, 16, 44, 22]. Also known as response surface models
or emulators, they mimic the behavior of the actual simulation model as
closely as possible while being computationally easier to evaluate. The
surrogate model proposed in our work is a multi-layer full-connected feed-
forward regression neural network. In this section, we first discuss in
details the network structure and the training process of our surrogate model
and then elaborate on the various post-hoc analysis techniques that can be
performed on trained networks to facilitate the eventual visual analysis
system.

###  4.1 Network Structure and Training Process

As shown in fig. 2(a), our surrogate model consists of 5 layers, comprising an
input layer of 35 neurons and an output layer of 400 neurons, corresponding to
the 35 simulation input parameters and 400 uniformly distributed spatial
locations along the cell membrane respectively. The intermediate hidden
layers, $H_{0}$, $H_{1}$ and $H_{2}$ are composed of 1024, 800 and 500 neurons
respectively. The network is fully-connected, therefore, the neurons of one
layer are connected with all the neurons of its subsequent layer. The output
of each neuron in the three hidden layers are passed through ReLU (rectified
linear unit) activation functions to model any non-linearity between the input
parameters and the output responses. We also apply dropout regularization to
the first ($H_{0}$) and second ($H_{1}$) hidden layers with a dropout rate of
0.3. Dropout regularization corresponds to randomly ignoring the activation
results of the neurons in a layer during the training process to avoid over-
fitted networks and achieve higher accuracy. A dropout rate of 0.3 refers to
the fact that we randomly ignore $30\%$ of the neuron outputs at layers
$H_{0}$ and $H_{1}$.

We trained the surrogate model on a training dataset of size 3000. Our experts
predetermined the ranges of the individual parameters and normalized them
independently to the range $[-1,1]$. The training data was created by first
randomly sampling the 35 parameters in their normalized value ranges to create
3000 random parameters configurations and then running the simulation model to
get the corresponding Cdc42 concentration values for each configuration ($\sim
27$ hours on a supercomputing cluster). It was observed that a large fraction
of the randomly sampled training data corresponds to instances with very low
Cdc42 polarization. Therefore, to train the network to predict the high
polarization instances (R1), we performed PF value weighted training of the
neural network. During the training iterations, this assigned high weightage
to the loss function values corresponding to training data instances with high
PF values. After training for 5000 epochs, with a batch size of 32, the model
achieved a stable RMSE (root mean square error) accuracy of $87.6\%$. Standard
mean squared error (MSE) was used as the loss function for training the
network and the accuracy was tested on a separate validation dataset of size
500.

###  4.2 Uncertainty Quantification in Neural Network

Traditionally, neural networks do not provide any measure of the uncertainty
associated with its predictions by default. However, in a recent work, Gal et
al. [14] showed that traditional neural networks can also be made to quantify
uncertainty by activating the dropout layers in the prediction (testing)
phase. As discussed in Section 5.1 above, dropout layers are generally used as
regularizers in the training phase to avoid over-fitting of training data by
randomly ignoring the neuron activations at different layers of the network.
Dropout is generally turned off when the network makes predictions. Gal et al.
[14] showed that if we apply dropout during prediction and randomly ignore the
activations of neurons in different layers, we get slightly varying
predictions every time the network is run with the same set of input. By
observing the variations of the predicted results for multiple instances, we
can quantify the uncertainty associated with the predicted results. Gal et al.
[14] further proved that dropout induced uncertainty for neural networks is
actually an approximation of the uncertainty obtained in Bayesian models like
Gaussian Processes. Therefore, using this feature in our trained neural
network-based surrogate model, we can incorporate uncertainty visualization
into our visual analysis system of the yeast simulation model.

Figure 2: (a) Architecture of our surrogate model. (b) Dropout-based
uncertainty visualization of neural networks for a synthetic dataset. Figure
3: Primary Visualizations and Interaction techniques: (a) Predicted Cdc42
concentration across the membrane along with uncertainty bands and selection
brushes. (b) Parameter control bar. (c) Spatial parameter sensitivity. (d)
Linear cluster tree for average parameter sensitivity. (e,f) Average parameter
sensitivities. (g) Radial cluster tree for predicted Cdc42. (h) First weight
matrix. (i) Final weight matrix. (j) Row selection probe. (k) Average
parameter sensitivity for selected pattern.

Fig. 2(b) demonstrates the uncertainty visualization results using dropout
layers in a simple 3-layer neural network on a synthetic dataset. Consider
using a neural network to learn a simple sinusoidal function $f(x)=sin(2\pi
x)-x$. Training data to learn this function was provided only for the $x$
ranges of $[-2.0,-1.5]$ and $[-1.0,0.5]$. Fig. 2(b1) shows the plot of the
true function values $y=f(x)$ for the training data ranges. Fig. 2(b2) shows
the result of the trained neural network predictions for $x$ values ranging
from $-2.0$ to $3.0$. The variation in the predicted result is captured using
dropout layers and is visualized as standard deviation bands (in shades of
green) around the mean predicted values. As can be seen, the uncertainty is
high for regions where the training data was not provided to the network to
learn from. The uncertainty visualization clearly shows that as we move away
from the training data range (i.e, $x>0.5$) the corresponding prediction
uncertainty also increases. In order to avoid misleading the users in their
decision making process and add a sense of trustworthiness, it is vital for a
visual analysis system to convey any underlying uncertain in the model.

###  4.3 Parameter Sensitivity Analysis

Sensitivity analysis is probably the most widely used post-hoc analysis
operation performed on trained neural network models. It is primarily applied
to identify the most important/salient input features. As a result, it has
served as an effective tool in driving many recent advances in the field of
explainable machine learning [38].

Sensitivity analysis of a neural network corresponds to computing the partial
derivative of the outputs with respect to the inputs. Consider the $i$-th
neuron in the output layer, predicting the function $f_{i}(\textbf{x})$ for an
$n$-dimensional input vector
$\textbf{x}\sim\\{x_{0},x_{1},...,x_{n}\\}\in\mathbb{R}^{n}$. The sensitivity
of $f_{i}$ with respect to the $j$-th input parameter can be denoted as
$\Big{(}\frac{\partial f_{i}}{\partial x_{j}}\Big{)}^{2}$. A high sensitivity
value corresponds to the fact that a small change in the value of the input
$x_{j}$ is going to have a significant change in the output value of
$f_{i}(.)$. The architecture of neural network is such that the output of
every neuron in the network is completely differentiable with respect to its
inputs, as a result, we can easily compute the required partial derivatives
for sensitivity analysis via chain-rule using the backpropagation technique
[18]. In our work, we utilize this to evaluate the sensitivity of the 35
simulation input parameters using the trained surrogate model. The visual
analysis system provides an interface for the scientists to query for such
parameter sensitivity information for different spatial regions of interest
along the cell membrane. Another advantage of using neural network for
sensitivity analysis is that we can also compute the sensitivity of the hidden
layer activation values with respect to the input parameters as well. We
utilize this to observe the parameter sensitivity towards interesting latent
space data patterns learned by the hidden layers of the surrogate model during
the training process.

###  4.4 Parameter Optimization

Another important category of post-hoc analysis operation performed on trained
neural networks is called activation maximization (AM). Activation
maximization corresponds to searching for an optimal input configuration in
the high-dimensional input space that maximizes the output response function.
It is often used to interpret a high-level concept learned by the neural
network, for example, in the field of image classification, it can be used to
create new images of what the trained network thinks a cat or a dog looks like
[40, 38].

Neural networks are essentially optimization machines that try to find the
optimal network configurations (various weight and bias values) during the
training process that can best map a given input to the desired output. Once
the training process is over, the network configuration is fixed and is used
to predict outputs for new and unseen input configurations. Activation
maximization corresponds to a reverse optimization process, where, keeping the
network configuration fixed, we search for optimal input configurations that
maximizes the function values of specific neurons in the output layer. For the
$i$-th neuron in the output layer predicting the function $f_{i}(\textbf{x})$
for an $n$-dimensional input vector $\textbf{x}\in\mathbb{R}^{n}$, we can find
an optimal input configuration $\textbf{x}^{*}$ by optimizing the following
objective function

$\max_{\textbf{x}}f_{i}(\textbf{x})-\lambda||\textbf{x}-\textbf{x}^{\prime}||^{2}$
(2)

where, the rightmost term is an $\ell_{2}$-norm regularizer to constrain the
input search space within a known confinement $\textbf{x}^{\prime}$. This
penalizes the optimizer from finding an arbitrarily different
$\textbf{x}^{*}$. The optimization involves a gradient ascent algorithm using
the gradients $\frac{\partial f_{i}}{\partial x}$ to update the inputs to
eventually find the optimal input configuration. A similar approach can also
be employed to minimize the activation of a selected neuron, i.e, activation
minimization, by negating the gradient values during the optimization steps.
In our work, we utilize activation maximization and minimization principles to
recommend simulations input parameter configurations to the scientists. They
can visually selected the spatial regions in the cell membrane that they want
to maximize/minimize the Cdc42 protein concentration for. By carefully
choosing to maximize Cdc42 concentration in certain regions and minimize in
the other regions scientists can query for parameter configurations that is
likely to produce high polarization profiles in the original simulation.

##  5 Neural Network Assisted Visual Analysis

In this section, we introduce our proposed interactive visual analysis system.
We first explain the primary visualizations and interaction techniques before
looking at the high-level analysis views in our system.

###  5.1 Primary Visualizations and Interactions

Cdc42 Visualization: To visualize the predicted Cdc42 concentration and other
cell membrane related information, we opted for radial layout designs [11] to
preserve the circular context of the simulation domain (fig. 1c). Fig. 3(a)
visualizes the mean predicted concentration values for the 400 uniformly
sampled points across the membrane (i.e, computational domain). By default,
the values are color-mapped to the maximum and minimum Cdc42 values observed
in the simulation by the experts. Radial coordinate axes (dashed-gray lines)
are provided in the backdrop as frame of reference. To efficiently utilize the
design space, we employed the popular design principle of superposition i.e,
visualizing multiple data subsets in the same coordinate system.

Uncertainty Visualization: The uncertainty associated with the predicted
values of the surrogate model is visualized using superpositioned standard
deviation bands around the circumference of the circular domain. The shapes of
first (inner) and second (outer) standard deviation bands, as shown in fig
3(a), highlight the deviation of the predicted values in the corresponding
locations of the membrane.

Selection Brushes and Interaction: As shown in fig. 3(a), we superposition
multiple interactive radial selection brushes in the same coordinate system as
the Cdc42 visualization. This facilitates in performing various visual queries
on different regions of the membrane. The sensitivity brush (gray) allows the
users to select the regions of the membrane where they want to perform detail
parameter sensitivity analysis. This brush is linked with the sensitivity
visualizations in fig. 3(c) and (f). The maximization brush (red), selects the
region where the users want to maximize the predicted concentration values
(Section 5.4). On clicking this brush, the corresponding optimal parameter
values, computed by the backend surrogate model, are reported in the parameter
control bars (fig. 3(b)). Similarly, the minimization brush (blue) selects the
region to minimize the predicted values. The green circular button at the
center performs a logical AND operation of the regions selected by the
maximization and minimization brushes.

Parameter Control Bars: Fig. 3(b) shows the parameter control bar for one of
the simulation input parameters. The parameter name is followed by an input
textbox to enter desired parameter values. The sliderbar, immediately below,
can also be used to adjust the parameter values. The parameter values
corresponding to different configuration instances show up in the last bar.
The value corresponding to currently loaded instance show up in black colored
text, whereas, the optimal parameter values recommended by activation
maximization, minimization and combined max-min show up as red, blue, and
green colored texts respectively. Users can click on these texts to adjust the
parameter value as well. The individual value ranges for the parameters were
predetermined and normalized to $[-1,1]$ by the experts. Therefore, the range
of the control bars in our system is also set to the same normalized range
that the experts are interested in working with.

Sensitivity Visualizations: For a given parameter configuration, the local
sensitivity of the 400 spatial locations across the membrane with respect to
the 35 parameters are visualized in a circular heatmap as shown in fig. 3(c).
The 35 parameters are laid out along the radial direction. A high sensitivity
score for a parameter implies that a small change in its current value is
going to trigger a relatively high change in the predicted Cdc42 value for the
specific region of the membrane. Finer spatial selections can be made using
the aforementioned sensitivity brush. The average sensitivity of the 35
different parameters across all the spatial locations is shown as a bar-chart
in fig. 3(e). The average parameter sensitivity information for a user
selected region of interest (via sensitivity brush) is shown in fig. 3(f),
juxtaposed with (e) to convey the relative variation in the sensitivities.

Cluster Visualization: To help analyze the current partitioning scheme of the
simulation domain (R4), we perform hierarchical clustering [29] of the 400
uniformly partitioned points based on their Cdc42 values and associated
uncertainty. The multi-level cluster information is visualized using a radial
dendogram as shown in fig. 3(g). Hovering over the nodes highlights the
corresponding selected clusters in the simulation domain (fig. 3(g1)). Similar
clustering is performed on the average sensitivities of the 35 parameter to
study their associations. Fig. 3(d) shows a linear dendogram view of the
parameter cluster information. Users can control the tree depth, which relates
to the number of clusters desired for the study. For selected nodes in the
tree, the corresponding cluster members get highlighted in fig. 3(e) and (f).

Weight Matrix Visualization: To extract the knowledge learned by the trained
neural network, and thereby, validate the surrogate model (R5), we present
various techniques to analyze its weight matrices. Fig. 3(h) shows the weight
matrix ($35\times 1024$) between the input layer and the first hidden layer
(H0). The rows correspond to the 35 input parameters and the columns
correspond to the final weights assigned to the 1024 neurons in H0 layer. On
clicking the matrix, the weights get sorted row-wise, which helps identify
interesting weight distribution patterns as shown in fig. 3(h1). On hovering
the mouse over the rows, we display the shape of the corresponding weight
distribution for the respective parameter in a pop-up window (fig. 3(h2)).
Based on the patterns observed in the final weight matrix ($500\times 400$)
between the last hidden layer (H2) and the output layer, as shown in fig.
3(i), we offer a separate set of interactions to study the matrix. We provide
a row selection probe in the form of a sliderbar with an arrowhead (fig. 3(j))
to select the rows with interesting weight patterns. The selected row index is
highlighted in the side and a zoomed-in view of the row is displayed (fig.
3(i1)). Fig. 3(k) shows the average parameter sensitivity chart corresponding
to the neuron in the penultimate layer (H2), which is responsible for the
selected weight pattern.

Colormap Adjustments: We offer two sets of value ranges for mappings the
colors when visualizing the predicted Cdc42 concentration. The first set
(default) is based on the minimum and maximum concentration values that the
experts feel is effective for studying cell polarization behavior. For the
current system, this range is set to $[0,400]$. The second set corresponds to
the local minimum and maximum values for individual prediction results. This
provides more control to the experts during the analysis period, because the
concentration values for different instances can have varying dynamic ranges.
We also offer 9 different carefully selected divergent colormap [3]
alternatives for the Cdc42 visualization (fig. 3(a)) and the spatial
sensitivity heatmap (fig. 3(c)).

Figure 4: Multiple high-level analysis views of our visual analysis system.
Figure 5: Discover new parameter configurations: (a) Predicted Cdc42 of a
specific parameter instance with relatively high polarization profile. (b)
Spatial parameter sensitivity of the parameter instance. (c) Corresponding
average parameter sensitivities. Results for slightly changing the highly
sensitive parameters k_42a(d), k_42d(e) and a less sensitive parameter
k_RL(f). Maximizing (g) and minimizing (h) predicted Cdc42 values in the
selected regions. (i,j) Maximizing and minimizing the predicted values for the
selected regions at the same time to get highly polarized predictions (i1,
j1).

###  5.2 Visual Analysis System

Using the visualizations and interaction techniques explained above, we design
our visual analysis system with multiple high-level views to provide a
structured and efficient analysis workflow for our experts. It comprises of
the following high-level views, each addressing different facets of the
analysis requirements set forth in Section 4.

Instance View: This view loads the visualizations corresponding to a specific
instance of input parameter configuration that the scientists wish to analyze
in detail (R3, R4). As shown in fig. 4(a), it comprises of two sub-views.
Cdc42 Viz displays the predicted Cdc42 concentration result for the currently
analyzed parameter instance, whereas, Parameter Sensitivity View displays the
corresponding spatial sensitivity as well as the overall average parameter
sensitivity for the specific instance. Both the sub-views have the
corresponding cluster trees described in Section 6.1 for detail analysis. In
Cdc42 Viz, there is a switch to toggle between the radial cluster trees
corresponding to the Cdc42 values and the uncertainty values (R4).

Parameter Control Board: This view serves as the main panel to visualize and
interactively modify the input parameter configurations (R1). As shown in fig.
4(c), the 35 different parameter control bars (Section 6.1) for the individual
parameters are laid out across four rows. It visualizes the parameter values
corresponding to the parameter instance currently analyzed in the Instance
View as well as the optimal parameters recommended by the interactive
optimization brushes. Users can modify the parameter values and click the Run
button to execute the neural network-based surrogate model in the backend to
generate the corresponding simulation prediction, which is visualized in the
Quick View (R2). The Save button lets us store the modified input
configuration in the Parameter List View, whereas, the Export button downloads
the list of saved configurations. Instead of manually adjusting the 35
different parameter sliders, users can click the Current, Maximize, Minimize
or MaxMin buttons to automatically set the parameter sliders/values to the
desired recommended configurations.

Quick View: As shown in fig. 4(b), it visualizes the predicted Cdc42
concentration for the user-modified parameter configurations via the Parameter
Control Board. This offers a means to perform rapid prototyping of the
expensive simulation using the surrogate model, thus facilitating exploratory
analysis with new and unseen parameter configurations (R1, R2). In order to
compare the predicted Cdc42 values vis-à-vis the results in the Instance View,
we provide a toggle switch to change the visualization in Quick View to
display the exact difference in Cdc42 concentration across the membrane.

Parameter List View: As shown in fig. 4(d), this view temporarily stores the
newly discovered parameter configurations. Additionally, users can click on
the rows in the list to load the selected configuration back in the Parameter
Control Board. This list of configurations can be exported/downloaded in a
file format which can be directly used to execute the original simulation
model. This offers a seamless integration between the analysis workflow
involving our visual analysis system and the actual simulation modeling
workflow of the experts (R1).

Model Analysis View: This view lets the users investigate the trained neural
network-based surrogate model to extract useful insights about the simulation
model (R5). As shown in fig. 4(e), the left-most panel shows the thumbnail
views of all the weight matrices of the trained network. Users can click on
the matrix images to open up the corresponding analysis views in the right
panel. Detail analysis, as explained in Section 6.1, can be performed on the
selected weight matrix to extract any data patterns and validate the knowledge
learned by the surrogate model.

##  6 Case Study and Evaluation

In this section, we perform two case studies using our visual analysis system
and evaluate the results by comparing against the original simulation outcomes
as well as the findings from a previous polynomial surrogate model based
analysis of the simulation [45].

###  6.1 Discover New Parameter Configurations

One of the key requirements from the system is to visually guide the users
towards discovering desired parameter configurations (R1), instead of having
to perform random sampling of the high-dimensional parameter space. This also
enables the experts to incorporate their domain knowledge into the parameter
discovery process. In this case study, we use our system to identify new
parameter configurations that can trigger high Cdc42 polarization in the
original simulation model. We support two different visual parameter discovery
approaches. According to the conceptual framework of Sedlmair et al. [48],
both of these approaches can be categorized under local-to-global and informed
trial and error visual parameter navigation strategies.

Guided by the Instance View: In this approach, users can center their
parameter discovery process around a known instance of input parameter
configuration, whose results get loaded in the Instance View as discussed in
Section 6.2. The Instance View offers in-depth analysis of the Cdc42
concentration as well as the corresponding parameter sensitivity information
for the loaded parameter instance. Fig. 5(a), (b) and (c) show the zoomed-in
views of the predicted protein concentration, spatial parameter sensitivity
and average parameter sensitivity respectively of a selected region for the
loaded parameter instance. As can be seen, the loaded instance corresponds to
a good polarization profile. Using this as the starting point, users can start
modifying the parameter configurations based on the parameter sensitivity
details of the loaded instance combined with their domain knowledge.

For example, from the sensitivity views in fig. 5(b) and (c), we can infer
that the parameters k_42a and k_42d are the most sensitive parameters for the
loaded configuration. This implies that a small change to these parameter
values will significantly change the current polarization profile. We use the
Quick View panel to visualize the predicted polarization profile generated by
the modified parameter values. Fig. 5(d) shows the results for decreasing and
increasing the current k_42a value ($-0.24$) by a step-size of $0.05$ in the
top and bottom images respectively. As can be seen, decreasing the parameter
value significantly brings down the protein concentration at the top of the
cell, while, increasing the parameter value increases the concentration. As
shown in fig. 5(e), a reverse trend is observed for k_42d, where increasing
the parameter values by $0.05$ reduces the concentration and vice-versa.

From the simulation perspective, this behavior makes sense because k_42a
corresponds to Cdc42 activation, whereas, k_42d corresponds to Cdc42
deactivation. Since the type of simulated protein is active Cdc42 (i.e, C42a),
k_42a have a positive impact on its concentration while k_42d have a negative
impact. Similarly, for a less sensitive parameter like k_RL, we can see in
fig. 5(f) that changing its parameter value by the same step-size does not
result in a significant change in the polarization profile. As discussed in
Section 6.2, the toggle switch in the Quick View panel helps visualize the
exact difference in the concentration values with respect to the Instance
View, thereby, conveying the relative change in concentration. Using this
approach, we identified 8 new parameter configurations which are likely to
produce high Cdc42 polarization results in the original simulation.

Figure 6: (a) Comparative evaluation of the simulation results using parameter
configurations discovered by our system (black) and previous analysis work
(red) [45]. Comparison curves of Cdc42 concentration for (b) a highly
uncertain prediction and (c) a good prediction instance.

Guided by Parameter Optimization Brushes: We also recommend new parameter
configurations based on the activation maximization/minimization analysis
framework of neural network described in Section 5.4. Users can utilize the
maximization brush, as shown in fig. 5(g), to select the region of the cell
membrane where they want to maximize the predicted Cdc42 value. The
corresponding optimal parameter configurations computed by the surrogate is
recommended in the Parameter Control Board. Fig. 5(g1) shows the result of
running the surrogate model with the recommended parameters. As can be seen,
the predicted Cdc42 values in the selected region sharply increases (even
beyond the maximum value of 400, set by the experts). Similarly, a
minimization brush, as shown in fig. 5(h), recommends a parameter
configuration that brings down the concentration values of the selected region
close to the minimum concentration value (fig. 5(h1)). For the particular case
of finding high polarization profiles, we are interested in maximizing the
concentration at the top of the cell and minimizing the concentration across
rest of the locations at the same time. We make the desired selection using
the two brushes to make this query as shown in fig. 5(i) and (j) for two
different selection ranges. The corresponding recommended parameters display
high Cdc42 polarization predictions, as indicated by the Quick View results in
fig. 5(i1) and (j1) respectively for the two different selections. On top of
the recommended parameters, users can further modify individual parameter
values to create new sets of parameter configurations. Using this approach, we
created a total of 7 new input parameter configurations.

Evaluation: We executed the simulation model using the 15 newly identified
parameter configurations and observed high degrees of Cdc42 polarization (PF
$>0.5$) for all the configurations. We found 5 parameter configurations with
PF values exceeding 0.8, whereas, in the initial training data that was
collected by randomly sampling the parameter space, we never found an instance
with PF value close to 0.8. The highest PF value recorded among the newly
discovered parameters was 0.82 and corresponds to the optimized configuration
recommended by the neural network for the selection shown in fig. 5(j). In
fig. 6(a), we compare the actual simulation result generated with our
discovered optimal parameter configuration versus using the parameters
estimated by previous polynomial surrogate model based analysis [45]. The
sharp blue curve (PF = 0.87) corresponds to the protein concentration obtained
by extracting the pixel intensity values of a real microscopic image of a
highly polarized yeast cell as shown in the blue box. This acts as the ground
truth for the simulation model to generate similar levels of polarization
results. The black plot shows the simulation result produced using the optimal
parameters discovered by our system (PF = 0.82). The solid red plot (PF =
0.57) and dashed red plot (PF = 0.64) corresponds to the simulation results
generated by the parameter configurations estimated in previous work [45].

This is a significant improvement over the previous parameter analysis results
for the same simulation model. This establishes that, given the right input
parameter setting, the simulation model is capable of generating sharp
polarization results similar to real laboratory results. We also visually
verified the predicted results of the surrogate model against the original
simulation outputs by plotting them together as curves. Fig. 6(b) and (c) show
the comparative plots for a highly uncertain prediction and a less uncertain
prediction instance respectively. The green dashed-line shows the mean
prediction curve, whereas, the solid black line is the original simulation
output.

Figure 7: Knowledge extraction: (a) Connections of one parameter with H0
layer. (b) Row-wise sorted first weight matrix. (c) Connections of a neuron in
H2 layer with the output layer. (d) Few selected weight patterns with high
weights at the center. (e) Corresponding average parameter sensitivity sorted
in descending order.

###  6.2 Knowledge Extraction from Surrogate Model

In this case study, we aim to extract the knowledge learned by the network
during its training process by analyzing its various weight matrices. This
also serves the purpose of validating the surrogate model to make sure that it
is making predictions based on some reasonable domain-aligned logic rather
than random ad-hoc predictions (R5).

First Weight Matrix: In the first weight matrix between the input layer and
first hidden layer (fig. 7(a)), we observe distinct patterns in the
distribution of weights for certain parameters. Fig. 7(b) shows the full
$35\times 1024$ matrix with the weight values sorted in ascending order for
each row (i.e, parameter) to highlight the patterns (fig. 3(h) shows the
original matrix view). We observed relatively high negative and positive
weights for parameters k_24cm0, k_24cm1, k_42a, k_42d, C42_t, q and h. High
positive and negative weights in the first matrix for a parameter corresponds
to the fact that the parameter values had to be scaled by the weights for some
neurons in the first hidden layers. This implies that the original range of
values provided for the parameters is not sufficient. Similar observations
were made for these parameters explicitly in the previous analysis work [45].
The experts feel that the range of these parameters need to be expanded to get
better simulation results. Besides, the matrix also verified that the pairs
(k_24cm0, k_24cm1), (k_42a, k_42d), and (q, h) showed relatively strong
correlation compared to the other parameters. The exact shape of the weight
distributions for these parameters are provided in the supplementary
materials.

Final Weight Matrix: We did not observe any distinct patterns in the second
and the third weight matrices. However, in the final weight matrix of
resolution $500\times 400$, corresponding to the third hidden layer and the
output layer, we found multiple interesting weight distribution patterns (full
matrix view is shown in fig. 3(i)). Each row of this matrix corresponds to the
weights assigned to individual neuron activation values in the penultimate
layer ($H_{2}$) towards the 400 output neurons, as illustrated in fig. 7(c).
We observed that different neurons in $H_{2}$ layer assign high positive or
high negative weights to different sets of output neurons. In the output
layer, the neurons at the middle section corresponds to the top of the cell
membrane modeled by the simulation. Therefore, it is interesting to identify
which neurons in the $H_{2}$ layer assigns high positive weights to the middle
section of the output layer, because those neurons are most likely to
contribute towards producing high Cdc42 polarization results. We identified 95
such neurons in the $H_{2}$ layer (fig. 7(d)) and evaluated their average
parameter sensitivity (Section 5.3) to find out which parameters are more
sensitive to produce the selected weight pattern in the penultimate layer.

Fig. 7(e) shows the sorted list of parameters based on descending order of
their average normalized sensitivities. We compared this
importance/sensitivity order of parameters for generating high polarization
patterns with that of the list of highly sensitive parameters identified in
the previous work of our experts [45]. We found that except the change in
order of the 3 parameters q, D_c42a, and D_c42 by one position (marked by blue
texts), the top 15 sensitive parameters (red texts) were in the same order as
previously identified by experts. Besides analyzing the global sensitivity of
parameters for high polarization patterns, we can utilize our visual analysis
framework to study many other interesting weight patterns, for example,
instances with high negative weights assigned to the top of the cell membrane.
This flexibility enables the experts to not only utilize the system to study
Cdc42 behavior, but also other protein species in the future, which can show
different polarization patterns.

##  7 Domain Expert Feedback

Our experts from the field of computational biology, who created the yeast
simulation model, feel that the proposed visual analysis system is a very
useful tool to fine-tune their simulation model. They found the visual
interface of our system to be simple and intuitive to work with. The ability
to quickly prototype different parameter combinations and interactively
visualize the predicted simulation output within seconds lets them easily
calibrate the simulation model.

Previously, there was no interactive visualization created for the yeast
simulation. Our experts feel that the visual analysis system will be a useful
medium to communicate with the non-expert collaborators and stakeholders of
the project, instead of explaining them the complex reaction-diffusion
equations involved in the simulation. As discussed in Section 7.1, using our
system we were able to discover new parameter configurations that can trigger
high Cdc42 polarization in the original simulation model. This is a
significant improvement over the previously estimated parameters using
polynomial surrogate model analysis [45].

The experts feel that the system is flexible to work with other protein
species besides Cdc42. The current backend, i.e, neural network-based
surrogate model, predicting Cdc42 concentration, can be easily replaced with
another neural network model predicting different species and still retain the
same visual interactions to analyze the simulation. Since the backend analysis
techniques are independent of the network structure, they can train a network
with a different architecture and still utilize our visual analysis frontend.
The experts also plan to utilize the radial clustering information to create
an adaptive mesh for the computational domain rather than the current 400
uniformly spaced resolution.

The model analysis view was helpful to validate the trained network and see if
the surrogate model is actually learning something relevant about the
simulation rather than making random predictions. However, they feel that the
model analysis view requires users to have a good understanding of the neural
network architecture to interpret the weight matrices. They feel it would be
helpful to make the weight matrix analysis more intuitive for people without
much machine learning background. Overall, the experts are satisfied with our
neural network assisted visual analysis system and feel that it meets all of
their expected requirements. They plan to use the findings from the visual
analysis system to improve the simulation and report in a systems biology
journal in future.

##  8 Discussion

Design Study: The radial layout for most of the visualizations in our system
is inspired from the circular shape of the computational domain (approximating
the shape of the yeast cell membrane) as shown in fig. 1(c). This helps retain
the context of the cellular structure during the visual analysis workflow,
especially, while querying for different spatial regions of the cell membrane
for detail analysis.

Throughout the course of this project, we iterated over different design
choices for various elements of our visual analysis system. To visualize the
Cdc42 concentration for the 400 uniformly sampled points across the
computational domain, we initially used 400 color-mapped circles along the
circumference of the circular domain, as shown in fig. 8(a). We realized that
as the system grew in size, we had to reduce the overall size of the protein
visualization. This makes the 400 circles very tiny to properly convey their
color. Increasing the size of the small circles leads to overlapping among the
spatially neighboring points as shown in fig. 8(b). Therefore, we changed the
visual design to use contiguous rectangular boxes instead of circles at each
point, as shown in fig. 8(c). The advantage of this design is that we can
scale the boxes radially, as shown in fig. 8(d), without overlapping, when the
overall view has to shrink in the system to make adjustments for other panels.

The next major challenge was in deciding how to layout the Parameter Control
Board with 35 different parameter control bars. To the best of our knowledge,
previous visual parameter analysis systems [48, 41, 7, 57] did not have to
deal with such large number of simulation parameters. One straight-forward
choice was to place the control bars for 35 parameters in a long
vertical/horizontal panel with scrollbars to scroll through the list of
individual control bars. However, the experts felt that it is important to
have all the 35 bars visible at the same time, without the need to scroll
around during the model calibration process. This leads to the issue of
finding the best way of showing multiple recommended parameter values in the
same view.

Fig. 8(e) shows an instance in our current system with 3 recommended parameter
values very close to each other. Instead of showing the parameter value text
in the same horizontal level, we lay them out vertically to make the close-by
values standout. This helps the users in clicking on the texts and adjusting
the parameter slider to that precise recommended value. Another choice to save
space in the Parameter Control Board panel was to show the values only when
the mouse hovers over the recommended nodes as shown in fig. 8(f). However, we
went with the first choice as it helps the experts to see all the recommended
parameter values in the same view and not just the nodes in the bar. As a
result, we allocate sufficient vertical space between the rows of parameter
control bars to make room for the recommended parameter value text
visualization. We believe that there could be better designs to address this
and plan to make changes to the next version of our system.

Figure 8: Design study: Using circles (a,b) versus using rectangular boxes
(c,d) across the membrane. Parameter control bar with (e) all the values
displayed versus using (f) mouse-hovering.

Implementation and Performance: We used the Keras python library (v2.2.4) [2],
with TensorFlow backend, to implement and train our neural network-based
surrogate model. We trained the model on a NVIDIA Pascal P100 GPU for 5000
epochs. It took 59.31 minutes to train the network for 5000 epochs and the
final accuracy of the model was $87.6\%$. The full accuracy plot during the
training process is provided in the supplementary materials. To perform post-
hoc operations like sensitivity analysis and activation maximization on the
trained network, we used the Keras-Vis [28], which is a high-level analysis
library for neural networks. To perform uncertainty quantification for neural
networks, we wrote custom code to turn on the dropout layers for trained Keras
models during prediction/testing phase. Our frontend visual analysis system
was designed using d3.js. We used flask framework [1] to interact with the
trained neural network from our visual analysis system. The average time to
get the predicted simulation output from the trained neural network for a new
parameter configuration is 0.25 seconds, whereas, running the original
simulation model for one configuration took 2.3 hours in a supercomputing
cluster.

##  9 Conclusion and Future Work

In this paper, we have proposed an interactive visual analysis system to study
and analyze a complex yeast cell polarization simulation model. The proposed
system uses a trained neural network-based surrogate model as the backend
analysis framework to facilitate interactive visual analysis. It allows the
experts to interactively calibrate the simulation input parameters as well
visually guide them towards discovering new parameter configurations. We also
analyze the surrogate model to extract interesting insights about the original
simulation model. We hope that our proposed approach can motivate researchers
to look at neural networks as more than a prediction tool, and start utilizing
them to conduct interesting analysis activities.

In future, we would like to extend the visual analysis framework to facilitate
more complex analysis tasks like the recently proposed testing with concept
activation vectors (TCAV) [26]. This will allow the experts to validate high-
level domain specific concepts in the surrogate model. We plan to apply
similar visual analytic approach for analyzing simulations from other
application domains as well. As suggested by our experts, we also plan to
simplify the model analysis and validation methods so that it is more
intuitive for people without much machine learning background.

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