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Naoki Yoshida, Yutaro Iwabuchi, Yasuhiko Igarashi, [Yuma Iwasaki](https://orcid.org/0000-0002-7117-277X)

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[Networking autonomous material exploration systems through transfer learning](https://mdr.nims.go.jp/datasets/a6ea884d-b205-4a37-b424-86def8485177)

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Networking autonomous material exploration systems through transfer learningnpj | computationalmaterials ArticlePublished in partnership with the Shanghai Institute of Ceramics of the Chinese Academy of Scienceshttps://doi.org/10.1038/s41524-025-01851-8Networking autonomous materialexploration systems through transferlearningCheck for updatesNaoki Yoshida 1, Yutaro Iwabuchi 1,2, Yasuhiko Igarashi 1,3,4 & Yuma Iwasaki 4Autonomous material exploration systems that integrate robotics, material simulations, and machinelearning have advanced rapidly in recent years. Although their number continues to grow, thesesystemscurrently operate in isolation, limiting the overall efficiency of autonomousmaterial discovery.In analogy to how human researchers advance materials science by sharing knowledge andcollaborating, autonomous systems can also benefit from networking and knowledge exchange.Here, we propose a framework in which multiple autonomous material exploration systems form anetwork via transfer learning, selectively utilizing relevant knowledge from other systems in real time.We demonstrate this approach using three distinct autonomous systems and show that suchnetworking significantly enhances the efficiency of material discovery. Our results suggest that theproposed framework can enable the development of large-scale autonomous material explorationnetworks, ultimately accelerating progress in material development.Thediscovery of newmaterials is amajor driver of technological innovation,enabling transformative advances acrossdiverse industries.However, recentprogress in materials science has led to increasingly complex materialstructures and compositions, resulting in an exponentially growing searchspace for novel materials. As a result, the process of identifying promisingmaterials has become increasingly challenging. Traditionally, researchershave explored this vast search space manually, evaluating each candidatematerial one by one. Figure 1a shows the conventional human-drivenmaterial exploration loop, where materials are synthesized manually, theirproperties are characterized experimentally, and the resulting data areanalyzed to guide the selection of the next material to be synthesized.Through repeated iterations of this loop, researchers can accumulateknowledge that can eventually lead to the discovery of new materials.However, this conventional approach has become inadequate for efficientmaterial exploration as the search space continues to expand1.To address these challenges, autonomousmaterial exploration systemsthat integrate robotics, material simulations, and machine learning, parti-cularly active learning, have garnered increasing attention in recent years2.These systems are broadly categorized into two types. The first type, shownin Fig. 1b, is an autonomous robotic material exploration system3. In thisapproach, robotic platforms automatically perform material synthesis andproperty characterization, whereasmachine learning algorithms are used toanalyze the resulting data to determine the next candidate material. Thisprocess forms a closed-loop cycle driven by data and experimentation,enabling continuous explorationwithout human intervention.Notably, thisapproach has accelerated the discovery of high-performance materials. Forexample, it has been demonstrated that a mobile autonomous robot canautonomously perform synthesis, characterization, and data analysis, suc-cessfully discovering new photocatalytic materials4. Several other autono-mous systems have been developed and are actively being used to facilitatethe discovery of novel materials5–17.The second approach, as shown in Fig. 1c, involves simulation-basedautonomous material exploration systems. For example, density functionaltheory (DFT) simulations can be regarded as virtual material synthesis andcharacterization, where a material’s composition and structure are used asinputs, and its physical properties are generatedasoutputs. By coupling suchsimulations with machine learning in a closed-loop framework, materialscan be explored autonomously in silico, ultimately leading to the discoveryof candidates with desirable properties. One notable example is asimulation-based autonomous system that combinesDFT calculationswithmachine learning to explore the large chemical space ofmagnetic materials,successfully identifying a new alloy with exceptionally high magnetization(M)18. Many other simulation-based systems have also been developed andare actively advancing the discovery of materials computationally19–28.1Degree Programs in Systems and Information Engineering, Graduate School of Science and Technology, University of Tsukuba, Tsukuba, Ibaraki, Japan.2ResearchCenter forMagnetic andSpintronicMaterials (CMSM), National Institute forMaterials Science (NIMS), Tsukuba, Japan. 3Tsukuba Institute for AdvancedResearch, Tsukuba, Ibaraki, Japan. 4Center for Basic Research on Materials (CBRM), National Institute for Materials Science (NIMS), Tsukuba, Japan.e-mail: IWASAKI.Yuma@nims.go.jpnpj Computational Materials |          (2025) 11:362 11234567890():,;1234567890():,;http://crossmark.crossref.org/dialog/?doi=10.1038/s41524-025-01851-8&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41524-025-01851-8&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41524-025-01851-8&domain=pdfhttp://orcid.org/0009-0002-6811-3178http://orcid.org/0009-0002-6811-3178http://orcid.org/0009-0002-6811-3178http://orcid.org/0009-0002-6811-3178http://orcid.org/0009-0002-6811-3178http://orcid.org/0009-0004-8235-1097http://orcid.org/0009-0004-8235-1097http://orcid.org/0009-0004-8235-1097http://orcid.org/0009-0004-8235-1097http://orcid.org/0009-0004-8235-1097http://orcid.org/0000-0003-1042-6657http://orcid.org/0000-0003-1042-6657http://orcid.org/0000-0003-1042-6657http://orcid.org/0000-0003-1042-6657http://orcid.org/0000-0003-1042-6657http://orcid.org/0000-0002-7117-277Xhttp://orcid.org/0000-0002-7117-277Xhttp://orcid.org/0000-0002-7117-277Xhttp://orcid.org/0000-0002-7117-277Xhttp://orcid.org/0000-0002-7117-277Xmailto:IWASAKI.Yuma@nims.go.jpwww.nature.com/npjcompumatsAs previously described, autonomous material exploration systemsthat integrate robotics, simulations, andmachine learning are being activelydeveloped worldwide and are operating in both physical and virtualenvironments. The applicability of these systems is expected to expandfurther across a vast material search space, contributing to the discovery ofnumerous novel materials.Despite this progress, current robotic and simulation-based systemstypically operate in isolation, which substantially limits their overall effi-ciency. To visualize this limitation, we consider the conventional human-driven approach to materials research. Figure 1d shows three researchers,each focusing on a distinct target property out of magnetization (M), Curietemperature (Tc), and spin polarization (Sp).M is a fundamental property ofmagnetic materials that is crucial for applications such as permanentmagnets andmagnetic devices.Tc represents the thermal threshold at whicha material transitions from a ferromagnetic to a paramagnetic state and isessential for ensuring thermal stability in magnetic systems. Sp, defined asthe imbalance between up-spin and down-spin electrons at the Fermi level,is critical for spintronic applications, including magnetic sensors and datastorage devices.Each researcher independently performs iterative cycles of synthesis,property characterization, anddata analysis to optimize the respective targetproperties. Notably, they also engage in discussions and exchange insights.For instance, a researcher investigating high-M materials (Researcher 1)may benefit from insights shared by colleagues studying high-Tc(Researcher 2) or high-Sp materials (Researcher 3). By incorporating thetrends observed in Tc or Sp, Researcher 1 can refine their experimentalstrategy, potentially improvingdiscovery efficiency. This examplehighlightsthe importance of interdisciplinary knowledge exchange in human-drivenresearch—an element currently lacking in most autonomous systems.Unlike human researchers, current autonomous material explorationsystems lack mechanisms for cross-domain knowledge sharing. Each sys-tem operates independently, relying solely on data related to its specifictarget properties. For example, an autonomous system designed to discovermaterials with highM—referred to as the autonomous system forM (ASM)—conducts Bayesian optimization using only M-related data. Even if thissystem receives additional data from other systems, such as Tc data fromASTc or Sp data from ASSp, integrating this external information into itspredictive models remains challenging. A naïve approach may involveincorporating Tc or Sp as additional input features in ASM’s predictionmodel for M. While this approach may improve predictive accuracy incertain cases, it limits themodel’s predictions tomaterials for whichTc or Spvalues are already available. Consequently, the optimization process of ASMbecomes confined to the subset of materials previously explored by ASTc orASSp, significantly reducing the system’s ability to discover new materials.Therefore, simply sharing raw data among autonomous systems isinsufficient for improving exploration efficiency. Instead, a novel frame-work is required—one that enables multiple autonomous materialexploration systems to form a collaborative network. Such a frameworkcould enhance overall performance by utilizing external knowledge ratherthan directly exchanging raw data, as illustrated in Fig. 1e.Transfer learning has potential to serve as a key technology of suchcollaborative networks by facilitating the transfer of knowledge acrossautonomous systems. It is a machine learning method in which knowledgeobtained from one task is adapted for use in a different but related task,thereby improving learning efficiency29. In materials science, transferlearning has been widely adopted and is recognized as a powerful andpromising approach30–33. However, its application within autonomousexploration systems has been scarcely investigated and remains in itsinfancy34.This study proposes a method that enables knowledge sharing amongmultiple autonomousmaterial exploration systems by combining ensembleneural networks (ENNs) with transfer learning. Instead of exchanging rawdata, these systems transfer learned representations, enabling the incor-poration of insights from other target domains. We demonstrate that thisFig. 1 | Autonomous material exploration systems and its networking.a Schematic of the conventional human-driven material exploration loop, includingmaterial synthesis, property characterization, and decision-making for the nextcandidate material. bRobotic autonomousmaterial exploration systemwith roboticexperimentation andmachine learning. c In silico autonomousmaterial explorationsystem with material simulation and machine learning. d Illustration of knowledgeexchange among various researchers for material discovery. e Illustration ofknowledge exchange among various autonomous material exploration systems.https://doi.org/10.1038/s41524-025-01851-8 Articlenpj Computational Materials |          (2025) 11:362 2www.nature.com/npjcompumatsapproach significantly improves the efficiency of autonomous materialexploration.ResultsNetworking of autonomous material exploration systemsTo evaluate the effectiveness of the proposed autonomous materialexplorationnetwork,wedemonstrate that the three systems,ASM,ASTc, andASSp, depicted in Fig. 1e, can successfully share knowledge through transferlearning. This networked configuration improves the efficiency of materialexploration compared with isolated operations.Figure 2a outlines the algorithm used by ASM within the autono-mous material exploration network. Initially, the ASM observes the Mvalues of a small set of candidatematerials (10 in this study) to constructan initial dataset. This design reflects the practical reality that autono-mous material exploration often begins with very limited prior data;accordingly, we intentionally kept the initial dataset small. Based on thisdataset, ensemble neural network models (ENMs) were constructed.Ensemble learning improves prediction accuracy and enables the esti-mation of predictive uncertainty (variance)35,36. A variety of machinelearning methods can be used for Bayesian optimization, includingGaussian Process Regression (GPR)37, the Sequential Model-basedAlgorithm Configuration (SMAC)38, and the Tree-structured ParzenEstimator (TPE)39. In this work, however, we adopted ENMs, which notonly support Bayesian optimization but also provide a straightforwardframework for incorporating transfer learning. Each of the 10 indivi-dual neural networks (NNs) in the ensemble consisted of three hiddenlayers containing 100, 100, and 10 neurons. Additional details regardingthe ENM architecture and training procedures are provided in the“Methods” section.Figure 2b shows theENMM,whichwas trained topredictM as the targetvariable YM using material descriptors (XM1 ;XM2 ; . . .XMN ) as explanatoryvariables.ENMM : YM ¼ f XM1 ;XM2 ; . . .XMN� � ð1ÞTo ensure generalizability, we employed simple composition-basedvectors with N components as material descriptors throughout this study.Because these descriptors dependonly on stoichiometry, they canbe appliedto both robotic and simulation-based autonomous material explorationsystems (Fig. 1b, c). Similarly, Fig. 2c shows the ENMTc, which was trainedto predict Tc using the data obtained from ASTc and its correspondingmaterial descriptors (XTc1 ;XTc2 ; . . .XTcN ).ENMTc : YTc ¼ f XTc1 ;XTc2 ; . . .XTcN� � ð2ÞFigure 2d shows the ENMSp, which was trained to predict Sp based ondata acquired from ASSp and its associated material descriptors(XSp1 ;XSp2 ; . . .XSpN ).ENMSp : YSp ¼ f XSp1 ;XSp2 ; . . .XSpN� �ð3ÞConsidering that the network consisted of three autonomous materialexploration systems, three correspondingENMswere constructed.Notably,the number of ENMs increases accordingly when additional autonomoussystems are incorporated.Subsequently, two transfer learning models (TLMs) were constructedto incorporate external knowledge into the prediction of M within ASM.Fig. 2 | Workflow of the autonomous material search exploration system usingENN and transfer learning for networking and sharing knowledge. a Schematicworkflow of the autonomous material exploration system for M (ASM).b–d Architecture of ENNs for predicting M, Tc, and Sp, respectively. e TLMTc!Mconstructed by fine-tuning the base model ENMTc for predictingM. f TLMSp!Mconstructed by fine-tuning the base model ENMSp for predicting M. The corre-spondingworkflows for ASTc andASSp are provided in Supplementary InformationsS1 and S2.https://doi.org/10.1038/s41524-025-01851-8 Articlenpj Computational Materials |          (2025) 11:362 3www.nature.com/npjcompumatsFigure 2e shows TLMTc!M, which transfers the knowledge and trendsobtained in ASTc regarding Tc to ASM for predicting M. Specifically, apretrained model ENMTc, trained on Tc, was used as the base model. Thefirst two hidden layers on the input side (blue) were frozen, whereas theoutput layer (red)wasfine-tuned using theMdata obtained fromASM. Thisapproach allows the model to utilize knowledge obtained from Tc toenhanceM prediction, yielding the following TLM :TLMTc!M : YTc!M ¼ f XM1 ;XM2 ; . . .XMN� � ð4ÞSimilarly, Fig. 2f depicts TLMSp!M, where ENMSp serves as the basemodel. The model was fine-tuned using theM data observed in ASM.TLMSp!M : YSp!M ¼ f XM1 ;XM2 ; . . .XMN� �ð5ÞConsequently, three models were obtained for predictingM: the non-transfer model ENMM and the transfer learning models TLMTc!Mand TLMSp!M.Subsequently, validation loss Vloss was compared among ENMM,TLMTc!M, and TLMSp!M using the M data and material descriptorsavailable in ASM. In this evaluation, 80% of the available material data wasused as training data, whereas the remaining 20% was used as validationdata. The best-performing model (BPM) was then selected based on thelowest validation loss.BPM ¼ argminD2ENMM ;TLMTc!M;TLMSp!MVloss Dð Þ ð6ÞThis model-selection step is critical for avoiding negative transfer, aneffect in which transfer learning may reduce prediction performance. Iftransfer learning proves beneficial, the BPM is either TLMTC!M orTLMSp!M; otherwise, the non-transfer model ENMM is adopted. Asincorporating external knowledge does not always lead to improvement,this validation-based selection process ensures that only beneficial modelsare used.The acquisition function is then calculated using the selected BPM toidentify the next material candidate forMmeasurement. In this study, theupper confidence bound (UCB) criterion was employed as the acquisitionfunction40. TheM of the selected target material (MTM) was measured andadded to the dataset. IfMTM did not satisfy the desired threshold, then themodels ENMM, ENMTc, and ENMSp were retrained using the updateddataset, as shown in Fig. 2a. In this dataset, the amount ofM data increased,alongwith that ofTc and Sp data, owing to the concurrent execution of ASTcand ASSp over time.This iterative process enables ASM to incorporate knowledge acquiredfrom ASTc and ASSp, although these systems focus on different targetproperties (Tc and Sp). Similarly, ASTc and ASSp can conduct autonomousexploration by utilizing knowledge from other systems. The details of theworkflow and methodology from the perspectives of ASTc and ASSp areprovided in Supplementary Information S1.DemonstrationTo evaluate the effectiveness of the proposed autonomous materialexploration network, a demonstration was conducted using a comprehen-sive dataset derived from high-throughput DFT calculations41. The datasetincludes values for Sp, Tc, and M for 16,908 ternary alloys with B2 crystalstructures. These materials are composed of elements selected from a set ofN = 38, including Li, Be, B, Mg, Al, Si, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn,Ga, Ge, As, Y, Zr, Nb, Mo, Ru, Rh, Pd, Ag, Cd, In, Sn, Sb, Hf, Ta, W, Ir, Pt,Au, and Pb.The number of initial observations was set to 10. The autonomousexploration speeds of ASTc andASSp were adjusted relative to ASM to reflectdifferences in the experimental complexity of measuring each target prop-erty. Specifically, ASTc was assigned a speed three times faster than ASSp,whereas ASM was operated three times faster than ASTc. These relativespeedswere designed to approximate the real-world feasibility of themodel.M can be measured relatively quickly using techniques such as vibratingsample magnetometry and superconducting quantum interferencedevices42,43. By contrast, measuring the Tc requires an evaluation of thetemperature dependence ofM, which is time-consuming44. Measuring Sp isparticularly challenging and typically involves complex experimentalmethods such as Andreev reflection45, nonlocal spin valve measurements46,and spin- and angle-resolved photoemission spectroscopy47.Figure 3a shows the progression of the maximum observed Sp duringautonomous exploration by ASSp. Light red lines represent results from 10trials conducted with networking enabled via transfer learning from ASTcand ASM, whereas the solid red line indicates the average performance. Forcomparison, results from the autonomous exploration using only local SpFig. 3 | Comparison of the autonomous material exploration with and withoutnetworking using transfer learning. a–c Progress of autonomous materialexploration in ASSp, ASTc, and ASM, respectively. The light red and blue linesindicate the results of autonomous exploration with and without networking usingtransfer learning. The solid lines represent the average of 10 demonstration trials.For comparison, results from a random search are shown in black. Green linesindicate 90% of the ground-truth values. While networking with transfer learningimproves autonomous exploration efficiency in ASSp and ASTc, it has no noticeableeffect in ASM.https://doi.org/10.1038/s41524-025-01851-8 Articlenpj Computational Materials |          (2025) 11:362 4www.nature.com/npjcompumatsdata (i.e., without networking) are shown in blue, while those from a ran-dom search are shown in black. In the non-networked demonstration (blueline in Fig. 3), we trained three ENMswith distinct random initializations ofthenetworkweights and selected theBPMfromamong them. In addition, atthe start of each exploration step, the network weights were randomlyreinitialized before training. The networked approach (red) consistentlyoutperformed both the non-networked (blue) and random (black) strate-gies, identifying high-Sp materials more rapidly. On average, reaching 90%of the ground-truth value (Sp = 0.862) required 17.4 observations withnetworking and 24.9 without.Figure 3b presents the results for ASTc. Similar to ASSp, the networkedapproachdemonstrated superior exploration efficiency comparedwithboththe non-networkedmethod and random search. The benefits of networkingwere particularly pronounced during the initial phase of autonomousexploration, where an improvement in efficiency was observed. Because thematerials discovery process typically operates in a low-data regime andexperimental or simulation throughput is limited, such early-stage gains areespecially valuable. The mean number of observations required to reach90% of the ground-truth value (Tc = 843.9) was 27.4 with networking,compared with 31.8 without networking.Figure 3c shows the corresponding results for ASM. While both net-worked and non-networked autonomous strategies significantly out-performed the random search, no significant difference was observedbetween them. This suggests that networking has a limited impact onexploration efficiency in ASM, at least under the current conditions.Reaching the ground-truth value (M = 2.352) required, on average, 19.5observations with networking and 20.2 without networking.Overall, these results indicate that transfer-learning-based networkingimproves the efficiency of autonomous exploration, particularly for systemssuch as ASSp and ASTc. Notably, the model selection step prevents negativetransfers by excluding models that degrade predictive performance. Con-sequently, networking does not reduce exploration efficiency. However, insome cases, such as ASM, networking may not yield substantial improve-ments. A detailed analysis of the phenomenon is presented in the followingsection.Validation loss transition on training dataWe analyzed the transition of the validation loss during autonomousexploration, along with the timing, frequency, and direction of transferlearning. Figure 4a shows the evolution of the validation loss associatedwiththe BPM in ASSp, where the candidate models include ENMSp, TLMTc!Sp,and TLMM!Sp. The red curve represents the validation loss when net-working via transfer learning is enabled,whereas the blue curve correspondsto a non-networked setting. Coloredmarkers indicate themodel selected asBPM at each step: orange for transfer from ASM (TLMM!Sp), green fortransfer from ASTc (TLMTc!Sp), and small black dots for the non-transfermodel (ENMSp). The results show that ASSp effectively utilizes externalknowledge fromASM andASTc, leading to amarked reduction in validationloss. This trend aligns with the enhanced exploration efficiency shown inFig. 3a.Figure 4b shows the validation loss trajectory of BPMs in ASTc, wherethe candidate models are ENMTc, TLMM!Tc, and TLMSp!Tc. Coloredmarkers indicate themodel selected as BPMat each step: orange for transferfrom ASM (TLMM!Tc), purple for transfer from ASSp (TLMSp!Tc), andblack for non-transfer model (ENMTc). The transfer learning-enabled set-ting showed a lower validation loss than the non-networked setting.Notably, transfer from ASM was frequently selected, suggesting that theknowledge gained by ASM, owing to its higher exploration speed and largerdata volume, was effectively transferred.Figure 4c shows the validation loss trajectory of BPMs in ASM, wherethe candidate models are ENMM, TLMTc!M, and TLMSp!M. The selectedmodels are marked in green for transfer fromASTc (TLMTc!M), purple fortransfer from ASSp (TLMSp!M), and black for the non-transfer model(ENMM). Unlike in the cases of ASSp and ASTc, no substantial improve-ments were observed in the transfer learning-enabled setting. This findingaligns with an earlier observation in Fig. 3c that networking has minimalimpact on ASM. In the later stages of exploration, the non-transfer modelENMM was selected almost exclusively. This pattern likely reflects fasteraccumulation ofM data by ASM compared with the data collection rates ofASTc or ASSp for Tc and Sp data, resulting in superior performance of thelocalmodel ENMMand limited benefit fromexternal transfer, thus avoidingnegative transfer.Generalization performance transition on unobserved dataWe then evaluated the generalization performance of the BPMs for theunobserved materials within the search space, which consisted of 16,908candidate materials. For instance, after 40 exploration steps conducted byASM, the dataset was divided as follows: 32materials were used for training,Fig. 4 |Validation loss transitionof BPM, and timing, frequency, anddirectionoftransfer learning during autonomous exploration. a–c Validation loss transitionof the selected BPM in ASSp, ASTc, and ASM, respectively. The red and blue linesshow the validation loss with and without networking using transfer learning,respectively. The selected BPMs are indicated as follows: green plots for the transferlearning fromASTc, purple plots for the transfer learning fromASSp, orange plots forthe transfer learning from ASM, and small black plots for the non-transfer model. InASSp and ASTc, networking improves the performance of the BPM, whereas nosignificant difference is observed in ASM. This trend is consistent with the results ofautonomous exploration efficiency shown in Fig. 3a–c.https://doi.org/10.1038/s41524-025-01851-8 Articlenpj Computational Materials |          (2025) 11:362 5www.nature.com/npjcompumats8 for testing, and the remaining 16,868were treated as unobserved.Notably,the generalization metrics computed using unobserved data were inacces-sible during the actual autonomous explorationprocess andwereused solelyfor retrospective evaluation in this study.Figure 5a–c shows the evolution of generalization performance onunobserved materials during autonomous exploration by ASSp, ASTc, andASM, respectively. As in Fig. 4a–c, the red and blue curves represent thegeneralization performance with and without networking via transferlearning, respectively. The coloredmarkers denote the origin of the selectedtransfermodels: orange for transfer fromASM, purple fromASSp, and greenfrom ASTc.As shown in Fig. 5a, b, the networking approach yielded improvedgeneralization compared with the non-networked setting. However, Fig. 5breveals a temporary degradation in the generalization performance of ASTcas the number of exploration steps increases. This decline is a knownartifactof Bayesian optimization and is commonly attributed to sampling bias48,49.For ASTc, the autonomous strategy favored materials with high Tc values,leading to a training set skewed toward a large Tc. The pool of unobservedmaterials included a substantial proportion of samples with low or zero Tc,resulting in a distribution mismatch that likely caused the observed drop ingeneralization performance.As shown in Fig. 5c, the generalization performance of ASM remainedsimilar across the networked and non-networked settings during the earlyphase (fewer than 100 observations). Beyond this point, degradation due totraining data bias became evident, similar to the case of ASTc. This degra-dation was mitigated more effectively in the networked scenario withtransfer learning, suggesting its role in maintaining robustness againstsampling bias in the later exploration stages.DiscussionTransfer learning is generally effective when the target properties exhibitunderlying correlations. To examine this phenomenon, Fig. 6a–c presentscatter plots of pairwise relationships among three material properties—Sp,Tc, and M—across the entire dataset. Figure 6a shows the relationshipbetween Sp and Tc. Notably, materials with Sp values below approximately0.6 tended to have Tc values near zero, whereas those with higher Sp valuesoften exhibited finite Tc. Although a strong linear correlation was notobserved, the distribution suggested amoderate dependence between Sp andTc. Figure 6b shows the plot ofM versus Sp. Despite considerable scatter, ageneral trend was observed. For M values below 0.5, Sp increased sharplywith increasingM. Above this threshold, the rate of increase became moregradual, suggesting a weak but non-negligible relationship betweenM andFig. 5 | Generalization performance transition of the BPM on unobserved data,and the timing, frequency, and direction of transfer learningduring autonomousexploration. a–c Generalization performance transition of the selected BPM inASSp, ASTc, and ASM, respectively. The red and blue lines represent the validationloss with and without networking using transfer learning, respectively. The selectedBPMs are color-coded as follows: green plots for the transfer learning from ASTc,purple plots for the transfer learning fromASSp, orange plots for the transfer learningfromASM, and small black plots for the non-transfer model. In all cases, networkingimproves the generalization performance of the BPM.Fig. 6 | Relationships among target propertiesM,Tc, and Sp. a Scatter plot of Sp versus Tc. b Scatter plot ofM versus Sp. c Scatter plot ofM versus Tc. Each plot reveals somedegree of correlation, indicating that transfer learning is likely to be effective for these material properties.https://doi.org/10.1038/s41524-025-01851-8 Articlenpj Computational Materials |          (2025) 11:362 6www.nature.com/npjcompumatsSp. Figure 6c shows the plot of M versus Tc, revealing a clear positive cor-relation. Additionally, the clustering of data points in the lower-right regionindicates thatMmaybe a limiting factor in achievinghighTcvalues.Overall,although no strong or universal correlations were observed, each pairwisecomparison showed some degree of relationship, supporting the feasibilityof applying transfer learning across these properties.This study demonstrated that forming a network of autonomousmaterial exploration systems via transfer learning enhanced the overallefficiency ofmaterial discovery.Notably, althoughnetworking enhances theefficiency of each autonomous exploration system, it never compromises orreduces their performance. When transfer learning introduced irrelevantexternal knowledge, the model selection mechanism defaulted to the non-transfer model. Consequently, knowledge sharing should be activelyimplemented in autonomous systems targeting seemingly unrelatedmaterials or properties, and large-scale networks of such systems should beutilized to accelerate material discovery.Moreover, analyzing the frequency, timing, and directionality oftransfer learning events within the network enables a quantitative assess-ment of the strength of the intersystem relationships across differentmaterial properties. This analysis may yield unexpected insights. Forinstance, if a strong transfer relationship emerges between systems focusedon distinct properties, it could motivate closer collaboration amongresearchers and communities working in these domains.In this study, we introduced the concept of an autonomous materialexploration network. Realizing such a system in practical deploymentspresents several challenges. We outline three of them below.First, material descriptors are a key consideration. In this study, weemployed simple composition-based vectors. Although such vectors areeffective in many settings, they are not universal; although effective forinorganic systems, they often struggle with polymers. To improveexploration accuracy, it may be necessary to incorporate additionaldescriptors tailored to the exploration modality (e.g., robotic and simula-tion-based). Future work should focus on developing versatile descriptorsthat generalize across diverse environments and material classes, and oninvestigating transfer learning strategies across heterogeneous descriptorspaces.Second, development aspects, such as communication protocols andmetadata management, remain open. In our current knowledge-sharingframework, coordination among autonomous materials exploration sys-tems can be achieved simply by exchanging trained models between sys-tems. As experimental platforms and optimization algorithms evolve,however, it may become necessary to exchange and store richer metadata(e.g., data provenance, measurement conditions, hyperparameters, andmodel uncertainty). For future deployments, research should develop andevaluate reference implementations across a range of network topologiesand establish communication protocols and interoperability standards.Third, algorithmic choices warrant consideration. In this work, wedemonstrated the concept using transfer learning with ENMs. Alternativemachine-learning approaches, such as Gaussian process regression (GPR),Sequential Model-based Algorithm Configuration (SMAC), and Tree-structured Parzen Estimators (TPE), may further improve explorationefficiency. Knowledge sharing does not need to rely solely on transferlearning; for example, multitask neural networks may enable efficientsharing without explicit transfer learning. As autonomous materialsexploration systems proliferate globally, frameworks and methods forknowledge sharing should be investigated systematically.In summary, this study proposes a novel framework for acceleratingmaterial discovery by networking multiple autonomous material explora-tion systems that integrate robotics, material simulations, and machinelearning. By utilizing ENNs and transfer learning, each system can extractknowledge fromthedata generatedbyother systems and apply it to improveits exploration efficiency. To validate this concept, we demonstrated anetworked setup involving three autonomous exploration systems, eachtargetingdistinctmaterial properties: highM,Tc, and Sp. These systemswereinterconnected through a transfer learning-based network, enablingdynamic knowledge sharing. The results confirmed that this networkedapproach improved exploration efficiency. Moreover, the proposed fra-mework incorporated a model selection mechanism that automaticallysuppressed negative transfers from systems with insufficient data or weakinterproperty correlations, ensuring that overall performance was notcompromised. Future studies should consider analyzing the connectionswithin large-scale networks of autonomous exploration systems, whichmaylead to the discovery of novel insights into the interfaces between differentmaterial systems. As autonomous material exploration systems continue tobe used globally, the ability to connect and coordinate these systems willbecome increasingly important. The proposed approach provides a scalableand robust foundation fordistributed, cooperative, anddata-drivenmaterialexploration and offers a promising path for accelerating the discovery ofnovel functional materials.MethodsENNsAn ENN is a machine learning framework for quantifying predictiveuncertainty by aggregating the outputs of multiple independently trainedNNs. In this study, each constituentmodel in the ensemble is a feedforwardNN(FNN) that receivesmaterial descriptors (i.e., elemental composition) asinputs and outputs a predicted material property, specifically,M, Tc, or Sp.The overall ENN prediction is obtained by averaging the outputs of theindividual FNNs, whereas the predictive uncertainty is estimated as thevariance across these outputs. By approximating a distribution over pre-dictions, the ENN provides uncertainty estimates comparable in expres-siveness to those of the Gaussian process regression35. Thus, ENNs can beeffectively employed instead of Gaussian processes for tasks such as Baye-sian optimization36.In this study, each FNN comprised an input layer for materialdescriptors, three fully connectedhidden layerswithdimensionsof 100, 100,and 10, and an output layer that returned the predicted property. All layersutilized a scaled exponential linear unit activation function. To improve theexpressive capacity of the network, weight initialization was performedusing a truncated normal distribution, as proposed by Klambauer et al. andLeCun et al.50,51.Training was conducted using early stopping, with 20% of the datareserved as a validation set. The same validation strategy was applied duringthe selection process for the TLMs, as described in the subsequent section.The FNNs were implemented using the Keras application programminginterface (API) in TensorFlow version 2.13.1, running in a Python 3.8.10environment. The learning rate, batch size, and L2 regularization penaltywere set as 0.0005, 8, and 0.001, respectively. The patience parameter forearly stopping was set to 100 epochs.Transfer learningTransfer learning is a technique that improves model performance byinitially pretraining on a source dataset—often associated with a differentbut related task—and subsequently fine-tuning the model on a targetdataset29–34. This approach enables the transfer of learned representationsfrom non-target properties, which may differ from the optimizationobjective of the current autonomous exploration system.In this study, transfer learning was applied by utilizing ENMs trainedby other autonomous materials exploration systems. To preserve thelearned features, the first two hidden layers (those closest to the input layer)of each sourcemodel were frozen, while the final hidden layer (closest to theoutput) was fine-tuned using the local target data. Using this approach,multiple ENMs were constructed, each corresponding to a different sourcesystem.All transfer learning procedures were implemented using the KerasAPI within TensorFlow version 2.13.1 running on Python 3.8.10. Thelearning rate, batch size, and L2 regularization coefficient were set as 0.0005,8, and 0.001, respectively. Early stopping was applied with a patienceparameter of 100 epochs using 20% of the data as the validation set, con-sistent with the procedure described for ENN training.https://doi.org/10.1038/s41524-025-01851-8 Articlenpj Computational Materials |          (2025) 11:362 7www.nature.com/npjcompumatsAcquisition functionThe acquisition function is a central component of Bayesian optimizationthat guides the selection of the next candidate material to be evaluated. Inthis study, we adopted the UCB strategy40, which balances exploration andexploitation based on both predictive uncertainty and expected perfor-mance. Using the ENN, we computed the predicted mean and standarddeviation of the target property across the entire search space. These valueswere then used to evaluate the UCB acquisition function, defined as:UCB ¼ μþ α � σ ð7Þwhere μ and σ denote the predictedmean and standard deviation for a givencandidate material, and α is a hyperparameter that governs the trade-offbetween exploration (favoring high uncertainty) and exploitation (favoringhigh predicted values). 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Kotsugi at the Tokyo University of Science fortheir valuable discussions. This study was supported by JST-CREST (GrantNo. JPMJCR21O1). This study was supported by JST-CREST under GrantNo. JPMJCR21O1.Author contributionsNaoki Yoshida andYutaro Iwabuchi developed the code, analyzed the data,and contributed to the discussion. Yasuhiko Igarashi participated in thediscussions. Yuma Iwasaki drafted themanuscript, designed the study, andmanaged the research.Competing interestsThe authors declare no competing interests.Additional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s41524-025-01851-8.Correspondence and requests for materials should be addressed toYuma Iwasaki.Reprints and permissions information is available athttp://www.nature.com/reprintsPublisher’s note Springer Nature remains neutral with regard tojurisdictional claims in published maps and institutional affiliations.Open Access This article is licensed under a Creative CommonsAttribution 4.0 International License, which permits use, sharing,adaptation, distribution and reproduction in anymedium or format, as longas you give appropriate credit to the original author(s) and the source,provide a link to the Creative Commons licence, and indicate if changeswere made. 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To view a copy of thislicence, visit http://creativecommons.org/licenses/by/4.0/.© The Author(s) 2025https://doi.org/10.1038/s41524-025-01851-8 Articlenpj Computational Materials |          (2025) 11:362 9https://doi.org/10.48505/nims.5364https://doi.org/10.48505/nims.5364https://doi.org/10.1038/s41524-025-01851-8http://www.nature.com/reprintshttp://creativecommons.org/licenses/by/4.0/www.nature.com/npjcompumats Networking autonomous material exploration systems through transfer learning Results Networking of autonomous material exploration systems Demonstration Validation loss transition on training data Generalization performance transition on unobserved data Discussion Methods ENNs Transfer learning Acquisition function Data availability Code availability References Acknowledgements Author contributions Competing interests Additional information