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[Yen-Ju Wu](https://orcid.org/0000-0003-2647-3407), [Lei Fang](https://orcid.org/0000-0003-4706-0521), [Yibin Xu](https://orcid.org/0000-0001-8600-8748)

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[Predicting interfacial thermal resistance by machine learning](https://mdr.nims.go.jp/datasets/c3c7ffd1-722c-4db5-97c7-980367f9c67a)

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Predicting interfacial thermal resistance by machine learningARTICLE OPENPredicting interfacial thermal resistance by machine learningYen-Ju Wu 1, Lei Fang1 and Yibin Xu1Various factors affect the interfacial thermal resistance (ITR) between two materials, making ITR prediction a high-dimensionalmathematical problem. Machine learning is a cost-effective method to address this. Here, we report ITR predictive models based onexperimental data. The physical, chemical, and material properties of ITR are categorized into three sets of descriptors, and threealgorithms are used for the models. Those descriptors assist the models in reducing the mismatch between predicted andexperimental values and reaching high predictive performance of 96%. Over 80,000 material systems composed of 293 materialswere inputs for predictions. Among the top-100 high-ITR predictions by the three different algorithms, 25 material systems arerepeatedly predicted by at least two algorithms. One of the 25 material systems, Bi/Si achieved the ultra-low thermal conductivity inour previous work. We believe that the predicted high-ITR material systems are potential candidates for thermoelectric applications.This study proposed a strategy for material exploration for thermal management by means of machine learning.npj Computational Materials            (2019) 5:56 ; https://doi.org/10.1038/s41524-019-0193-0INTRODUCTIONThermal transport across the interfaces of two different materialsis a crucial issue in micro/nanoscale electronic, photonic, andphononic devices. A temperature discontinuity exists between theinterface of dissimilar materials; this discontinuity can bedescribed as interfacial thermal resistance (ITR) in the equationR= q/ΔT, where q is the heat flux and ΔT is the temperaturedifference at the interface. In nanostructured devices, in which thecharacteristic length scales are shorter than the phonon mean freepaths, the transport mode is ballistic rather than diffusive, and ITRbecomes the dominant factor of phonon transport as the lengthscale decreases. Practically, phonon transport in thin films isaffected by a variety of interfacial properties, including roughness,binding energy, and the presence of impurities or intermediatelayers of mixed atoms. Even when the interfaces are in perfectcontact, phonon reflections occur across the boundary as a resultof differences in the acoustic properties of adjacent materials.Thus, several characteristics contribute to ITR, making it difficult todescribe or predict.Methods such as acoustic mismatch model (AMM), diffusemismatch model (DMM), and molecular dynamics (MD) arecommonly used to predict ITR. In AMM and DMM, which wereintroduced by Khalatnikov in 1952 and Swartz and Pohl in 1989,respectively, phonons in the equilibrium state are modeledwithout accounting for the nonequilibrium distribution ofphonons.1,2 AMM assumes that incident phonons at an interfaceundergo specular reflection or transmission, however, high-frequency or high-temperature phonons are scattered diffuselybecause of the interface roughness, leading researchers todevelop more accurate methods to predict ITR. Prasher proposedthe scattering-mediated acoustic mismatch model (SMAMM) andmodified traditional AMM for weakly bonded atoms at aninterface.3 DMM assumes that phonons are elastically scatteredand lose their memory of transport modes at the interface. Inaddition, the transmission probability depends on the ratio of thephonon density of states (PDOS). Therefore, the assumption ofelastically scattering will result in failure when inelastic phononsare present, as at the imperfect interfaces, where they createenergy channels. In AMM and DMM models, properties includingtemperature, density, sound velocity (longitudinal and transverse),and unit cell volume, are used as descriptors. However, AMM andDMM result in large discrepancies between the predicted andexperimental values, with correlation coefficients of 0.6 and 0.62,and with RMSE of 121.3 and 91.4 (10−9 m2K/W), respectively.4 BothAMM and DMM assume that the phonons are in equilibrium oneach side of the interface; however, in systems where the layerthickness is smaller than the phonon mean free path (e.g., systemswith multiple quantum wells and superlattices), the nonequili-brium distribution of phonons should be taken into account. Thus,AMM and DMM have important shortcomings that need to beaddressed.The effect of lattice mismatch at the interface on ITR can beevaluated by MD simulation. Equilibrium MD is more suitable forthe analysis of transient response measurements, whereas none-quilibrium MD is applied for steady-state measurements. Inclassical MD, atomic motion is calculated from classical Newtonianmechanics rather than quantum theory, and the zero-point energyis assumed to be zero. In contrast, ab initio MD provides a higheraccuracy than classical MD, however, the simulation time andparticle numbers are restricted to allow the full quantumcalculation of the electronic structure for every configuration ofatoms. All trajectories of the system often need more informationthan that which is known.Predicting the ITR for various material systems is a time-consuming process. Generally, the physical explanation with thedifferent prediction methods mentioned above can be used onlyin specific cases. It is difficult to consider every property that mightaffect ITR in a single equation, particularly for interfacialconditions. Machine learning is a cost-effective and time-efficient method to address this high-dimensional problem. TheReceived: 21 December 2018 Accepted: 10 April 20191Center for Materials Research by Information Integration (MI2I), Research and Services Division of Materials Data and Integrated System (MaDIS), National Institute for MaterialsScience (NIMS), 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, JapanCorrespondence: Yibin Xu (Xu.Yibin@nims.go.jp)www.nature.com/npjcompumatsPublished in partnership with the Shanghai Institute of Ceramics of the Chinese Academy of Scienceshttp://orcid.org/0000-0003-2647-3407http://orcid.org/0000-0003-2647-3407http://orcid.org/0000-0003-2647-3407http://orcid.org/0000-0003-2647-3407http://orcid.org/0000-0003-2647-3407https://doi.org/10.1038/s41524-019-0193-0mailto:Xu.Yibin@nims.go.jpwww.nature.com/npjcompumatsmachine learning has been implemented for thermal transportproperties in many reported works. Xin Qian et al. developedGaussian approximation potential models for analyzing thephonon dispersion stability.5 Shenghong Ju et al. designed theSi/Ge interfacial structure for controlling heat conduction throughatomistic Green’s function and Bayesian optimization.6 MasakiYamawaki et al. used Bayesian optimization for multifunctionalstructural design of graphene nanoribbons for thermoelectricmaterials.7 Our previous work also shows promising improve-ments of ITR predictive performance compared with the common-used AMM and DMM models through machine learning.4 And, themelting point, heat capacity, unit cell volume, density, and filmthickness were proposed to be important descriptors for ITRprediction.4In general, the larger dissimilarities of phonon properties lead tohigh ITR corresponding to the temperature. However, the inelasticinterfacial scattering processes, which would be influenced by theinterfacial quality, interfacial bonding, and phonon transmissioncoefficient, become important at and above the room tempera-ture. Therefore, the physical and chemical properties which affectthe interfacial quality should be carefully considered. Based on thethermophysical properties selection of our previous work,4 in thisstudy, we will further discuss how we consider lots of importantfactors, especially the interfacial conditions, through machinelearning. In the following, we will introduce how we evaluated themodels, analyzed the predictions. The details of data collection,descriptor selection, and algorithms selection can be found in theMethod section.RESULTS AND DISCUSSIONPredictive performanceThe predictive performance by three different algorithms wasestimated by R, R2 and RMSE as shown in Table 1. The R values ofRegression tree ensembles of LSBoost (simplified as LSBoost),support vector machines (SVMs), and Gaussian RegressionProcesses (GRPs) models trained with all the descriptors are0.958, 0.938, and 0.957, whereas the RMSE values are 8.944,10.897, and 9.073 (10−9 m2K/W), respectively. The R and R2 valuesof the LSBoost, SVMs, and GRPs models with all descriptor sets areall higher than those with only the thickness and propertydescriptors, while all the RMSE are further reduced. It is said thatintroducing the compound and process descriptors, whichprovides chemical characteristics and material compositionsinformation, can enhance the predictive performance of all threemodels. Take LSBoost model for example, the experimental ITRvalues against predicted ITR values are shown in Fig. 1. The navycircles are the results predicted by the SVMs model with alldescriptors while the orange squares are the results predicted withthickness and property descriptors. The orange circles are morescattered and far away from the black diagonal line. In other words,by including all the descriptor sets, the mismatch between thepredicted and experimental values becomes smaller. To furtherinvestigate the effect of descriptors on the ITR prediction, threematerial systems with the largest improvement were taken asexamples in larger scale. Figure 2 shows the ITR experimental valuesagainst predicted values of Pb/diamond (circle), Au/GaN (square),and Au/Ti/GaN (triangle), respectively. The predictive performance ofall of these material systems are improved by the models with alldescriptors, even for the material system with interlayer such as Au/Ti/GaN. For the Pb/diamond, the predicted ITR value get closer tothe experimental value by 16.5 (10−9 m2K/W).Table 1. The predictive performance evaluation of R, R2 and RMSE byvarious algorithmsAlgorithms R R2 RMSEAll descriptorsLSBoost 0.958 0.919 8.944SVM 0.938 0.879 10.897GPR 0.957 0.916 9.073Property descriptors, thicknessLSBoost 0.952 0.907 9.575SVM 0.815 0.664 18.171GPR 0.934 0.871 11.271Note: The top are the models predicted with all descriptors listed in Fig. 8and the bottom are the models predicted with property descriptors andthicknessFig. 1 The mismatch between experimental and predicted ITRvalues by LSBoost model. The navy spheres represent the valuespredicted by the model with all descriptor while the orange squaresare predicted by the model with property descriptors and thicknessFig. 2 The mismatch between experimental and predicted ITRvalues by LSBoost model of three interfaces, Pb/diamond, Au/GaN,and Au/Ti/GaN, are represented as circle, square, and triangle,respectively. The navy symbols represent the values predicted bythe model with all descriptor while the orange symbols arepredicted by the model with property descriptors and thicknessY.-J. Wu et al.2npj Computational Materials (2019)    56 Published in partnership with the Shanghai Institute of Ceramics of the Chinese Academy of Sciences1234567890():,;Generally, the database is not sufficiently large (e.g., lack ofexperimental results for some material systems; more data forbinary systems than for ternary or quaternary systems), therefore,the known physical and chemical knowledge should be includedas descriptors to assist the machine in learning from the data.ITR predictionAfter achieving high predictive performance, we input 80,282material systems (metal/metal is excluded) to predict by the threemodels of LSBoost, GPRs, and SVMs. The 80,282 material systemsare composed of 293 materials that the similarities betweenmaterials can be found in Fig. 3. These 293 materials are elementsor binary compounds. The materials included in the trainingdataset are defined as red stars and the other materials aredefined as navy spheres in Fig. 3. The similarities are evaluated byEuclidean distance of all descriptors (except for thickness,interlayer) and then projected in the two-dimensional plotthrough metric Multidimensional scaling (MDS),8 which uses asimilarity matrix to plot the graph between a series of n objects tothe coordinates of the same objects in an m-dimensional space.The m is usually fixed at two or three so as to be visualized easily.That is to say, the metric MDS seeks a low-dimensionalrepresentation of the data in which the distances between outputtwo points are as close as possible to the similarity in the originalhigh-dimensional space. The distance between two points isshorter, the similarities of their descriptors (properties) are higher.For examples, the metals which are located in the left bottomhave different EN and IP properties compared with otherinorganic compounds, Pr6O11 and Fe7Se8 which are far awayfrom the other materials have large unit cell volumes, and LiHwhich is on the top alone has high heat capacity and low densitythan the averages.From the ranking of ITR predictions, we compared the top-100high-ITR material systems predicted by models of LSBoost, GPR,and SVM. Among the top-100 high-ITR material systems, there are25 material systems repeatedly predicted by at least two modelsas shown in Fig. 4a. The predicted top-100 high-ITR materialsystems are illustrated by circles in Fig. 4a, and the intersectionsshow the repeatedly-predicted material systems. There are 13 and15 material systems predicted by SVMs and LSBoost, and SVMsand GPRs, respectively as shown in Fig. 4a. Besides, there are threematerial systems, Bi/graphite, Bi/diamond, and Bi/B, predicted byall three models corresponding to the orange points in Fig. 4b.The similarities of the 25 material systems are plotted by two-dimensional MDS in Fig. 4b. These 25 material systems in the MDSplot are mainly separated into two groups: Bi/oxides and AsI3/Tellurides or Iodides (such as Sb2Te3, and CdI2).The linear correlation by Pearson heatmap between thedescriptors and ITR by the three models can be found in Fig. 5.If the color is lighter yellow or darker navy, it shows strongerpositive or negative linear correlation with ITR, respectively. Fromthe prediction of 80,282 various material systems, there is noobvious correlation except melting point and mass in Fig. 5a–c. Onthe other hand, from the prediction of the top-100 high-ITRmaterial systems, the stronger linear correlation of compounddescriptors, such as atomic coordinates, binding energy and ionicpotential, can be found in Fig. 5d–f. Besides, some descriptors ofFig. 3 The two-dimensional MDS plot of 293 materials by theirproperties including heat capacity, density, melting point, unit cellvolume, composition ratio, atomic coordinate (AC), electronegativity(EN), ionization potential (IP), mass, and binding energy. The redstars are the materials included in the training dataset, and othermaterials are navy spheres. The similarities of properties are higher,the distance between two points is closerFig. 4 a The circle regions represent the top-100 high-ITR material systems predicted by the three models of LSBoost, GPR, and SVM. The blueand orange intersection regions express the 25 material systems repeatedly predicted at least by two models. b The two-dimensional MDSplot of the 25 material systems according to the blue and orange regions in a. The three orange points are predicted by all three models. Thesimilarities of properties are higher, the distance between two points is closerY.-J. Wu et al.3Published in partnership with the Shanghai Institute of Ceramics of the Chinese Academy of Sciences npj Computational Materials (2019)    56 the two materials in Fig. 5d–f, (e.g., f_melt and s_melt, f_densityand s_density, f_AC1y and s_AC1y), show opposite linear trends. Itis said that if the differences of several descriptors between thetwo materials are larger, the ITR might be increased. However, theeffect of descriptors on the target (ITR) cannot be consideredindividually, but a combination effect based on various algorithms.Although all three models have similar improved trend onpredictive performance after introducing all descriptors, theimprovement of various material systems might differ amongthree models. The predicted ITR of the 25 material systems by thethree models can be found in Fig. 6. Some material systems, suchas Bi/BeO, Bi/Al2O3, and Bi/Si, have very close predicted values,while some material systems, such as AsI3/ PtTe2 and AsI3/Bi2Te3,have larger differences. It is normal that the predicted values differamong various algorithms even if the predictive performance areall higher than 93 %. It is also implied that the correlation betweenthe descriptors and the target (ITR) might have various regulationsand be fitted by several algorithms. In order to prevent the partialand inadequate analysis, the intersection region among the threemodels with high accuracy would be a good way to seek thecandidates from the prediction.We measured the ITR of Bi/Si interface by frequency-domainthermoreflectance9 as 51.8 ± 4.5 (10−9 m2K/W), which is in therange of the predicted ITR of 50.68–61.13 (10−9 m2K/W) as shownin Fig. 6. The Bi/Si material systems, the red points in Fig. 4b andFig. 6, achieved the ultralow thermal conductivity of0.16Wm−1K−1.10 This thermal insulating Bi/Si nanocomposite thinfilm, which was proposed for the first time, was composed ofcrystallized-Bi in an amorphous-Si matrix by a laboratory-builtcombinatorial sputtering system. The low thermal conductivitycan be attributed to the high ITR, high ratio of interfacial surfacearea to volume and high atomic ratio of Si/Bi. The details ofinterfacial design and nanostructure analysis can been found inour previous paper.10 It is proved that the high-ITR predictions arepotential candidates for thermal insulating applications. Throughthe ITR prediction by machine learning, the material systemsexploration for thermal management can be accelerated.A precise ITR prediction through machine learning with highcorrelation coefficient R of 0.96 was achieved by furtherconsidering the interfacial conditions based on chemical, physical,and material properties. The descriptors are categorized into threedescriptor sets: property descriptors, compound descriptors, andprocess descriptors, respectively, as shown in Fig. 8. From the top-100 high-ITR prediction among 80,282 kinds of material systems,25 material systems were repeatedly predicted by at least two ofthe models of LSBoost, GPRs, and SVMs. There are two maingroups of the 25 material systems as shown in MDS plot: Bi/oxidesand AsI3/ Tellurides or Iodides. One of the 25 material systems, Bi/Si, accomplished the ultralow thermal conductivity of0.16Wm−1K−1. The high-ITR prediction is proved to be thepotential candidates for thermal insulating or thermoelectricapplications. The ITR predictive model can also be extended formore specific thermal needs by limiting the material searchingspace, such as high melting point for high temperatureFig. 5 The Pearson heatmap of the correlation between the descriptors and ITR. The (a–c) are the predictive results of 80,282 differentmaterial systems by SVM, GPR, and LSBoost, respectively. The (d–f) are the predictive results of top-100 high-ITR material systems by SVM, GPR,and LSBoost, respectively. The f and s represent the two materials in the material system. The property descriptors [heat capacity (heatcap),density, melting point (melt), and unit cell volume (unit).] and compound descriptors [composition ratio (R), atomic coordinate (AC),electronegativity (EN), ionization potential (IP), mass, and binding energy (Eb)]. The R1 and R2 represent the composition ratio of first andsecond elements. The AC coordinates are defined as (ACix, ACiy), where i represents the order of the element of the compound, and x and yare the group and period in the periodic table, respectively. ENc and ENa, and IPc and IPa represent the EN and IP of cation and anion,respectivelyFig. 6 The distribution of predicted ITR by the three models of SVM(square), GPR (circle), and LSBoost (triangle). The input conditions ofthickness and temperature are set as 90 nm and 298 K. The orangepoints are the three material systems in the orange intersectionregion corresponding to Fig. 4a. The red points show the predictedITR of Bi/Si which was proved to have similar value with experimentsof 51.8 ± 4.5 (10−9 m2K/W) as black starY.-J. Wu et al.4npj Computational Materials (2019)    56 Published in partnership with the Shanghai Institute of Ceramics of the Chinese Academy of Sciencesenvironment. This strategy can accelerate the material develop-ment for thermal management.METHODSData of ITRThe ITR database in this study contained 1317 data entries describing 456interface samples composed of 54 materials, including metals, semicon-ductors and insulators. The materials are elements or binary compounds.The 456 interfaces are defined by the film, interlayer, substrate materials,measurement temperatures and experimental conditions. The 1317 dataentries contained in the database are experimental data collected from 85published papers as shown in Fig. 7.9,11–93 Generally, the ITR decreaseswith the temperature increasing as shown in Fig. 7. The main contributionfor heat transfer of metals is mobile electrons, however the heat transfer ofnon-metals is lattice vibrations. Therefore, the metal/metal interfaces arenot considered together in the training dataset. Besides, the interfacesincluding 2D materials (e.g., graphene, MoS2), compounds with uncertaincompositions (e.g., TiOx), polymers, or under specific treatment such asplasma bombardment are not considered this time.Descriptor selectionLots of factors, such as interface conditions, thermal properties of materialsadjacent to the interface and temperature, can affect the ITR; theseproperties determine the transfer mode and efficiency of the carriers. Ingeneral, constructing the machine learning model in material sciencesuffers from the lack of data or the inconsistency from the references,especially some material properties such as thermal conductivity, soundspeed, and Debye temperature. If the data has missing properties, then itcannot be used for training or further predicting and the size of the datasetwill shrink a lot. From our previous paper, the thermal related properties ofheat capacity, density, melting point, and unit cell volume, as well as thematerial property of thickness were selected as good descriptors with highdata-consistency among the references and high data-availability, andachieved good predictive performance.4However, when two materials meet at an interface, the new binding willform aside materials and tend to reduce the total energy of the system.The mode of phonon transfer changes based on the interfacial conditions,and the PDOSs of the two materials forming the interface shift to reducemismatch between the materials, thereby improving the thermalconductance.94,95 Thus, the interfacial conditions which become importantespecially at or above the room temperature should be further consideredin the model. In order to enhance the machine predictive power based onthe known knowledge, we further considered the interfacial properties andcategorized these properties into three descriptor sets (property descrip-tors, compound descriptors, and process descriptors), as shown in Fig. 7.Property descriptors include the physical thermal properties, which isbased on the previous results,4 of the materials on both sides of theinterface, whereas compound descriptors include the properties that candescribe the chemical characteristics of the interfaces (e.g., binding energy,electronegativity, and ion potential). Process descriptors include theproperties that can be tuned during the experimental procedure, suchas film thickness and interlayer (e.g., Al/SiO2/Si: with interlayer and Al/Si:without interlayer). These descriptors were collected from various sources,including Atom Work Adv in NIMS,96 TPRC data series,97 and publishedpapers.9,11–93The compound descriptors were atomic ratio (R), atomic coordinate(AC), electronegativity (EN), ionization potential (IP), mass, and bindingenergy (Eb) as shown in Fig. 8. The atomic ratio of the compounds for thefirst and second elements was defined as R1 and R2, respectively; takeAl2O3 for example, R1 and R2 are 2 and 3. AC represents atomic coordinatesdefined from the periodic table: the group as the x coordinate and theperiod as the y coordinate as (ACix, ACiy), where i represents the order ofthe elements of the compound. For a binary compound, the coordinates ofeach element of the compound are introduced. As an example, thecoordinates of (AC1x, AC1y) and (AC2x, AC2y) for AlN are (13, 3) and (15, 2),respectively. These coordinates also provide the information of atomicradius and electronic configuration. In the periodic table, the atomic radiusincreases from right to left of group and from up to bottom of period.Groups 2 and 15 of the periodic table are more stable as a result of thecompletely filled and half-filled electronic configurations, respectively.Element in groups 2 or 15 are thought to need more energy to removeelectrons from the outside orbitals. EN reflects the ability of an atom toattract an electron and can be used to predict the formation of ionic orcovalent bonds. EN ranges from 0 to 4, with a higher EN indicating greaterattraction to electron. IP is the energy required for an isolated atom todischarge an electron and become a cation. The degree of mismatch inmass and bond energy also affects the ITR of two dissimilar materials. Choiet al. reported that differences in mass and bond energy result inmismatches between phonon dispersion and limit high frequency phonontransport at the interface.98The process descriptors include film thickness and interlayer. Filmthickness is proved to be an important descriptor and affect the predictiveperformance a lot in our previous paper.4 The change in phonontransmission probability at the interface corresponds to the change inthickness.60,94 The interlayer reflects whether an interlayer is presentbetween the materials at the interface; it is assigned a value of either 1 (ifan interlayer is present) or 0 (if no interlayer is present). In many cases, theadhesion layer, a naturally or thermally formed oxidation layer, and surfaceplasma treatment will form interlayers or a mixed region between thematerials instead of a clear interface. Hopkins et al. reported that increasedatomic mixing and disorder at the interface have detrimental effects onITR.52 Deng et al. proposed that in the weak interfacial coupling, thedetailed interfacial nanostructure and thickness of the heterojunctionsignificantly affect the ITR; whereas the structural effects are not obvious incases of strong interfacial coupling.99 In other words, the interfacial servesas a coupling layer to tune the phonon transport mode and DOS,particularly when the interfacial film has mediating vibrational proper-ties.94 Moreover, the interlayers or materials with mediating propertiesalong the heat flux may possibly enhance the channels for thermalconductance.95 After selecting the descriptors, the three descriptor setswere used to train and generate the predictive models.Fig. 7 The interfacial thermal resistance against the measurementtemperature of the experimental data collected from 85 publishedpapers. The ITR of metal/metal interfaces are represented by half-filled orange squares, and the other interfaces are represented bynavy spheresFig. 8 List of the three descriptor sets: property descriptors,compound descriptors, and process descriptorsY.-J. Wu et al.5Published in partnership with the Shanghai Institute of Ceramics of the Chinese Academy of Sciences npj Computational Materials (2019)    56 Machine learningThe entire dataset was randomly separated into ten folds: one testing foldand nine training folds. This process was repeated ten times while keepingthe testing folds orthogonal to each other so that the testing data were notduplicated. During each iteration of this process, embedded ten-fold crossvalidation was conducted to generate appropriate hyperparameters foroptimizing the model. After the ten times iterations, the correlationcoefficient R, R2 and the root-mean-squared error (RMSE) of the ten testfolds from each process were used to estimate the models.According to the previous paper, the linear repressor which has worsepredictive performance and the auto-descriptors-selected regressors (e.g.,Least-absolute shrinkage and selection operator regularization (LASSO-GLR)) which neglects the necessary descriptors (e.g., measurementtemperature) are not suitable for this dataset.4 Therefore the supportvector machines (SVMs), Gaussian Regression Processes (GRPs) andRegression tree ensembles of LSBoost (simplified as LSBoost)100,101 wereused in terms of the dataset size and non-linear based regressors. SVMsand GPRs are kernel-based algorithms, the front constructs an optimalhyperplane as a decision surface to separate and train the observations,and the latter is a nonparametric method which finds a distribution overpossible functions f(x) consistent with the observations. The kernelfunctions used for SVMs and GPRs in this study are both Radial BasisFunction. LSBoost performs least-squares boosting, which fits regressionensembles to minimize mean-squared error. The ensemble fits a newlearner using the difference between the observed response and thepredictions of all previous learners. The algorithms were run using MATLABstatistical software.101 The acquisition function for hyperparametersoptimization was expected-improvement-plus for all algorithms. The initialalgorithm settings and additional algorithms details can be found in ourprevious paper and the Matlab Statistics and Machine LearningToolbox.4,101DATA AVAILABILITYThe data that support the findings of this study are available from the correspondingauthor upon reasonable request.ACKNOWLEDGEMENTSThis work was supported by “the Materials research by Information Integration”Initiative (MI2I) project of the Support Program for Starting Up Innovation Hub fromJapan Science and Technology Agency (JST).AUTHOR CONTRIBUTIONSY.X. led the design of the work; Y.W. collected the data, did the data analysis andwrote the paper; L.F. preformed the predictive models by machine learning.ADDITIONAL INFORMATIONCompeting interests: The authors declare no competing interests.Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claimsin published maps and institutional affiliations.REFERENCES1. Park, H. S. & Punch, J. 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To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.© The Author(s) 2019Y.-J. Wu et al.8npj Computational Materials (2019)    56 Published in partnership with the Shanghai Institute of Ceramics of the Chinese Academy of Scienceshttp://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/ Predicting interfacial thermal resistance by machine learning Introduction Results and Discussion Predictive performance ITR prediction Methods Data of ITR Descriptor selection Machine learning Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.Acknowledgements Acknowledgements Author contributions Competing interests ACKNOWLEDGMENTS