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LAMBARD Guillaume, BAJAN Christophe Marie Olivier

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[Bayesian optimization, an active learning method for optimising experimental parameters](https://mdr.nims.go.jp/datasets/259ef794-7f84-4cfe-a861-beaf4b341266)

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The Bayesian optimization  an active learning method for optimising experimental parametersThe Bayesian optimizationan active learning method for optimising experimental parametersSébastien Junier1,2, Céline Barreteau1 Christophe Bajan2, Guillaume Lambard2 andJean-Claude Crivello21Univ Paris Est Créteil, CNRS, ICMPE, UMR 7182, 2 rue Henri Dunant, 94320 Thiais, France2CNRS – Saint-Gobain – NIMS, Laboratory for Innovative Key Materials and Structures (LINK, IRL 3629), 1-1 Namiki, 305-0044 Tsukuba, JapanICMMO seminar – Thursday the 7th of November, 2024Header BackgroundMy backgroundStudies1 Undergraduate’s degree : Physics–Chemistry, Paris Saclay (2020)2 Master’s degree : Materials Science, Paris Saclay (2022)3 PhD in ICMPE (3nd year) : Prediction of ESO by DFT and machine learningInternships1 CoAg nanoparticles : study by Monte Carlo simulation, ICMMO, Orsay, 4 months (2021)2 Screening of ESO by DFT and machine learning, ICMPE, Thiais, 5 months (2022)3 Accelering ESO discovery using active learning, LINK, Tsukuba JAPAN, 3 months (2022)Poster presentations in international congreeInternational Conference on high-entropy Materials 2023STAC-13 and D2Mat symposium, Tsukuba, Japan, February 2024 (Outstanding PosterAward)S. Junier (ICMPE-LINK) BO for optimising experimental parameters ICMMO seminar – 07/11/2024 2 / 13Header OutlookOutlook1 IntroductionMachine LearningInterest2 ModelsRegression modelBayesian OptimisationMADGUI: User Interface developed by NIMS3 Theoretical ExamplesOne dimensionTwo dimensions4 Real examplesApplication on SPS optimisation5 ConclusionS. Junier (ICMPE-LINK) BO for optimising experimental parameters ICMMO seminar – 07/11/2024 3 / 13Introduction Machine LearningIntroductionMachine learningARTIFICIAL INTELLIGENCEThe theory and development of computer systems to perform task normally requiring human intelligenceRegressionθ1 θ2 θ3 y1 y2θa1 θa2 θa3 ya1 ya2θb1 θb2 θb3 yb1 yb2θc1 θc2 θc3 yc1 yc2θd1 θd2 θd3 yd1 yd2θi =θi1θi2θi3 Yi =(yi1yi2) From the table above, welook for the functionf : θ → Yθe1 θe2 θe3 ? ?θf1 θf2 θf3 ? ?Formalismθ : features Y : targetsS. Junier (ICMPE-LINK) BO for optimising experimental parameters ICMMO seminar – 07/11/2024 4 / 13Introduction Machine LearningIntroductionMachine learningARTIFICIAL INTELLIGENCEThe theory and development of computer systems to perform task normally requiring human intelligenceMACHINE LEARNINGAlgorithms with the ability to learn withoutbeing explicitly programmedRegressionθ1 θ2 θ3 y1 y2θa1 θa2 θa3 ya1 ya2θb1 θb2 θb3 yb1 yb2θc1 θc2 θc3 yc1 yc2θd1 θd2 θd3 yd1 yd2θi =θi1θi2θi3 Yi =(yi1yi2) From the table above, welook for the functionf : θ → Yθe1 θe2 θe3 ? ?θf1 θf2 θf3 ? ?Formalismθ : features Y : targetsS. Junier (ICMPE-LINK) BO for optimising experimental parameters ICMMO seminar – 07/11/2024 4 / 13Introduction Machine LearningIntroductionMachine learningARTIFICIAL INTELLIGENCEThe theory and development of computer systems to perform task normally requiring human intelligenceMACHINE LEARNINGAlgorithms with the ability to learn withoutbeing explicitly programmedSUPERVISED LEARNINGPredicting values from known data Regressionθ1 θ2 θ3 y1 y2θa1 θa2 θa3 ya1 ya2θb1 θb2 θb3 yb1 yb2θc1 θc2 θc3 yc1 yc2θd1 θd2 θd3 yd1 yd2θi =θi1θi2θi3 Yi =(yi1yi2) From the table above, welook for the functionf : θ → Yθe1 θe2 θe3 ? ?θf1 θf2 θf3 ? ?Formalismθ : features Y : targetsS. Junier (ICMPE-LINK) BO for optimising experimental parameters ICMMO seminar – 07/11/2024 4 / 13Introduction Machine LearningIntroductionMachine learningMACHINE LEARNINGAlgorithms with the ability to learn withoutbeing explicitly programmedSUPERVISED LEARNINGREGRESSION quantitativevaluesPredicting values from known data ARTIFICIAL INTELLIGENCEThe theory and development of computer systems to perform task normally requiring human intelligenceRegressionθ1 θ2 θ3 y1 y2θa1 θa2 θa3 ya1 ya2θb1 θb2 θb3 yb1 yb2θc1 θc2 θc3 yc1 yc2θd1 θd2 θd3 yd1 yd2θi =θi1θi2θi3 Yi =(yi1yi2) From the table above, welook for the functionf : θ → Yθe1 θe2 θe3 ? ?θf1 θf2 θf3 ? ?Formalismθ : features Y : targetsS. Junier (ICMPE-LINK) BO for optimising experimental parameters ICMMO seminar – 07/11/2024 4 / 13Introduction Machine LearningIntroductionMachine learningMACHINE LEARNINGAlgorithms with the ability to learn withoutbeing explicitly programmedSUPERVISED LEARNINGREGRESSION quantitativevaluesPredicting values from known data ARTIFICIAL INTELLIGENCEThe theory and development of computer systems to perform task normally requiring human intelligenceRegressionθ1 θ2 θ3 y1 y2θa1 θa2 θa3 ya1 ya2θb1 θb2 θb3 yb1 yb2θc1 θc2 θc3 yc1 yc2θd1 θd2 θd3 yd1 yd2θi =θi1θi2θi3 Yi =(yi1yi2) From the table above, welook for the functionf : θ → Yθe1 θe2 θe3 ? ?θf1 θf2 θf3 ? ?Formalismθ : features Y : targetsS. Junier (ICMPE-LINK) BO for optimising experimental parameters ICMMO seminar – 07/11/2024 4 / 13Introduction Machine LearningIntroductionMachine learningMACHINE LEARNINGAlgorithms with the ability to learn withoutbeing explicitly programmedSUPERVISED LEARNINGREGRESSION quantitativevaluesPredicting values from known data ARTIFICIAL INTELLIGENCEThe theory and development of computer systems to perform task normally requiring human intelligenceRegressionθ1 θ2 θ3 y1 y2θa1 θa2 θa3 ya1 ya2θb1 θb2 θb3 yb1 yb2θc1 θc2 θc3 yc1 yc2θd1 θd2 θd3 yd1 yd2θi =θi1θi2θi3 Yi =(yi1yi2) From the table above, welook for the functionf : θ → Yθe1 θe2 θe3 ? ?θf1 θf2 θf3 ? ?Formalismθ : features Y : targetsS. Junier (ICMPE-LINK) BO for optimising experimental parameters ICMMO seminar – 07/11/2024 4 / 13Introduction Machine LearningIntroductionMachine learningMACHINE LEARNINGAlgorithms with the ability to learn withoutbeing explicitly programmedSUPERVISED LEARNINGREGRESSION quantitativevaluesPredicting values from known data ARTIFICIAL INTELLIGENCEThe theory and development of computer systems to perform task normally requiring human intelligenceRegressionθ1 θ2 θ3 y1 y2θa1 θa2 θa3 ya1 ya2θb1 θb2 θb3 yb1 yb2θc1 θc2 θc3 yc1 yc2θd1 θd2 θd3 yd1 yd2θi =θi1θi2θi3 Yi =(yi1yi2) From the table above, welook for the functionf : θ → Yθe1 θe2 θe3 ? ?θf1 θf2 θf3 ? ?Formalismθ : features Y : targetsS. Junier (ICMPE-LINK) BO for optimising experimental parameters ICMMO seminar – 07/11/2024 4 / 13Introduction InterestSome examplesheating ratecooling ratepressure...featureselasticityzT...targetsSPS synthesis volumetemperaturemol numberfeaturespressuretargetIdeal gasatom number symmetryelementstypeconcentrationstrucutre...featuresenergyDOSmagnetic moment...targetsDFT calculationS. Junier (ICMPE-LINK) BO for optimising experimental parameters ICMMO seminar – 07/11/2024 5 / 13Introduction InterestSome examplesvolumetemperaturemol numberfeaturespressuretargetIdeal gasAnalytic : atom number symmetryelementstypeconcentrationstrucutre...featuresenergyDOSmagnetic moment...targetsDFT calculationheating ratecooling ratepressure...featureselasticityzT...targetsSPS synthesis S. Junier (ICMPE-LINK) BO for optimising experimental parameters ICMMO seminar – 07/11/2024 5 / 13Introduction InterestSome examplesvolumetemperaturemol numberfeaturespressuretargetIdeal gasAnalytic : atom number symmetryelementstypeconcentrationstrucutre...featuresenergyDOSmagnetic moment...targetsDFT calculationAnalytic : ?heating ratecooling ratepressure...featureselasticityzT...targetsSPS synthesis Analytic : ?S. Junier (ICMPE-LINK) BO for optimising experimental parameters ICMMO seminar – 07/11/2024 5 / 13Models Regression modelRegression Model (RM)Complete databaseθ YSplited databaseθtrain Ytrainθtest YtestModelModely1 y2q1 qnq3q2 ...1 - TrainingThe model is trained on θtrainto fit Ytrain2 - TestingThe model is tested on θtestand the results are comparedwith YtestDatabase sizeFrom 100 to several 1000 pointsS. Junier (ICMPE-LINK) BO for optimising experimental parameters ICMMO seminar – 07/11/2024 6 / 13Models Regression modelRegression Model (RM)Complete databaseθ YSplited databaseθtrain Ytrainθtest YtestModelModely1 y2q1 qnq3q2 ...1 - TrainingThe model is trained on θtrainto fit Ytrain2 - TestingThe model is tested on θtestand the results are comparedwith YtestDatabase sizeFrom 100 to several 1000 pointsS. Junier (ICMPE-LINK) BO for optimising experimental parameters ICMMO seminar – 07/11/2024 6 / 13Models Regression modelRegression Model (RM)Complete databaseθ YSplited databaseθtrain Ytrainθtest YtestModelModely1 y2q1 qnq3q2 ...1 - TrainingThe model is trained on θtrainto fit Ytrain2 - TestingThe model is tested on θtestand the results are comparedwith YtestDatabase sizeFrom 100 to several 1000 pointsS. Junier (ICMPE-LINK) BO for optimising experimental parameters ICMMO seminar – 07/11/2024 6 / 13Models Regression modelRegression Model (RM)Complete databaseθ YSplited databaseθtrain Ytrainθtest YtestModelModely1 y2q1 qnq3q2 ...1 - TrainingThe model is trained on θtrainto fit Ytrain2 - TestingThe model is tested on θtestand the results are comparedwith YtestDatabase sizeFrom 100 to several 1000 pointsS. Junier (ICMPE-LINK) BO for optimising experimental parameters ICMMO seminar – 07/11/2024 6 / 13Models Regression modelRegression Model (RM)Complete databaseθ YSplited databaseθtrain Ytrainθtest YtestModelModely1 y2q1 qnq3q2 ...1 - TrainingThe model is trained on θtrainto fit Ytrain2 - TestingThe model is tested on θtestand the results are comparedwith YtestDatabase sizeFrom 100 to several 1000 pointsS. Junier (ICMPE-LINK) BO for optimising experimental parameters ICMMO seminar – 07/11/2024 6 / 13Models Regression modelRegression Model (RM)Complete databaseθ YSplited databaseθtrain Ytrainθtest YtestModelModely1 y2q1 qnq3q2 ...1 - TrainingThe model is trained on θtrainto fit Ytrain2 - TestingThe model is tested on θtestand the results are comparedwith YtestDatabase sizeFrom 100 to several 1000 pointsS. Junier (ICMPE-LINK) BO for optimising experimental parameters ICMMO seminar – 07/11/2024 6 / 13Models Bayesian OptimisationBayesian Optimisation (BO)AimFind features θi which correspond to an optimum of targets YGaussian ProcessDatabase{θ}={Y}BO frameworksuggest n new θ BOreal calcul of YDatabase{θ}={Y}Graphic Gaussian ProcessθyTarget functionCalculated valuesGaussian modelAquisition functionM. Krasser, “Bayesian Optimization”, github (2018)S. Junier (ICMPE-LINK) BO for optimising experimental parameters ICMMO seminar – 07/11/2024 7 / 13http://krasserm.github.io/2018/03/21/bayesian-optimization/Models Bayesian OptimisationBayesian Optimisation (BO)AimFind features θi which correspond to an optimum of targets YGaussian ProcessDatabase{θ}={Y}BO frameworksuggest n new θ BOreal calcul of YDatabase{θ}={Y}Graphic Gaussian ProcessθyTarget functionCalculated valuesGaussian modelAquisition functionM. Krasser, “Bayesian Optimization”, github (2018)S. Junier (ICMPE-LINK) BO for optimising experimental parameters ICMMO seminar – 07/11/2024 7 / 13http://krasserm.github.io/2018/03/21/bayesian-optimization/Models Bayesian OptimisationBayesian Optimisation (BO)AimFind features θi which correspond to an optimum of targets YGaussian ProcessDatabase{θ}={Y} GPBO frameworksuggest n new θ BOreal calcul of YDatabase{θ}={Y}Graphic Gaussian ProcessθyTarget functionCalculated valuesGaussian modelAquisition functionM. Krasser, “Bayesian Optimization”, github (2018)S. Junier (ICMPE-LINK) BO for optimising experimental parameters ICMMO seminar – 07/11/2024 7 / 13http://krasserm.github.io/2018/03/21/bayesian-optimization/Models Bayesian OptimisationBayesian Optimisation (BO)AimFind features θi which correspond to an optimum of targets YGaussian ProcessDatabase{θ}={Y} GP suggestnew θBO frameworksuggest n new θ BOreal calcul of YDatabase{θ}={Y}Graphic Gaussian Processa.u.θyTarget functionCalculated valuesGaussian modelAquisition functionM. Krasser, “Bayesian Optimization”, github (2018)S. Junier (ICMPE-LINK) BO for optimising experimental parameters ICMMO seminar – 07/11/2024 7 / 13http://krasserm.github.io/2018/03/21/bayesian-optimization/Models Bayesian OptimisationBayesian Optimisation (BO)AimFind features θi which correspond to an optimum of targets YGaussian ProcessCalculate/Measure real value of YDatabase{θ}={Y} GP suggestnew θBO frameworksuggest n new θ BOreal calcul of YDatabase{θ}={Y}Graphic Gaussian Processa.u.θyTarget functionCalculated valuesGaussian modelAquisition functionM. Krasser, “Bayesian Optimization”, github (2018)S. Junier (ICMPE-LINK) BO for optimising experimental parameters ICMMO seminar – 07/11/2024 7 / 13http://krasserm.github.io/2018/03/21/bayesian-optimization/Models Bayesian OptimisationBayesian Optimisation (BO)AimFind features θi which correspond to an optimum of targets YGaussian ProcessDatabase{θ}={Y} GP suggestnew θGP(θ)estimateYn timesBO frameworksuggest n new θ BOreal calcul of YDatabase{θ}={Y}Graphic Gaussian Processa.u.θyTarget functionCalculated valuesGaussian modelAquisition functionM. Krasser, “Bayesian Optimization”, github (2018)S. Junier (ICMPE-LINK) BO for optimising experimental parameters ICMMO seminar – 07/11/2024 7 / 13http://krasserm.github.io/2018/03/21/bayesian-optimization/Models Bayesian OptimisationBayesian Optimisation (BO)AimFind features θi which correspond to an optimum of targets YGaussian ProcessDatabase{θ}={Y} GP suggestnew θGP(θ)estimateYn timesBO frameworksuggest n new θ BOreal calcul of YDatabase{θ}={Y}Graphic Gaussian Processa.u.θyTarget functionCalculated valuesGaussian modelAquisition functionM. Krasser, “Bayesian Optimization”, github (2018)S. Junier (ICMPE-LINK) BO for optimising experimental parameters ICMMO seminar – 07/11/2024 7 / 13http://krasserm.github.io/2018/03/21/bayesian-optimization/Models Bayesian OptimisationBayesian Optimisation (BO)AimFind features θi which correspond to an optimum of targets YGaussian ProcessDatabase{θ}={Y} GP suggestnew θRM is good ?estimateYGP(θ)RM(θ)yesnon timesBO frameworksuggest n new θ BOreal calcul of YDatabase{θ}={Y}Prediction modelRM : θ    YRMGraphic Gaussian ProcessθyGPRMAquisition functionpredictionsTarget functionCalculated valuesa.u.M. Krasser, “Bayesian Optimization”, github (2018)S. Junier (ICMPE-LINK) BO for optimising experimental parameters ICMMO seminar – 07/11/2024 7 / 13http://krasserm.github.io/2018/03/21/bayesian-optimization/Models MADGUI: User Interface developed by NIMSMADGUIFully graphical interface developed by C. Bajan andG. Lambard to makes BO accessible to researcherswithout extensive programming experience.Global useDatabase{θ}={Y}give n suggestedθ user-set parameters graphical resultsGithub : github.com/Lambard-ML-Team/MADGUIWEB app : lambard-ml-team-madgui.streamlit.apppre-print article : dx.doi.org/10.2139/ssrn.4855240WEB applicationS. Junier (ICMPE-LINK) BO for optimising experimental parameters ICMMO seminar – 07/11/2024 8 / 13https://github.com/Lambard-ML-Team/MADGUIhttps://lambard-ml-team-madgui.streamlit.app https://doi.org/10.1016/j.actamat.2024.120342Theoretical Examples One dimensionOptimisation of one functionGlobal objectiveFind the minimum yGraphical representation5 0 5 10 153.02.52.01.51.00.50.00.51.0ytarget functionnoisy datainitial dataHow it works on MADGUIS. Junier (ICMPE-LINK) BO for optimising experimental parameters ICMMO seminar – 07/11/2024 9 / 13Theoretical Examples One dimensionOptimisation of one functionStepImport file : numeric tableGraphical representation5 0 5 10 153.02.52.01.51.00.50.00.51.0ytarget functionnoisy datainitial dataHow it works on MADGUIS. Junier (ICMPE-LINK) BO for optimising experimental parameters ICMMO seminar – 07/11/2024 9 / 13Theoretical Examples One dimensionOptimisation of one functionStepSelect features and targetsGraphical representation5 0 5 10 153.02.52.01.51.00.50.00.51.0ytarget functionnoisy datainitial dataHow it works on MADGUIS. Junier (ICMPE-LINK) BO for optimising experimental parameters ICMMO seminar – 07/11/2024 9 / 13Theoretical Examples One dimensionOptimisation of one functionStepWe have an analysis of dataGraphical representation5 0 5 10 153.02.52.01.51.00.50.00.51.0ytarget functionnoisy datainitial dataHow it works on MADGUIS. Junier (ICMPE-LINK) BO for optimising experimental parameters ICMMO seminar – 07/11/2024 9 / 13Theoretical Examples One dimensionOptimisation of one functionStepChoose domain of featureGraphical representation5 0 5 10 153.02.52.01.51.00.50.00.51.0ytarget functionnoisy datainitial dataHow it works on MADGUIS. Junier (ICMPE-LINK) BO for optimising experimental parameters ICMMO seminar – 07/11/2024 9 / 13Theoretical Examples One dimensionOptimisation of one functionStepSelect parameters of BOGraphical representation5 0 5 10 153.02.52.01.51.00.50.00.51.0yGPtarget functionsuggestiondataHow it works on MADGUIS. Junier (ICMPE-LINK) BO for optimising experimental parameters ICMMO seminar – 07/11/2024 9 / 13Theoretical Examples One dimensionOptimisation of one functionStepCalculate y, add to in database and repeatGraphical representation5 0 5 10 153.02.52.01.51.00.50.00.51.0yGPtarget functionsuggestiondataHow it works on MADGUIS. Junier (ICMPE-LINK) BO for optimising experimental parameters ICMMO seminar – 07/11/2024 9 / 13Theoretical Examples One dimensionOptimisation of one functionStepCalculate y, add to in database and repeatGraphical representation5 0 5 10 153.02.52.01.51.00.50.00.51.0yGPtarget functionsuggestiondataHow it works on MADGUIS. Junier (ICMPE-LINK) BO for optimising experimental parameters ICMMO seminar – 07/11/2024 9 / 13Theoretical Examples One dimensionOptimisation of one functionStepCalculate y, add to in database and repeatGraphical representation5 0 5 10 153.02.52.01.51.00.50.00.51.0yGPtarget functionsuggestiondataHow it works on MADGUIS. Junier (ICMPE-LINK) BO for optimising experimental parameters ICMMO seminar – 07/11/2024 9 / 13Theoretical Examples One dimensionOptimisation of one functionStepCalculate y, add to in database and repeatGraphical representation5 0 5 10 153.02.52.01.51.00.50.00.51.0yGPtarget functionsuggestiondataHow it works on MADGUIS. Junier (ICMPE-LINK) BO for optimising experimental parameters ICMMO seminar – 07/11/2024 9 / 13Theoretical Examples One dimensionOptimisation of one functionStepCalculate y, add to in database and repeatGraphical representation5 0 5 10 153.02.52.01.51.00.50.00.51.0yGPtarget functionsuggestiondataHow it works on MADGUIS. Junier (ICMPE-LINK) BO for optimising experimental parameters ICMMO seminar – 07/11/2024 9 / 13Theoretical Examples One dimensionOptimisation of one functionStepCalculate y, add to in database and repeatGraphical representation5 0 5 10 153.02.52.01.51.00.50.00.51.0yGPtarget functionsuggestiondataHow it works on MADGUIS. Junier (ICMPE-LINK) BO for optimising experimental parameters ICMMO seminar – 07/11/2024 9 / 13Theoretical Examples One dimensionOptimisation of one functionStepCalculate y, add to in database and repeatGraphical representation5 0 5 10 153.02.52.01.51.00.50.00.51.0yGPtarget functiondataHow it works on MADGUIS. Junier (ICMPE-LINK) BO for optimising experimental parameters ICMMO seminar – 07/11/2024 9 / 13Theoretical Examples Two dimensionsOptimisation of two functionsGlobal objectiveFind θ corresponding to the highest value of y1and the lowest value of y2Graphical representation5 0 5 10 153210123ytarget 1target 2How it works on MADGUIS. Junier (ICMPE-LINK) BO for optimising experimental parameters ICMMO seminar – 07/11/2024 10 / 13Theoretical Examples Two dimensionsOptimisation of two functionsGlobal objectiveFind θ corresponding to the highest value of y1and the lowest value of y2Graphical representation5 0 5 10 153210123ytarget 1target 2How it works on MADGUIS. Junier (ICMPE-LINK) BO for optimising experimental parameters ICMMO seminar – 07/11/2024 10 / 13Theoretical Examples Two dimensionsOptimisation of two functionsGlobal objectiveFind θ corresponding to the highest value of y1and the lowest value of y2Graphical representation5 0 5 10 153210123ytarget 1target 2How it works on MADGUIS. Junier (ICMPE-LINK) BO for optimising experimental parameters ICMMO seminar – 07/11/2024 10 / 13Theoretical Examples Two dimensionsOptimisation of two functionsGlobal objectiveFind θ corresponding to the highest value of y1and the lowest value of y2Graphical representation5 0 5 10 153210123ytarget 1target 2Results representation3.0 2.5 2.0 1.5 1.0 0.5 0.0target 20.00.51.01.52.02.53.03.5target 10.000.250.500.751.001.251.501.752.00deviation from ideal ppintS. Junier (ICMPE-LINK) BO for optimising experimental parameters ICMMO seminar – 07/11/2024 10 / 13Real examplesReal examplesFramework in precedent examplesCalculate/Measure real value of YDatabase{θ}={Y} GP suggestnew θproblemOnly one compound can be calculated at a timeCompleat frameworkDatabase{θ}={Y} GP suggestnew θRM is good ?estimateYGP(θ)RM(θ)yesnoPrediction modelRM : θ    YRMsuggest n new θ BOreal calcul of YDatabase{θ}={Y}n timesS. Junier (ICMPE-LINK) BO for optimising experimental parameters ICMMO seminar – 07/11/2024 11 / 13Real examplesReal examplesFramework in precedent examplesCalculate/Measure real value of YDatabase{θ}={Y} GP suggestnew θproblemOnly one compound can be calculated at a timeCompleat frameworkDatabase{θ}={Y} GP suggestnew θRM is good ?estimateYGP(θ)RM(θ)yesnoPrediction modelRM : θ    YRMsuggest n new θ BOreal calcul of YDatabase{θ}={Y}n timesS. Junier (ICMPE-LINK) BO for optimising experimental parameters ICMMO seminar – 07/11/2024 11 / 13Real examples Application on SPS optimisationSPS applicationOptimise SPS synthesise parameter to obtain the best zTon thermo-electric compound.Prediction modelRM : θ    YRMsuggest n new θ BOreal calcul of YDatabase{θ}={Y}C. Bourgès, G. Lambard et al., Acta Materialia 281, 120342 (2024)S. Junier (ICMPE-LINK) BO for optimising experimental parameters ICMMO seminar – 07/11/2024 12 / 13Real examples Application on SPS optimisationSPS applicationMADGUI can display some information on databasePrediction modelRM : θ    YRMsuggest n new θ BOreal calcul of YDatabase{θ}={Y}C. Bourgès, G. Lambard et al., Acta Materialia 281, 120342 (2024)S. Junier (ICMPE-LINK) BO for optimising experimental parameters ICMMO seminar – 07/11/2024 12 / 13Real examples Application on SPS optimisationSPS applicationModelsElasticNet : very quickRandomForestRegressor : usually goodXGBRegressor : usually goodCross validationLeaveOneOut : for less than 10 dataK-Fold (3-4-5) : for more dataPrediction modelRM : θ    YRMsuggest n new θ BOreal calcul of YDatabase{θ}={Y}C. Bourgès, G. Lambard et al., Acta Materialia 281, 120342 (2024)S. Junier (ICMPE-LINK) BO for optimising experimental parameters ICMMO seminar – 07/11/2024 12 / 13Real examples Application on SPS optimisationSPS applicationRegression model results (plot by MADGUI)Database{θ}={Y} GP suggestnew θRM is good ?estimateYGP(θ)RM(θ)yesnoPrediction modelRM : θ    YRMsuggest n new θ BOreal calcul of YDatabase{θ}={Y}C. Bourgès, G. Lambard et al., Acta Materialia 281, 120342 (2024)S. Junier (ICMPE-LINK) BO for optimising experimental parameters ICMMO seminar – 07/11/2024 12 / 13Real examples Application on SPS optimisationSPS applicationRegression model results (plot by MADGUI)Database{θ}={Y} GP suggestnew θRM is good ?estimateYGP(θ)RM(θ)yesnoPrediction modelRM : θ    YRMsuggest n new θ BOreal calcul of YDatabase{θ}={Y}C. Bourgès, G. Lambard et al., Acta Materialia 281, 120342 (2024)S. Junier (ICMPE-LINK) BO for optimising experimental parameters ICMMO seminar – 07/11/2024 12 / 13Real examples Application on SPS optimisationSPS applicationRegression model results (plot by MADGUI)Database{θ}={Y} GP suggestnew θRM is good ?estimateYGP(θ)RM(θ)yesnoPrediction modelRM : θ    YRMsuggest n new θ BOreal calcul of YDatabase{θ}={Y}C. Bourgès, G. Lambard et al., Acta Materialia 281, 120342 (2024)S. Junier (ICMPE-LINK) BO for optimising experimental parameters ICMMO seminar – 07/11/2024 12 / 13Real examples Application on SPS optimisationSPS applicationSet BO parameter [Limits]Database{θ}={Y} GP suggestnew θRM is good ?estimateYGP(θ)RM(θ)yesnoPrediction modelRM : θ    YRMsuggest n new θ BOreal calcul of YDatabase{θ}={Y}n timesC. Bourgès, G. Lambard et al., Acta Materialia 281, 120342 (2024)S. Junier (ICMPE-LINK) BO for optimising experimental parameters ICMMO seminar – 07/11/2024 12 / 13Real examples Application on SPS optimisationSPS applicationSet BO parameter [Constraints]Database{θ}={Y} GP suggestnew θRM is good ?estimateYGP(θ)RM(θ)yesnoPrediction modelRM : θ    YRMsuggest n new θ BOreal calcul of YDatabase{θ}={Y}n timesC. Bourgès, G. Lambard et al., Acta Materialia 281, 120342 (2024)S. Junier (ICMPE-LINK) BO for optimising experimental parameters ICMMO seminar – 07/11/2024 12 / 13Real examples Application on SPS optimisationSPS applicationBOPrediction modelRM : θ    YRMsuggest n new θ BOreal calcul of YDatabase{θ}={Y}Database{θ}={Y} GP suggestnew θRM is good ?estimateYGP(θ)RM(θ)yesnon timesC. Bourgès, G. Lambard et al., Acta Materialia 281, 120342 (2024)S. Junier (ICMPE-LINK) BO for optimising experimental parameters ICMMO seminar – 07/11/2024 12 / 13Real examples Application on SPS optimisationSPS applicationBO (with prediction)Database{θ}={Y} GP suggestnew θRM is good ?estimateYGP(θ)RM(θ)yesnoPrediction modelRM : θ    YRMsuggest n new θ BOreal calcul of YDatabase{θ}={Y}n timesC. Bourgès, G. Lambard et al., Acta Materialia 281, 120342 (2024)S. Junier (ICMPE-LINK) BO for optimising experimental parameters ICMMO seminar – 07/11/2024 12 / 13Real examples Application on SPS optimisationSPS applicationRestart for several cycles0 5 10 15 20 25 30 35Sample #0.100.150.200.250.300.350.40zTInitial setcycle 1cycle 2cycle 3cycle 4In each cycle some points are not good because these pointscorrespond to features selected by BO to minimise theuncertainty on the unknown θ regionsPrediction modelRM : θ    YRMsuggest n new θ BOreal calcul of YDatabase{θ}={Y}Database{θ}={Y} GP suggestnew θRM is good ?estimateYGP(θ)RM(θ)yesnon timesC. Bourgès, G. Lambard et al., Acta Materialia 281, 120342 (2024)S. Junier (ICMPE-LINK) BO for optimising experimental parameters ICMMO seminar – 07/11/2024 12 / 13ConclusionConclusionRegression machine learning modelAllows you to predict information about a compound rather thancalculate/measure itNeed a lot of dataBayesian Optimisation (active learning)Allows you to optimise the properties of a compound with a minimum of samplesCan be applied to calculated or experimental valueMADGUIIs a fully graphical interface that makes BO accessible to researchers without extensiveprogramming experienceS. Junier (ICMPE-LINK) BO for optimising experimental parameters ICMMO seminar – 07/11/2024 13 / 13Thanks for your attention Header Background Outlook Introduction Machine Learning Interest Models Regression model Bayesian Optimisation MADGUI: User Interface developed by NIMS Theoretical Examples One dimension Two dimensions Real examples Application on SPS optimisation Conclusion Appendix End