Wyatt Bridgman, Uma Balakrishnan, Reese E. Jones, Jiefu Chen, Xuqing Wu, Cosmin Safta, Yueqin Huang, Mohammad Khalil
{"title":"A novel probabilistic transfer learning strategy for polynomial regression","authors":"Wyatt Bridgman, Uma Balakrishnan, Reese E. Jones, Jiefu Chen, Xuqing Wu, Cosmin Safta, Yueqin Huang, Mohammad Khalil","doi":"10.1615/int.j.uncertaintyquantification.2024052051","DOIUrl":null,"url":null,"abstract":"In the field of surrogate modeling and, more recently, with machine learning, transfer learning methodologies have been proposed in which knowledge from a source task is transferred to a target task where sparse and/or noisy data result in an ill-posed calibration problem. Such sparsity can result from prohibitively expensive forward model simulations or simply lack of data from experiments. Transfer learning attempts to improve target model calibration by leveraging similarities between the source and target tasks.This often takes the form of parameter-based transfer, which exploits correlations between the parameters defining the source and target models in order to regularize the target task. The majority of these approaches are deterministic and do not account for uncertainty in the model parameters. In this work, we propose a novel probabilistic transfer learning methodology which transfers knowledge from the posterior distribution of source to the target Bayesian inverse problem using an approach inspired by data assimilation.While the methodology is presented generally, it is subsequently investigated in the context of polynomial regression and, more specifically, Polynomial Chaos Expansions which result in Gaussian posterior distributions in the case of iid Gaussian observation noise and conjugate Gaussian prior distributions. The strategy is evaluated using numerical investigations and applied to an engineering problem from the oil and gas industry.","PeriodicalId":48814,"journal":{"name":"International Journal for Uncertainty Quantification","volume":"6 1","pages":""},"PeriodicalIF":1.5000,"publicationDate":"2024-08-01","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.2024052051","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}
引用次数: 0
Abstract
In the field of surrogate modeling and, more recently, with machine learning, transfer learning methodologies have been proposed in which knowledge from a source task is transferred to a target task where sparse and/or noisy data result in an ill-posed calibration problem. Such sparsity can result from prohibitively expensive forward model simulations or simply lack of data from experiments. Transfer learning attempts to improve target model calibration by leveraging similarities between the source and target tasks.This often takes the form of parameter-based transfer, which exploits correlations between the parameters defining the source and target models in order to regularize the target task. The majority of these approaches are deterministic and do not account for uncertainty in the model parameters. In this work, we propose a novel probabilistic transfer learning methodology which transfers knowledge from the posterior distribution of source to the target Bayesian inverse problem using an approach inspired by data assimilation.While the methodology is presented generally, it is subsequently investigated in the context of polynomial regression and, more specifically, Polynomial Chaos Expansions which result in Gaussian posterior distributions in the case of iid Gaussian observation noise and conjugate Gaussian prior distributions. The strategy is evaluated using numerical investigations and applied to an engineering problem from the oil and gas industry.
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.