Shape Memory Alloy Wire Actuators for Soft, Wearable
Haptic Devices
George Chernyshov
Keio University Graduate
School of Media Design
Yokohama, Japan
chernyshov@kmd.keio.ac.jp

Benjamin Tag
Keio University Graduate
School of Media Design
Yokohama, Japantagbenja@kmd.keio.ac.jp

Cedric Caremel
Keio University Graduate
School of Media Design
Yokohama, Japan
cedric@keio.jp

Feier Cao
Keio University Graduate
School of Media Design
Yokohama, Japanfeier@kmd.keio.ac.jp

Gemma Liu
Keio University Graduate
School of Media Design
Yokohama, Japan
gemmaliu@kmd.keio.ac.jp

Kai Kunze
Keio University Graduate
School of Media Design
Yokohama, Japan
kai@kmd.keio.ac.jp

ABSTRACTThis paper presents a new approach to implement wearable
haptic devices using Shape Memory Alloy (SMA) wires. The
proposed concept allows building silent, soft, flexible andlightweight wearable devices, capable of producing the senseof pressure on the skin without any bulky mechanical actuators.
We explore possible design considerations and applications
for such devices, present user studies proving the feasibilityof delivering meaningful information and use nonlinear autoregressive neural networks to compensate for SMA inherent
drawbacks, such as delayed onset, enabling us to characterize
and predict the physical behavior of the device.
ACM Classification Keywords

H.5.2 User Interfaces: Haptic I/O; H.5.m.Information Interfaces and Presentation (e.g. HCI)Miscellaneous
Author Keywords

Soft Robotics; Haptics; Wearable Devices; Shape Memory
Alloys.

Figure 1. The prototype of a whole-finger haptic device with 3 SMA wirerings

INTRODUCTION

The sense of touch is one of the oldest and most importantsenses that life on earth has developed. While primitive life
forms such as nematodes have developed complex neural circuitry for touch perception [2], even the building blocks ofcomplex life already show the ability to sense touch, e.g. eukaryote cells [10]. The human perception of touch relies ona more complicated somatosensory system [15]. Cutaneous
senses are traditionally divided into four distinct modalities:
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DOI: 10.1145/3267242.3267257

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tactile (pressure, vibration, etc), thermal (temperature), pruritic (itch), and pain [15, 14]. The tactile sensing modality
can be further distinguished based on the cutaneous receptors
responsible for sensing different stimuli. Whereas lamellar
corpuscles are, together with their ability to sense pressure,especially sensitive to vibrations [26], the sense of pressure ismostly relying on the Merkel cells [13]. Both sensory stimuli are considered to follow the same neural pathways to thesomatosensory cortex, they are complementary to each otherrather than being two different sensing modalities.
In this paper, we present an alternative approach to traditional
haptic interfaces that are mainly based on vibration and require the use of servomotors, solenoids or vibration motors.
By utilizing Shape Memory Alloy (SMA) wires, we developed lightweight, soft, flexible, silent haptic actuators. The
material is flexible, has a small diameter, is silent and ca-

pable of producing sufficient force for the device actuation.
These properties open various interesting application cases
for SMAs as actuators in soft haptic devices. Especially where
the placement of hard mechanical actuators would sacrifice
the wearability, user comfort, or design and appearance, SMA
wires can be easily integrated and allow for an unobtrusive design, e.g. in wearables of various forms or smart garments. We
demonstrate the viability of our approach by presenting andevaluating different SMA device designs in different use cases,
discuss the advantages and disadvantages of our approach andthe possible application scenarios.
Furthermore, we present user studies that demonstrate thepossibility to deliver different kinds of information to the user
using pressure based haptic sensations.
The main contributions of our work are threefold.
• We present and evaluate a novel approach to wearable haptic
devices using SMA wires for giving pressure based haptic
feedback. We implement several wearable prototypes andpresent insights in using the material.
• We compare our setup with traditional feedback methods.
• We propose a neural network model characterizing andpredicting the behavior of the device, compensating forcomplicated thermo-physical properties of the prototypes.
RELATED WORKS
Soft Robotics

The field of traditional robot mechanics is mostly based on
rigid skeletons, typically made of metal, mechanical joint bearings, and actuator. This often results in heavy setups that are
only suitable for stable environments [12]. Apart from theprevious traditional and rigid machine setting, new kinds ofsoft machines have been evolving from the research domainsof rapid prototyping and proprioception. Soft robots offer a
new approach to get rid of limitations well known to traditional robotics. Soft robotics utilizes their lifelike non-linear
responses to actuation for motions and tasks in a relatively
simple way [8]. Within this field of soft hardware, more specifically SMAs present with extremely reduced size, weight, andcomplexity compared to traditional machines [21]. Especially,
because of SMAs extraordinary power-to-weight ratio andease of construction, they are a suitable alternative for small
robots [11]. For example, Fearing et al. [7] proposed a novel
hexapedal walking millirobot using SMA. Their work is designed to achieve an alternating tripod gait with considerationof size and power constraints. Hino and Maeno created aminiature robot finger using SMA as the actuator [6]. Due
to SMA wires’ nonlinear features similar to human muscles,
its structure is capable of imitating the musculoskeletal system of humans [11]. This adds to the compatibility with thehuman body, due to SMA’s compact, lightweight, dexterous
and powerful features.
Suhonen et al. [25] presented an early prototype, a wrist-typewearable using SMA to provide squeeze feedback in interpersonal communication. In their work, they linked the squeeze
feedback to an emotional feeling of grip of a hand or a hug
and concluded that compared to the other two vibrotactile andthermal feedback, squeezes were regarded as the most pleasant
type of haptic feedback. However, they only talked about thewrist-type wearable. Another work called HapticClench created by Gupta et al. [4] is a wrist-type wearable using SMA,
which set the baseline study for both wrist-type and ring-type
SMA. Using six different types of wires including SMA, they
did a JND study and detected the thresholds of ring-type SMA,
which is 0.25kg(95%CI[0.18,0.32]). This was helpful in ourwork.
Finger Augmentation Devices

In the realm of Human-Computer-Interfaces, haptic technology has gained great popularity because of its characteristics
to bring additional feedback modalities to the field. For instance, as the research Virtual Reality (VR) and Augmented
Reality (AR) develops and new application domains are explored, haptic feedback simulation is used more frequently tosupport more intuitive and immersive experience [23].
Finger augmentation devices became a major topic in thefield due to the fact that fingers and fingertips show a highconcentration of nerve cells and nerve endings enabling therecognition of even very subtle tactile stimuli [1]. Various
actuators in finger augmentation devices and the primary andthe most widespread being experimented was vibration [24].
Vibration is widely used to give haptic feedback [23], however,motors and coils are usually larger in size than SMA wire,
and the vibration has tendencies to be irritating rather thanexpressive [22].
In comparison, non-vibratory feedback mainly comes in theform of compression and shear force. Non-vibratory devices
promise to be less obtrusive than traditional vibration, because
they can be designed using different types of actuators, such as
electromagnetic, piezoelectric, and electrostatic actuators [23].
For example, Feng et al. [3] presented a wearable fingertip
haptic display utilizing speakers to generate air pressure that
inflates and deflates airbags. Pressure haptic feedback wasalso studied by Je et al. [9], who uses a solenoid in the form ofa poking ring on the finger as an eyes-free human-computerinterface. The finger-wrap gives a direct pinching pressure
on the finger. A different work by Minamizawa et al. [16]uses servomotors to generate vertical shearing force to createa weight sensation in VR environments that enable the simulation of gravity. Although the airbags are comparatively small
on the finger, the speakers for pumping air are still large insize. A hand exoskeleton designed by Polygerinos et al. [19]uses soft actuators to augment hand rehabilitation, however,the setup is rather bulky.
PROOF OF CONCEPT
DesignIn this section, we describe possible designs for different
implementations. Considering the sensitivity of the palmar
glabrous skin and the unique properties of the proposed approach we decided to concentrate on hand-worn devices only.
They are in the form of a ring.

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the presented devices and provide haptic sensations. However, most of the setups used currents higher than 340 mA toprovide sharper feedback and faster contraction times.

Figure 2. SMA wire ring with FR-4 supports and rubber coated fabricsubstrate.

Our approach relies on SMA wires (Biometal® Fiber BMF150, D=150 microns, Toki corp. ) for the device actuation. SMA’s properties enable us to make our devices soft,
lightweight, silent and flexible. BioMetal Fiber (BMF) isan anisotropically structured wire made of Nitinol (nickeltitanium alloy), which characteristically shrinks when heated.
Additionally, its electrical properties allow resistive heatingby simply applying an electric current to it. Using this property of the wire we built several prototypes discussed below,
implementing our approach.
SMA Wire Ring

The evaluated devices are made of rings of SMA wire encapsulated into a silicone tube. The tube is attached to an elastic
substrate using FR-4 or 3D-printed supports (See Fig. 2, 1).
Since there is no insulation on the SMA wire by default, asilicone tube is meant to prevent the device from short-circuits
and protect the users in case if the wire overheats as a resultof a device malfunction or over-current. The haptic feedback
is provided in form of pressure that results from SMA wire
ring’s contraction and expansion. Contraction and expansionof the wire can be controlled by varying the electric current
using PWM or voltage regulation.
Haptic GloveUsing multiple rings placed on a glove, we made a haptic
device capable of providing more complex feedback. For thisprototype, we used one ring per each phalanx of the finger.
Due to the small size of each ring, we could have placed
more than three rings per finger, but for the sake of simplicity
chose to use only three. Using this setup, we managed topresent users with more complex feedback patterns and show
the possibility of presenting numbers from 1 to 100 range.
Implementation

According to the manufacturer, one meter of BMF-150 wire
produces a force of 144 gf when a current of 340 mA is applied.
This significantly simplifies the control circuitry required toactuate the presented prototypes, reducing it to a single MOSFET or any other component that can act as a power switch.
Even at 340 mA BMF-150 was perfectly capable of actuating

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Every device presented is actuated in a similar fashion. Devices are controlled by a STM32 NUCLEO-F446RE board
and IRLML6344 power MOSFETs controlling current flowing through the BMF wire. MOSFETS are controlled witha 10 KHz PWM signal from F446RE. IRLML6344 is capable of handling up to 4A@10V currents, which is sufficientfor multiple parallel SMA rings. It presents with an R(D-S)
ranging from 29 to 37 mOhm, resulting in minimized voltage drops and heat emission. Moreover, it comes in a SMD
SOT-23 package (approx. 2×3×1 mm including the pins),
which makes it small enough to be incorporated in clothing or
wearable devices.
Both of the implementations, the two rings, are capable ofproviding senses that traditionally require bulky mechanicalactuators. Using SMA wire for actuation allowed us to makethe devices soft, flexible, silent, small and lightweight. These
characteristics are vital for the design of unobtrusive wearable
devices. The capability of providing non-vibrational haptic
feedback using the sense of pressure can open many new
possible application scenarios, such as exploring the sense ofaffective touch or enabling more realistic haptic sensations forvirtual environments.
USER STUDIESIn the following, we are going to explain the two user studies
we ran in order to evaluate our prototypes.
Users were presented with a scenario where they had to recognize the haptic feedback and map it to data related to the
hypothetical situation they were in. This adds complexity
to the task, but makes the study more realistic and gives agood perspective on real-world application scenarios of the
prototypes.
Study 1 - Applications

We conducted a series of studies, where we tested the possibility of providing information to the users using the glove
prototype with three SMA rings on the index finger of the righthand, one ring per finger phalanx. Further on, the rings will bereferred to by the name of the phalanx: proximal, intermedial,and distal.
In total eight users (Female: 4, Male: 4, Age: 19-27, AVG:
23.75, SD: 2.44) participated in two different application scenarios. In each scenario, we presented the users with a pieceof information 10 times and asked users what information did
they perceive. Users were wearing our device during the whole
testing session. Two out of eight participants had smaller palm
size and were not able to perceive some of the nuances. Since
the ring size is not adjustable these participants were wearing
an extra glove under the prototype, acting as an additional
layer of substrate transferring the force to the participant’s
finger.
Bank Account Balance

In order to investigate the discriminability of different haptic
patterns, we conducted a test were we presented users with

information regarding a hypothetical credit allowance. In total
we expressed four possible conditions (100%, 66%, 33%, 0%)
through different haptic patterns. For instance, one strong,long contraction (1500ms) on the proximal and intermedialphalanges, would be equal to 66% available from the credit
allowance; a weak yet repetitive (three times), short (125ms), contraction, on all the phalanges, suggested instead thatthe account was empty. We briefed the users on the device
setup and the scale we were using. Then the participants were
given a credit card, as soon as the card was touched, a pulse
signal was sent, contracting the rings; then the practitioner was
asking what is the card balance. The test resulted in an 81%
accuracy for identifying the right credit balance, summarized
in Fig. 3-A.

Figure 3. Confusion matrices for the experiment "Bank Account Balance"(A) and "Timing Reminder"(B), 0 represents the "home station",1 - a station away, 2 - two stations away

Timing Reminder

The second setting aimed at testing how haptic feedback presentation on different phalanges could be distinguished. For
this purpose, we designed a "Timing Reminder" test. Eachring on the finger represented a train station on a train line. For
the sake of this test the station closest to home was considered
the destination and represented by the distal phalanx ring; theneighboring station, on the intermedial phalanx; the furthest
station, on the proximal phalanx. Then the users were asked
to imagine a scenario, where they are on a train bound home,
and that they will be given haptic feedback representing thenext station on their way. Then they were presented with ahaptic sensation corresponding to one of the stations and asked
what is the next stop. Users were able to determine the station
correctly in 97.5% cases (see Fig. 3-B).
Progress Bar

For the last session, we were aiming at emulating a progressbar. It is worth noting that we used only three rings on theindex finger to represent values ranging from 1% to 100%.
We modulated the value using the timing of contraction andrelease on each phalanx. The sequence consists of 1000 ms
in total. For lower percentages, the sequence was stopped at
the time corresponding to the percentage. E.g. at 53% percent
progress the sequence was interrupted at 530ms. Participants
had a short training session, where they were showed how
100%, 75%, 50%, 25% and 15% would feel like.The sequence
representing 100% was the following: 0ms - proximal contraction, 250 ms - intermedial contraction, 500 ms - proximal
release and distal contraction, 750 ms - intermedial release,1000 ms - distal release. After that, they were asked to estimate
the progress of 10 sequences of random length. The results
show that the average error is 9.61%, SD: 8.28, SE: 0.93 (seeFig. 4).

Figure 4. Progress Bar experiment confusion chart with trend line.

custom-made shield for feedback actuation. As the input
device, we use a capacitive touchpad.
The LED was placed directly in front of the participants, thebuzzer about 1 meter in front. Participants were wearing
SMA ring on the index finger of their left hand. During thevibration reaction time test, the vibro-actuator was placed on
the glabrous skin of the palmar side of the same phalanx of thefinger as the SMA ring and fixated using Velcro tape. We used
3 Rings of different sizes to assure that the rings sit tightly on
fingers of any size.
Experiment

The study was split into four sections of 20 stimulations per
section. In each section, we used only one type of feedback.
To eliminate the ordering effects we used a counterbalanced design. Participants were asked to touch the touchpad as quickly
as they can after the stimulus onset using their right hand. The
times between stimuli onsets were randomly selected from the3000 - 10 000milliseconds range.
The measured average reaction times are as follows.

Study 2 - Reaction TimeLRA 252.41ms (SD = 55.65)

In this study, we compared users’ reaction time to the stimulus
given through the SMA ring with the reaction times to either avisual stimulus (red LED, OSRAM LS M67K, 630nm, 14mcd,
120deg), an audible stimulus (2000 Hz sound from a piezo
buzzer, manufacturer unknown), and vibro-haptic feedback(Nidec-Copal LD14-002 LRA driven with 5V power using
A3909 Full bridge driver at 100 Hz frequency). Timing wascontrolled by an STM 32 NUCLEO-F446RE board with a

LED 253.40ms (SD = 47.50)
AUDIO 232.19ms (SD = 64.88)
SMA 358.83ms (SD = 78.95)
Participants

16 users (female:7, male:9, age: 22-39 AVG:25.25, MED:25)
participated in the experiment. The participants reported no115

hearing or vision illnesses or disabilities nor any other healthrelated issues that could affect the study. Every participant had
to give written consent to the study and was informed about the
motivations, procedures, possible disadvantages, and benefitsof the study.
Discussion

To investigate the causes of slower reaction time to SMA alloy
wire rings contraction we filmed a series of contractions of
the ring using a 960 fps camera (Sony RX100-V). Frameby-frame visual analysis of the video showed that the ring
contraction starts around 90-125ms after the current onset. As
the current onset indicator, we used an LED. Furthermore,
the expansion of the ring to its normal state was slow (3-4seconds), which is probably caused by the silicone tube acting
as a heat insulator. The estimated time and the contraction
delay may vary depending on the thermal properties of therings.
To provide crisp and distinguishable feedback the ring needssome resting time to cool down and come to its normal shape,
otherwise, the perceived pressure is much weaker. The perceived sensation depends on many variables, such as the temperature of the wire, thermodynamics of the ring, ambient
temperature, tension of the wire, etc. Most of these parameters
have complicated non-linear effects on the physical behaviorof the device. To overcome this problem we developed a modelusing neural networks characterizing the device and capableof predicting its behavior. Using a model that can predict the
behavior of the device we can time the onset of the feedback
as we please. This approach would allow synchronizing theonset of pressure-based haptic feedback with other devices
or modalities that do not have an onset delay, e.g. visual or
acoustic. This would enable us to design various cross-modal
experiences using the sense of pressure. The modeling andresults are discussed in the next section.
BEHAVIORAL MODEL AND PREDICTION

Providing crisp and distinguishable feedback using this approach requires to control the SMA actuators state precisely.
However, due to the complexity of its behavior, it is hard todevelop a good mathematical model of its behavior. However,as previously mentioned, one of our shape-memory alloy’s
main characteristic is that its behavior largely depends on exposure time and temperature, with persisting effects, such as
how a short increase of the temperature may influence thedisplacement over a long period of time, even after the temperature has dropped. This has been described extensively in theliterature and is otherwise known as the hysteresis behavior of
SMA [20], a clear disadvantage that we also experience with
Nitinol, the memory alloy we are using [18].
Several sophisticated models can be used to simulate the behavior of SMA, such as the Preisach model and the JilesAtherton model, both used for ferromagnetism; however, therecent advances in neural networks allow us to simulate nonlinear systems with a minimal set of parameters [17]. Thisapproach has been introduced by Wang et al. [5]. In our current setup, the difficulty is that the resting time needed after
each contraction of the ring is hardly predictable with conventional methods. This resting parameter is critical in our

116

Figure 5. Picture of the test setup: a high accuracy laser displacement
meter acquires a peak displacement of 0.8224 mm during contraction.
The red LED indicates that the current is applied to the SMA, and wasused for time synchronization.

testing sessions: understanding the hysteresis of the SMA canhelp us triggering adequately timed haptic feedback. Indeed,
if the contraction peak is reached instantly after a current is applied to the SMA it takes more time for the ring to retrieve its
original resting shape. The SMA cannot be quickly elongatedunless it is forced-cooled, which would drastically complexify the design of our wearable device. Therefore, the stateof the system is highly dependent on variables such as theroom temperature and the devices’ history. Although the room
temperature can be easily controlled, the previous states ofthe system do not exhibit linearity, which makes predictiona difficult challenge. Therefore, anticipating the future statesof the system is of crucial importance for a fully-controllable
device.
Testing Setup

First, we designed a setup consisting of a high-speed/highaccuracy laser displacement meter (Keyence LC-2400
with LC-2440 measuring head) measuring the contraction
displacement relative to the sensor head, in a horizontal
plane. As the silicone tube, containing the SMA wire, goes
through four FR-4 supports (exerting pressure on the finger),a reflector was placed on one of them. This support wasplaced in front of the laser and the sensor was calibrated
based on its reflectance. The three other supports were
fixed on the horizontal plane so that each contraction would
move the reflector only farther away from the sensor. The
frictions to the horizontal plane, a slick plastic plate, were
negligible at this scale, as the reflective marker could movefreely without any significant difference compared to a test
done in mid-air. The whole experiment was recorded at 240
fps. First, a constant current of 850mA, at 5V was applied
to the SMA for 1s. The ring instantly contracted and wemeasured the displacement in mm, in the range 0.8004-0.881(minimum-maximum). We repeated this procedure multiple
times to evaluate the resting duration of the SMA ring, i.e.
when the displacement measured by the sensor drops tonear 0 (Fig. 5). It is worth noting the peak displacements bycontraction are remarkably invariable over successive trials.
However, the resting time is what is problematic here: after
each short contraction, it takes more time for the alloy toFigure 6. The simple fit, a spline interpolation between peak values, try
to capture the nonlinear resting behavior of the SMA but does not properly describe all the characteristics of the alloy, especially the early stage(left values on the graph).

Figure 7. Resting time after displacement: it takes more time for the
SMA to recover after successive contractions.

recover its original shape, which we assessed here over 10
successive trials, with 9 resting intervals (Fig. 7).
Behavioral Modeling

The data we collected in order to build a model consist in atime series that was acquired following the protocol describedin the previous section and depicted in Fig. 5: we monitored
the displacement dynamics of the ring by noting its magnitude
and the associated time reference. Every time we triggered acontraction, the time it took for the ring to recover its original
shape is not the same as previously noted. The resulting data,
as shown in blue in Fig. 6, is as expected very noisy and therefore very difficult to model. Here, we want to use the rightmethod to correctly assess the behavior of our SMA-actuatedring. Usually, smoothing methods are used to fit noisy data.
We decided to test a conventional ’smoothing spline’ model,using the MATLAB Curve Fitting toolbox: when calling thefit function, it returns a vector of values defined by the splineinterpolation of x (time) and y (displacement). However, as
shown in red in Fig. 6, only the values collected after about
1 min are properly fitted by this model; the displacement dynamic between 0 and 1 min is not well-captured. Indeed, thedegree of the polynomial of the spline is high, with a relatively high Root Mean Square Error (RMSE) of 0.3391. A
value closer to 0 would indicate that the fit is better for prediction. Likewise, the R-Squared error being weak at 0.6845, it
performs better than a horizontal line, but the proportion ofvariance in the dataset is not fully captured by the fit.
Prediction using Neural Network

By stark contrast, we applied a Nonlinear Autoregressive Neural Network (NARX) to the model and it largely outperformed
the simple fit, making it useful for prediction. The RMSE wasevaluated at 0.0851 (1 order of magnitude smaller comparedto the previous results with simple fit) and the R-squared error
was 0.832, a clear indicator that the predictive model is robust.
Plotting the results of the NARX model compared to the original data (Fig. 8), we see how the early trials are now fully
captured by the model. Besides, the main advantage of thisFigure 8. The Neural Network models and predicts the correct values
much more accurately than the simple fit.

model architecture is that we could implement a predictivefunction. Unlike Wang et al. [5], we didn’t use the LevenbergMarquardt algorithm for the gradient descent but the FletcherReeves conjugate method, giving fast results. Also, we only
needed n=8 in our hidden layers (8 neurons) which we found
was the optimal configuration for a better generalization acrossthe repeat of the trained network. We divided the data into
three subsets: the training set (60%), the validation set (20%)
and the test set (20%), using the ’dividerand’ function in MATLAB, with its ’divideMode’ property set as ’time’ for dynamic
network. The results are shown in Fig. 10. The neural network
computes the weights and biases of its network based on the
training set. As the training advances, the error on this set
will typically decrease. Meanwhile, a second set is used forvalidation: when the network starts to overfit the data, theerror on the validation set, instead, increases: the training is
stopped (Fig. 9).
The third set, the testing set, is never used while training toensure that we can objectively evaluate the performance ofthe trained model over a new set of data. We run the neuralnetwork multiple times until we get a satisfying model thatgeneralizes well, without over-fitting. The linear regression
value R between outputs and targets on the training, validationand test sets is R=0.97 (1 is ideal) for the test set, see Fig. 10.

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pressure, in a soft, flexible and lightweight form, unlike traditional mechanical actuators. We demonstrate the feasibility ofusing SMA wires and pressure for haptic feedback in a seriesof studies, where the participants were able to recognize theinformation they were presented with. We also present ourcharacterization of the device using neural networks, capableof predicting the device’s behavior. Our model enables simple timing and modeling of the crucial thermal and physicalproperties of the device, and provides feedback, rendering
complicated calculations unnecessary.
The proposed design solutions minimize the drawbacks, inherent to SMA wires, e.g. we propose the usage of silicone tubes
to serve as heat insulators. Moreover, we utilize a NARX
model to successfully predict the device’s onset delay andincrease of necessary resting period after consecutive contractions. In future works, we plan to explore the subjective
perception of the pressure haptic sense provided by the prototypes. Using various senses and modalities opens the way formany interesting research questions, especially in the domainsof cross-modal feedback and subjective perception of haptic
interfaces.
Figure 10. The four sub-plots represent the training, validation, andtesting data. The colored lines represent the best fit linear regression line
between outputs and targets, with the value R defining the relationshipbetween outputs and targets.

ACKNOWLEDGMENTS

This work is supported by JST CREST Grant Number JPMJCR16E1.
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