{"title":"索博尔敏感度指数--利用给定数据动态自适应方差估计器的机器学习方法","authors":"Ivano Azzini, Rossana Rosati","doi":"10.1615/int.j.uncertaintyquantification.2024051654","DOIUrl":null,"url":null,"abstract":"Global sensitivity analysis is today a widely recognized discipline with an extensive application in an increasing number of domains. Today, methodological development and available software, as well as a broader knowledge and debate on the topic, make investigations feasible which were simply impossible or too demanding a few years ago.\nAmong global sensitivity methods, the variance-based techniques and Monte Carlo-based estimators related to Sobol’ sensitivity indices are mostly implemented due to their versatility and easiness of interpretation. Nevertheless, the strict dependency of the analysis cost on the number of the investigated factors and the need of a designed input are still a major issue.\nA reduction of the required model evaluations can be achieved with the use of quasi-Monte Carlo sequences, the study of groups of inputs, and the sensitivity indices computation through higher performing estimators such as the Innovative Algorithm based on dynamic adaptive variances recently proposed by the authors. However, all these strategies even cutting significantly the necessary model runs are not able to overcome the barrier of a structured input.\nThis paper proposes a machine learning approach that allows us to estimate Sobol’ indices using the outstanding dynamic adaptive variances estimator starting from a set of Monte Carlo given data. Tests have been run on three relevant functions. In most cases, the results are very promising and seem to positively overcome the limit of a design-data approach keeping all the advantages of the Sobol’ Monte Carlo estimator.","PeriodicalId":48814,"journal":{"name":"International Journal for Uncertainty Quantification","volume":"64 1","pages":""},"PeriodicalIF":1.5000,"publicationDate":"2024-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Sobol’ sensitivity indices– A Machine Learning approach using the Dynamic Adaptive Variances Estimator with Given Data\",\"authors\":\"Ivano Azzini, Rossana Rosati\",\"doi\":\"10.1615/int.j.uncertaintyquantification.2024051654\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Global sensitivity analysis is today a widely recognized discipline with an extensive application in an increasing number of domains. Today, methodological development and available software, as well as a broader knowledge and debate on the topic, make investigations feasible which were simply impossible or too demanding a few years ago.\\nAmong global sensitivity methods, the variance-based techniques and Monte Carlo-based estimators related to Sobol’ sensitivity indices are mostly implemented due to their versatility and easiness of interpretation. Nevertheless, the strict dependency of the analysis cost on the number of the investigated factors and the need of a designed input are still a major issue.\\nA reduction of the required model evaluations can be achieved with the use of quasi-Monte Carlo sequences, the study of groups of inputs, and the sensitivity indices computation through higher performing estimators such as the Innovative Algorithm based on dynamic adaptive variances recently proposed by the authors. However, all these strategies even cutting significantly the necessary model runs are not able to overcome the barrier of a structured input.\\nThis paper proposes a machine learning approach that allows us to estimate Sobol’ indices using the outstanding dynamic adaptive variances estimator starting from a set of Monte Carlo given data. Tests have been run on three relevant functions. In most cases, the results are very promising and seem to positively overcome the limit of a design-data approach keeping all the advantages of the Sobol’ Monte Carlo estimator.\",\"PeriodicalId\":48814,\"journal\":{\"name\":\"International Journal for Uncertainty Quantification\",\"volume\":\"64 1\",\"pages\":\"\"},\"PeriodicalIF\":1.5000,\"publicationDate\":\"2024-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal for Uncertainty Quantification\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.1615/int.j.uncertaintyquantification.2024051654\",\"RegionNum\":4,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"ENGINEERING, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal for Uncertainty Quantification","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1615/int.j.uncertaintyquantification.2024051654","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENGINEERING, MULTIDISCIPLINARY","Score":null,"Total":0}
Sobol’ sensitivity indices– A Machine Learning approach using the Dynamic Adaptive Variances Estimator with Given Data
Global sensitivity analysis is today a widely recognized discipline with an extensive application in an increasing number of domains. Today, methodological development and available software, as well as a broader knowledge and debate on the topic, make investigations feasible which were simply impossible or too demanding a few years ago.
Among global sensitivity methods, the variance-based techniques and Monte Carlo-based estimators related to Sobol’ sensitivity indices are mostly implemented due to their versatility and easiness of interpretation. Nevertheless, the strict dependency of the analysis cost on the number of the investigated factors and the need of a designed input are still a major issue.
A reduction of the required model evaluations can be achieved with the use of quasi-Monte Carlo sequences, the study of groups of inputs, and the sensitivity indices computation through higher performing estimators such as the Innovative Algorithm based on dynamic adaptive variances recently proposed by the authors. However, all these strategies even cutting significantly the necessary model runs are not able to overcome the barrier of a structured input.
This paper proposes a machine learning approach that allows us to estimate Sobol’ indices using the outstanding dynamic adaptive variances estimator starting from a set of Monte Carlo given data. Tests have been run on three relevant functions. In most cases, the results are very promising and seem to positively overcome the limit of a design-data approach keeping all the advantages of the Sobol’ Monte Carlo estimator.
期刊介绍:
The International Journal for Uncertainty Quantification disseminates information of permanent interest in the areas of analysis, modeling, design and control of complex systems in the presence of uncertainty. The journal seeks to emphasize methods that cross stochastic analysis, statistical modeling and scientific computing. Systems of interest are governed by differential equations possibly with multiscale features. Topics of particular interest include representation of uncertainty, propagation of uncertainty across scales, resolving the curse of dimensionality, long-time integration for stochastic PDEs, data-driven approaches for constructing stochastic models, validation, verification and uncertainty quantification for predictive computational science, and visualization of uncertainty in high-dimensional spaces. Bayesian computation and machine learning techniques are also of interest for example in the context of stochastic multiscale systems, for model selection/classification, and decision making. Reports addressing the dynamic coupling of modern experiments and modeling approaches towards predictive science are particularly encouraged. Applications of uncertainty quantification in all areas of physical and biological sciences are appropriate.