Materials Discovery and Properties Prediction in Thermal Transportvia Materials Informatics: A Mini ReviewXiao Wan,†,‡,∥ Wentao Feng,‡,∥ Yunpeng Wang,†,‡ Haidong Wang,§ Xing Zhang,§ Chengcheng Deng,*,‡

and Nuo Yang*,†,‡

†State Key Laboratory of Coal Combustion and ‡School of Energy and Power Engineering, Huazhong University of Science andTechnology, Wuhan 430074, China§Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China

ABSTRACT: There has been increasing demand for materials with functional thermal properties, but traditional experimentsand simulations are high-cost and time-consuming. The emerging discipline, materials informatics, is an effective approach thatcan accelerate materials development by combining material science and big data techniques. Recently, materials informatics hasbeen successfully applied to designing thermal materials, such as thermal interface materials for heat-dissipation, thermoelectricmaterials for power generation, and so forth. This Mini Review summarizes the research progress associated with studiesregarding the prediction and discovery of materials with desirable thermal transport properties by using materials informatics.On the basis of the review of past research, perspectives are discussed and future directions for studying functional thermalmaterials by materials informatics are given.

KEYWORDS: Materials informatics, machine learning, material discovery, thermal conductivity, thermoelectric properties,interfacial thermal conductance

Thermal properties, such as thermal conductivity, inter-facial thermal conductance (ITC), and so forth, play a

critical role in micro/nanoelectronics, optoelectronics, thermo-electrics, and other thermal/phonon engineering areas.1,2 Forexample, there is an increasing demand for materials with highthermal conductivities that can dissipate the massive heat inelectronic devices.3−6 In addition, ITC dominates the thermaldissipation of composites with interfaces on the micro/nanoscale.7,8 Therefore, the effective discovery of materialswith high thermal conductivities or ITC is crucial forimproving the performance and extending the lifetime of awide variety of related devices. On the other hand, thermo-electric power generation is essential for utilizing low-gradewasted heat. Researchers have been seeking materials with highconversion efficiency for decades to improve their perform-ance9−14 for which materials with low thermal conductivity areessential.Because of the limitations of cost, time, and hardware, the

discovery of materials with desirable thermal propertiesremains challenging in both experiments and simulations.15

Materials informatics (Figure 2) introduces a brand new way

of accelerating the discovery of materials with specialproperties.16,17 Intrinsically, materials informatics is the processthat allows one to survey complex, multiscale information in ahigh-throughput, statistically robust, and yet physically mean-ingful manner.17 Materials informatics is an emerging area ofmaterials science16−18 based on simulations or experiments inmaterials science and machine learning algorithms.16

Materials informatics can effectively and accurately capturethe relationship between structures and properties by datamining techniques for materials discovery and propertiesprediction. Seeking structure−property relationships is anaccepted paradigm in materials science, yet these relationshipsare often nonlinear and complicated.17 There is rarely a well-accepted multiscale relationship that is accurately captured bytraditional theory or experiments because there are differentphysical laws that act at the macro-/microscale. Hence, there

Received: December 29, 2018Revised: May 13, 2019Published: May 15, 2019

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are opportunities for using materials informatics, which canbuild these relationships by data mining without concern forthe principles. Data mining is a new field that merges ideasfrom statistics, machine learning, databases, and parallel anddistributed computing.19 Data mining takes the form ofbuilding models from a given data set, which can capture thenonlinear mapping relations between material structures andproperties for materials discovery. In addition to patternrecognition, data mining in big data techniques has anotherprimary function in understanding materials behavior:prediction. The predictive aspect of data mining, classificationand regression analysis can help facilitate the understanding ofmultivariable correlations in the “processing−structure−properties” paradigm that form the core of materialsdevelopment.16 In light of this feature, materials informatics,seeking material structure−property relationships using the bigdata technique, can significantly advance all functionalmaterials fields, such as optical/electronic/phononic materials,acoustics materials, magnetic materials, mechanical materials,nuclear materials, and so forth. The role of materialsinformatics is popular throughout all fields and applicationsin materials science and engineering.17

Recently, materials informatics has been successfully appliedin the search for materials or structures with desirable thermalproperties, such as thermal conductivity, ITC, and thermo-electric properties.20−23 Considering that there have alreadybeen studies in this emerging field, it is necessary to reviewtheir progress and provide an outlook on future work, whichwill be helpful for the development of materials informatics inthe thermal field.In this paper, a mini-review is given of the recent research

progress on the applications of materials informatics instudying thermal transport. First, we provide a briefintroduction of materials informatics. Then, the related studiesof using materials informatics in thermal properties, includingthermal conductivity, interfacial thermal conductance, andthermoelectric conversion efficiency, are summarized. Finally,some perspectives on the challenges, shortcomings andoutlook are provided to aid future investigations related tothis topic.Materials Informatics. The framework of materials

informatics mainly consists of three parts: (1) data procure-ment, or the acquisition of data generated by simulations orexperiments in materials science; (2) data representation, orsystematic storage of representative information about thestructures and properties of these materials; and (3) datamining, or data analysis aimed at searching for relationshipsbetween structure information and desired properties.17 The

procedure of materials informatics in the thermal field is shownin Figure 1, and the specific contents of the three steps aredescribed as follows.

Data Procurement. Data procurement is acquiring thephysical properties and structural information on givenmaterials. Calculations (such as first-principles,21,24 moleculardynamics,23,25,26 lattice dynamics,27,28 and so forth), experi-ments29 and online libraries30 have been used to collect thesedata. With these different techniques, database repositoriescontaining effective training data can be constructed.

Data Representation. Data representation refers to thesystematic storage of representative information about thestructures and properties of materials. The key component ofdata representation is the selection of characteristics (e.g.,formation energies, band structure, density of states, magneticmoments) to describe the materials, which are called“descriptors”. The descriptors represent different kinds ofmaterials, and they are only one part of the input in datamining. One purpose of materials informatics is to establishmapping relations between the descriptors and target proper-ties, which, herein, are thermal properties. Thus, gooddescriptors are the key to effective materials informatics.Once a series of good descriptors is identified, the search foroptimum materials or properties prediction within the databasecan be performed intrinsically or extrinsically.31

Data Mining. Data mining aims at searching for novelmaterials or exploring new physical insights in which machine

Figure 1. Schematics of applying the materials informatics method to studying thermal transport issues.

Figure 2. Processing−structure−property−performance relationshipsof materials science and engineering, and how materials informaticsapproaches can help decipher these relationships via forward andinverse models. Adapted with permission from ref 16, licensed under aCreative Commons Attribution (CC BY) license. Copyright 2016 AIPpublishing.

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learning is widely used.17 The main machine learningalgorithms used in materials informatics include supervisedlearning, the task of which is finding a function that maps aninput to an output based on samples.32 Through the trainingmodels built by machine learning algorithms, materials withnovel properties can easily be selected or predicted. Currently,the most popular algorithms include Bayesian optimization,random-forest regression, and artificial neural networks. A briefintroduction of these algorithms is provided below.Bayesian optimization is a well-established technique for the

global optimization of black-box functions.33,34 Bayesianprediction models, most commonly based on the Gaussianprocess, are usually employed to predict the black-boxfunction, where the uncertainty of the predicted function isalso evaluated as predictive variance.35 The Bayesianoptimization algorithm (BOA) typically works by assumingthat the unknown predicted function is sampled from aGaussian process and maintains a posterior distribution for thisfunction as observations are made.34 The procedure forBayesian optimization is as follows. First, a Gaussian processmodel is developed from two observations that are randomlyselected from the database. The model is updated by (i)sampling the point at which the observation property isexpected to be the best and (ii) updating the model byincluding the observation at the sampled point. These twosteps are repeated until all data are sampled.31

Random forest36 is a prominent ensemble method adaptedfrom bagging, which combines multiple decision trees into onepredictive model to improve performance.20 Random forest isrelatively robust to various problems, such as compoundclassification, and can handle outlier data or high-dimensionaldata well.36,37 A random forest model consists of K decisiontrees that are established in three steps. First, K sets of data aregenerated from the initial data set by a bootstrap method.Second, a tree is grown with a particular random selectionalgorithm to obtain the predictions for each data point. Third,the final prediction is made by a weighted vote (inclassification) or weighted average (in regression) of all forestpredictions.37 In addition to performing the prediction task,random forest also provides an intrinsic metric to evaluate theimportance of each descriptor.20

The artificial neural network (ANN) and deep neuralnetwork are well-developed machine learning methods thatmimic human brains to learn the relationships between certaininputs and outputs based on experience.38 The ANN hasrecently been successfully applied in the fields of modeling andprediction in many thermal engineering systems.39−41 The

ANN has become increasingly attractive in the past decade.The assets of the ANN compared to classical methods are itshigh speed and simplicity, which decrease engineeringefforts.29,42,43 The most basic and commonly used ANNconsists of at least three or more layers, including an inputlayer, an output layer, and a number of hidden layers.29 Thenumber of neurons in the input layer equals the number ofparameters in the material selection process. The output layerrepresents the fitness of the candidate materials. In addition,the hidden layer represents the relationships between the inputand output layers. Through training and testing stages, theANN model is well-established. In the training stage, thenetwork is trained to predict an output based on input data.The training stage is stopped when the testing error is withinthe tolerance limits. In the testing stage, the network is testedto stop or continue training according to measures oferror.29,40−42

In addition to the three machine learning algorithmsmentioned above, there are some other efficient algorithmsin progress, such as autoencoder, convolutional neuralnetworks and generative adversarial networks, which aremore advanced and powerful. The autoencoder is a type ofartificial neural network that is used to learn efficient datacoding in an unsupervised manner. The convolutional neuralnetwork (CNN) is a class of deep neural networks thatrequires relatively little preprocessing compared to other imageclassification algorithms.44 The generative adversarial network(GAN) is a class of machine learning systems in which twoneural networks contest with each other in a zero-sum gameframework.45 Recently, these three machine learning algo-rithms have become widely used for image recognition anddata generation.

Thermal Conductivity. As a popular topic, thermalconductivity is one of the most important material properties.In some cases, materials with ultralow or superhigh thermalconductivities are essential for engineering applica-tions.2,3,8,46−50 Many studies have focused on low thermalconductivity materials for thermoelectrics and thermalinsulation materials.10,14 In search of compounds with ultralowthermal conductivity, several studies have been performed onpredicting the lattice thermal conductivity by materialsinformatics. In addition, high thermal conductivity materialsfor improving the thermal management of electronic deviceshave also attracted wide attention, such as single-crystal boronarsenide with special band structure.46−50 However, norelevant reports on predicting high thermal conductivitymaterials by machine learning algorithms currently exist. In

Figure 3. (a) Prototype Half-Heusler structure with primitive vectors and a conventional cell. (b) Elements considered in this study. Adapted withpermission from ref 20, licensed under a Creative Commons Attribution (CC BY) license. Copyright 2014 APS publishing.

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addition to the discovery of lattice thermal conductivity, thereare also some studies of thermal conductivity predictionmodels for porous composites and liquids built by machinelearning algorithms.In the study of lattice thermal conductivity (LTC, κω), via

random-forest regression among 79 000 entries of the database(Figure 3), Carrete et al. proposed three half-Heuslersemiconductors with LTCs below 5 Wm−1 K−1 for furtherexperimental study.20 These authors also found that materialswith larger average atomic radii in positions A and B tend tohave lower thermal conductivity. More importantly, efficientmethods are introduced for reliably estimating the κω for aseries of compounds, which are based on a combination ofrandom-forest regression and first-principles calculations. Thatis, there is a very good prospect for machine learning methodsfor applications in accelerating material design. In this study,we note that the performance in predicting LTC usingmachine learning algorithms is largely affected by the selecteddescriptors.To find suitable descriptors, in 2017 Tanaka’s group

proposed a procedure to generate a series of compounddescriptors from simple atomic representations.31 When theprocedure was applied to the LTC data set, these descriptors interms of Bayesian optimization exhibited good predictiveperformance, which verified the accuracy of this approach. Inaddition to the bulk lattice thermal conductivity, machinelearning algorithms can also predict the thermal conductivitiesof composite materials. In August 2018, Wei et al. proposedmodels obtained from the support vector regression, includingGaussian process regression and convolution neural network.51

The prediction of effective thermal conductivity based on these

models and effective medium theory is consistent withexperimental data.Furthermore, Tanaka’s group combined the Bayesian

optimization and first-principles anharmonic lattice-dynamicscalculations to find materials with ultralow thermal con-ductivity.21 In 2015, these authors discovered 221 materialswith very low thermal conductivity in a library containing54,779 compounds. Two compounds even have an electronicband gap <1 eV, which makes them promising for thermo-electric applications. Compared to other methods, this strategydoes not have excessive computation costs due to the use offewer initial data. However, Tanaka’s methods could justdetermine materials with low thermal conductivity instead ofhigh thermoelectric figures of merit.In addition to the prediction and optimization of the thermal

conductivity of solids, some studies have focused on fluids. Inearly 2009, Kurt et al. reported an ANN model to predict thethermal conductivity of ethylene glycol/water solutions basedon experimentally measured variables.29 The regressionanalysis between the prediction by the model and theexperimental data proved the high accuracy of the ANNmodel. The superiority of this model compared to practicalexperiments lies in its lower time consumption and cost, whichis the advantage of machine learning algorithms. In addition, amultilayer perceptron−artificial neural network (MLP-ANN)model was reported by Zendehboudi et al. to predict theeffective thermal conductivity of nanofluids with desiredaccuracy.52

Overall, machine learning algorithms have been successfullyapplied to predict the thermal conductivity of crystals,composites and liquids. The predictions match well with abinitio calculations and experimental data. It is noted that

Figure 4. Correlation between the experimental values and the values of interfacial thermal resistance predicted by the AMM, DMM, GLR, GPR,and SVR using the same descriptors. Adapted with permission from ref 54, licensed under a Creative Commons Attribution (CC BY) license. Andno changes were made. Copyright 2017 Springer Nature publishing.

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different descriptors should be investigated and compared inorder to decrease the deviation of the prediction. Althoughmachine learning algorithms have been successfully applied ininvestigating thermal conductivity, some issues remain. Theaccuracy of prediction via machine learning algorithms must befurther improved. High-precision machine learning modelsusually need to be trained using massive numbers of data.However, the initial training data we obtain from experiments,simulations, or online databases are often inadequate. Moreprecise machine learning algorithms that do not depend onmassive initial data must be applied in the research of thermalproperties, such as autoencoder or generative adversarialnetwork. In addition, well-accepted descriptors that representthe candidates must be established and verified. Further, themachine learning prediction model has a limited scope ofapplication and is only valid to a certain or specific situationextent. For instance, the model that merges the effectivemedium theory and artificial neural network51 is suitable fordealing with macroscopic materials only. Prediction modelsaimed at the meso-/micro/nanoscale or multiscale arenecessary to develop in the future.Interfacial Thermal Transport. Interfacial thermal trans-

port plays an important role in the thermal management ofhigh power micro- and optoelectronic devices in which a largenumber of interfaces exist.7,8,53 Prediction of the interfacialthermal transport property is important for guiding thediscovery of interfaces with ultralow or superhigh interfacialthermal conductance, which can further adjust the thermalconductivity of the whole system.In 2017, three different machine learning algorithms were

used by Zhan et al. to predict ITC, who compared their resultswith the commonly used acoustic mismatch model (AMM)and diffuse mismatch model (DMM) to verify the accuracy.54

The three different machine learning algorithms includedgeneralized linear regression (GLR), Gaussian processregression (GPR), and support vector regression (SVR). Theresulting correlation coefficient (R) (Figure 4) showed thecorrelations between the experimental data and the prediction

by different methods, demonstrating that these methods havebetter accuracy compared to traditional AMM and DMM.54

Then, via trained machine learning models, Yang et al.predicted the ITC between graphene and hexagonal boron-nitride (h-BN) using only the known parameters of systemtemperature, coupling strength and tensile strains.23 Themachine learning algorithms used in these predictions includedlinear regression, polynomial regression, decision trees, randomforest and artificial neural network. In addition, the perform-ances of these different methods were compared withmolecular dynamics simulations. It was shown that theartificial neural network made the best predictions. Theseresults illustrated the simplicity and accuracy of machinelearning methods for the prediction of interfacial thermaltransport properties.In addition to the prediction of the interfacial thermal

transport property, the optimization of interfacial structures isalso significant for the discovery of materials with specialthermal transport properties. To minimize or maximize thevalue of ITC across Si−Si and Si−Ge interfaces (Figure 5), Juet al. proposed a method combining atomistic Green’s function(AGF) and Bayesian optimization in May 2017 which couldobtain the optimal interfacial structures with a fewcalculations.22 Then, these authors applied this method to aSi/Ge superlattice and determined the interfaces with thehighest and lowest ITC by calculating a few interfacestructures. These results deepen the understanding of themechanisms in interfacial thermal transport. These results alsoindicate the effectiveness of materials informatics in designingnanostructures with desirable thermal properties.It has been reviewed that the interfacial thermal conductance

was predicted via three different machine learning algorithms.The accuracy of machine learning results was confirmed bycomparing the results to experimental measurements. Differentmachine learning methods had different accuracies. Somesimple models, such as generalized linear regression andsecond order polynomial regression, were not accurate enough,whereas some complicated models, such as random forest and

Figure 5. Interfacial Si/Ge alloy structure optimization. (a−d) Optimal structures with the maximum and minimum interfacial thermalconductance for Si−Si and Si−Ge interface. (e,f) The 10 optimization runs with different initial choices of candidates, where the insets show theprobability distributions of ITC obtained from calculations of all candidates. Adapted with permission from ref 22, licensed under a CreativeCommons Attribution (CC BY) license. Copyright 2017 APS publishing.

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artificial neural network, were much more accurate. Moreover,accelerating methods were proposed for searching interfacialstructures with the highest/lowest ITC. However, there arestill many challenges that have not been overcome by existingstudies. First, the studies have shown prediction accuraciesusing different algorithms and have determined the bestalgorithms but they do not provide the physical explanations ormechanism for why those algorithms are best. The accuracyresults of various algorithms cannot be simply referred to andused by other researchers in the selection of appropriatealgorithms. That is, other researchers must test the accuraciesof different algorithms themselves. Second, descriptors areselected as empirical parameters or by intuition, andcorrelations are ignored. In fact, data processing methods,such as principal component analysis and partial least-squaresregression, can discover the weight power of descriptors andprovide the criteria for descriptor selection, further improvingthe accuracy of prediction. Third, the structures used in theprediction of ITC are quite simple and many practical factorsare ignored, ultimately leading to poor applicability ofpredictions.Thermoelectricity. The performance of thermoelectric

materials is characterized by the dimensionless thermoelectricfigures of merit (ZT), which is defined as TσS2/κ, where T, σ,S, and κ are temperature, electrical conductivity, Seebeckcoefficient, and thermal conductivity, respectively.55,56 Athermoelectric material with a high ZT is an “electron-crystalphonon-glass”, which has a low thermal conductivity, highelectrical conductivity, and high Seebeck coefficient. Recently,materials informatics has been used in the design and searchfor high-ZT thermoelectric materials, diminishing the need forexhaustive experiments and simulations.In 2014, Carrete et al. used the decision tree method to

determine the rules that dictate the thermoelectric perform-ance of a nanograined half-Heusler compound, good or bad.57

These authors found two key properties for high ZT, which area large lattice parameter and either a wide gap (at hightemperatures) or a large effective mass of holes (at roomtemperature). These results could stimulate experimentalresearch for improving the thermoelectric performance ofhalf-Heusler semiconductors. In 2018, Yamawaki et al. realizedthe goal of searching structures with high ZT.58 These authorsused Bayesian optimization to obtain an optimized graphenestructure with a higher ZT. The procedure is similar to theirgroup’s previous work.22 Bayesian optimization was superiorfor accelerating the searching procedure.In addition to the prediction of figures of merit (ZT)

directly, materials informatics were also used to predict the keyfactors that affect ZT. The Seebeck coefficient is an importantfactor related to ZT. To precisely predict the Seebeckcoefficients of different crystalline materials, Furmanchuk etal. used the random forest algorithm and had great success.59

Some experimental results were used as inputs in their study toobtain an accurate prediction, indicating that it is unnecessaryto synthesize or calculate materials to obtain their Seebeckcoefficients. These authors also determined some importantattributes of the Seebeck coefficient and explored therelationship between the Seebeck coefficient and ZT atdifferent temperatures, the results of which will guideresearchers to find materials with higher thermoelectricconversion efficiencies.It is also important to compare the feasibility and

practicability of different methods. To guide the selection of

materials for experimental researchers, a recommendationengine (http://thermoelectrics.citrination.com) based onmachine learning was proposed by Gaultois et al. in 2016.30

To ensure accuracy, these authors tested an example set ofcompounds generated by the engine, RE12Co5Bi (RE = Gd,Er), which exhibited surprising thermoelectric performance(Figure 6). Materials with low thermal conductivity and high

electrical conductivity that were predicted by this engine werealso confirmed experimentally. It is suggested that thisparadigm could greatly promote the discovery of goodthermoelectric materials. In summary, the studies mentionedabove will accelerate advances in the procedures for findingmaterials with high ZT.This section shows that thermoelectric properties may be

predicted by machine learning algorithms, such as the decisiontree method. Specifically, some rules that determine the ZT ofmaterials were revealed by the machine learning algorithm. Inaddition, an open-source machine learning-based recommen-dation engine was proposed to find new materials with highZT. Although some studies of thermoelectric properties havebeen performed, a method to predict ZT is lacking. This lack isbecause the function of ZT has a complex correlation with theSeebeck coefficient, thermal conductivity, and electricalconductivity. In addition, the predictions, which use experi-ment results as inputs, ignore the sample differences insynthesis, experimental conditions, material microstructuresand phase diagrams, carrier concentrations, and so forth, whichcould cause deviations in the predictions. With this in mind, apossible extension of the presented work lies in the exhaustivecollection of such information for known thermoelectricmaterials.

Summary. To date, there have been increasing inves-tigations in the interdisciplinary field of materials informaticsand thermal science. In this Mini Review, we summarize recentrepresentative research progress on thermal transport bymaterials informatics. The procedures for the practicalimplementation of materials informatics are presented,including the introduction of some important machine learning

Figure 6. Thermoelectric characterization of RE12Co5Bi (RE = Gd,Er). (a) Electrical resistivity, (b) Seebeck coefficient, (c) thermalconductivity, and (d) thermoelectric ZT as a function of temperature.Adapted with permission from ref 30, licensed under a CreativeCommons Attribution (CC BY) license. Copyright 2016 AIPpublishing.

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algorithms. A comprehensive framework and main conclusionsare exhibited in discovering materials with optimal thermalconductivity, interfacial thermal conductance, and thermo-electricity efficiency. Moreover, some critical factors that affectthe discovery efficiency and predictive efficacy are discussed.The superiority of materials informatics in discovering novelmaterials with desirable thermal properties is also emphasized.For prediction accuracy via machine learning, present

studies show reliable results. Most studies produced a highcoefficient of determination (R2 > 0.88), showing that thecomputational accuracy is acceptable. The accuracy is largelyinfluenced by the selection of models and descriptors.Generally, simple models, such as generalized linear regressionand second order polynomial regression, show bad perform-ance. Complicated models, such as random forest and artificialneural network, can be much more accurate. Moreover, asophisticated selection of descriptors could also improve theaccuracy; for example, it is observed that the coefficient ofdetermination is improved from 0.92 to 0.96 in the predictionof ITC.54 Interestingly, the predicted value of the Seebeckcoefficient is comparable to the measurement of recentlymanufactured materials, which is not included in the trainingdatabase.59

However, machine learning methods can do little to predictabnormal properties. The machine learning model can predicta new sample within the normal scope, but the amount ofabnormal data usually is not large enough to precisely predictoutliers.60 For instance, in 2019 superhigh thermoelectricfigures of merit (ZT > 400) were reported.61 However, thishigh ZT could only exist at the structure phase transitiontemperature; because there are insufficient similar data aroundthat temperature, this abnormal value of ZT is difficult topredict using machine learning methods.Aside from the challenge of materials informatics in thermal

field, there are some common issues that must be resolved.When performing materials informatics, it remains challengingto generate more multipurpose and time-saving machinelearning algorithm codes, select fast and effective descriptors,and transfer data to practical knowledge or physical pictures.The main challenge lies in the physical interpretation of theprocess by machine learning. The underlying physicalmechanism cannot be fully understood only by machinelearning, which benefits from the use of other theoretical orsimulative methods. Advances in studying heat transfer innanomaterials/nanostructures are needed by machine learning.Additionally, when preparing data, especially for complexstructures, simulations or experiments require much time toobtain enough data for training. For example, the neuralnetwork usually requires a large amount of data. To avoid thedifficulty in obtaining massive numbers of data, researchersmay make full use of data reported in existing papers, insteadof collecting all data themselves. Therefore, an online databasecontaining comprehensive reported thermal properties ofdifferent materials is necessary and urgent.Perspectives. Looking beyond the success and shortage of

materials informatics applications, there are some areas ofprogress that could be addressed in the near future. Weconclude this paper by illustrating several important challengesthat deserve further investigation.Recently, in the field of thermal transport three main

machine learning methods, including Bayesian optimization,random forest, and artificial neural network, have been used inpredicting the thermal transport properties of materials. With

the development of machine learning methods, more efficientand powerful machine learning models, such as autoencoder,convolutional neural networks, generative adversarial network,and so forth, have been developed, which have beensuccessfully used in other fields. Compared to the threemachine learning algorithms that have already been used forinvestigating thermal properties, these newly developedalgorithms are very suitable to model complex nonlinearrelations, deal with small data sets, and flexibly capture therelationships between different types of characteristic variables.These powerful methods are expected to be able to address thedifficult problems associated with thermal transport (such asthe size dependence function of thermal conductivity acrossmultiscales) as mentioned above, or the direct prediction ofZT).Although materials informatics has been successfully applied

in a few thermal problems, it is still controversial that materialsinformatics could make contributions in solving other, moredifficult issues. For example, there is a multiscale problem innanostructured/composite materials. The multiscale predictionof thermal transport properties is still far from reality.62 Thethermal conductivity is size-dependent at the micro/nanoscale,and Fourier’s law is no longer applicable when the materials’sizes are comparable to the phonon mean free path.63−65 Thegap between nano and macro is large; therefore, it remains tobe seen if machine learning methods could make a differencein the multiscale prediction of thermal transport properties.Another important issue is the wave-particle duality of

phonons, which are the main heat carriers in semiconductors.In the past decades, most of the approaches to control phonontransport and tailor thermal properties have been based onparticle66,67 or wave nature.68,69 As the phonon particle andwave transport are governed by different physical laws, thecollective manipulations of two strategies can lead to ultralowthermal conductivity.70,71 However, the phonon particle andwave effects are intertwined, and their direct individualcontributions to the modulation of thermal conductivity havenot been well established. It is possible that machine learningmethods would make a contribution and a convincing analysisin this field.As reviewed in this paper, previous materials informatics

studies have mostly been based on the combination ofsimulations and machine learning algorithms. Therefore, howcan we use these predictions to guide experiments? Moreover,how do we combine experimental techniques and machinelearning algorithms? In terms of machine learning models, theprediction of new materials with desirable thermal properties isobtained. Then, an experimental synthesis will be conductedaccording to the structure information (such as crystalconfiguration and element species) that corresponds to thedesired properties. Further, to apply materials informatics inexperiments a clear iteration loop must be clarified, whoseprocedure is divided into three steps. First, a large amount ofexperimental data is needed. The combinatorial experimentsare proposed to be controlled by work flows for meeting thisrequirement.72 Second, based on data mining, machinelearning models could be built to search for or predict newmaterials with desired properties. The key metrics lie in therelationships learned by the machine learning models betweenthe structure information and desirable thermal properties,which form the foundation of materials’ property prediction.Finally, if material properties meet the necessary requirements,the materials can be synthesized in terms of machine learning

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predictions. Otherwise, the predicted data will be added to thetraining database to improve the machine learning models.Hence, it may be possible to merge different machine learningmodels and a combinatorial experiments strategy to realize aloop process in materials informatics. The critical issues mayinclude the management of work flows, the tracking ofmultivariable measurements and data storage.In addition, machine learning can be used to fit parameters

in experiments. Recently, the regression algorithms in machinelearning have become very popular in economics and statisticsand may also be widely applied to measuring the thermalproperties of materials, especially at nanoscales. A properregression algorithm can establish a specific mathematicalmodel and obtain the quantitative relationship between thetarget properties and the experimental data, after which theunknown thermal properties can be calculated. The essence ofthe regression algorithm is to adjust a smooth and balancedmodel function f (x, y.....), which aims to minimize the fittingerror and avoid overfitting problems. In measurements ofthermal properties, there are hard issues caused by fittingcurves for which machine learning algorithms could make adifference. For instance, in the measurements of time-domainthermoreflectance (TDTR) or in the 3ω method, thermalproperties, such as thermal conductivity, electron−phononcoupling factor, and interfacial thermal conductance, can becalculated by multivariable fitting the experimental data.Traditional successive iterations can produce a fitting curvewith slight deviation, where the fitting result is sensitive to thesetting of the initial values. Interestingly, in the machinelearning algorithms, the kernel ridge regression can solve thismultiple nonlinear model and avoid the sensitivity problem ofinitial values.On the other hand, many environmental parameters are

involved in the fabrication of materials, such as temperature,time, humidity, intensity of illumination, and so on. Theseparameters may have a great influence on the thermalproperties of nanomaterial samples. For instance, in thefabrication of metallic nanofilms by physical vapor deposition,parameters, such as the pressure and temperature of chamber,deposition rate and time, thickness of adhesion layer, andannealing temperature, have significant effects on the finalthermal properties of samples. Similarly, in Si nanowiresynthesis by chemical vapor deposition, the ambient temper-ature and pause time in the ablation also have great influenceon the final morphology of the Si nanowires.73 By principalcomponent analysis or random forest algorithm, a relationshipbetween the desired thermal properties and complicatedenvironmental parameter setting can be obtained. Then, asample with desired properties can be obtained by tuning theenvironmental parameters.Materials informatics has emerged as a powerful tool for

many fields in materials science and engineering. It is highlydesirable that materials informatics be applied in more fields tosolve more difficult thermal issues.

■ AUTHOR INFORMATION

Corresponding Authors*E-mail: dengcc@hust.edu.cn (C.D.).*E-mail: nuo@hust.edu.cn (N.Y.).

ORCIDNuo Yang: 0000-0003-0973-1718

Author Contributions∥X.W. and W.F. contributed equally to this work.

NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTS

The work was sponsored by National Natural ScienceFoundation of China No. 51576076 (N.Y.), No. 51606072(C.D.), No. 51711540031 (N.Y. and C.D.), the NaturalScience Foundation of Hubei Province No. 2017CFA046(N.Y.), and Fundamental Research Funds for the CentralUniversities No. 2019kfyRCPY045 (N.Y.). We are grateful toXiaoxiang Yu, Dengke Ma, and Han Meng for usefuldiscussions. The authors thank the National SupercomputingCenter in Tianjin (NSCC-TJ) and the China ScientificComputing Grid (ScGrid) for providing assistance incomputations.

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