We introduce a method to construct a stochastic surrogate model from the results of dimensionality reduction in forward uncertainty quantification. The hypothesis is that the high-dimensional input augmented by the output of a computational model admits a low-dimensional representation. This assumption can be met by numerous uncertainty quantification applications with physics-based computational models. The proposed approach differs from a sequential application of dimensionality reduction followed by surrogate modeling, as we "extract" a surrogate model from the results of dimensionality reduction in the input-output space. This feature becomes desirable when the input space is genuinely high-dimensional. The proposed method also diverges from the Probabilistic Learning on Manifold, as a reconstruction mapping from the feature space to the input-output space is circumvented. The final product of the proposed method is a stochastic simulator that propagates a deterministic input into a stochastic output, preserving the convenience of a sequential "dimensionality reduction + Gaussian process regression" approach while overcoming some of its limitations. The proposed method is demonstrated through two uncertainty quantification problems characterized by high-dimensional input uncertainties.
Batch simulations and uncertainty quantification in Gaussian process surrogate approximate Bayesian computation
Department of Biostatistics, University of Oslo（奥斯陆大学生物统计系）；Helsinki Institute for Information Technology HIIT, Department of Computer Science, Aalto University（赫尔辛基信息技术研究所，阿尔托大学计算机科学系）
Comparison of Polynomial Chaos and Gaussian Process surrogates for uncertainty quantification and correlation estimation of spatially distributed open-channel steady flows
Uncertainty Quantification for Machine Learning-Based Prediction: A Polynomial Chaos Expansion Approach for Joint Model and Input Uncertainty Propagation
School of Mechanical Engineering（机械工程学院）；Purdue University（普渡大学）
A Bayesian latent Gaussian process framework for aerodynamic uncertainty quantification
Aerospace Engineering, The Pennsylvania State University, University Park, PA 16802（航空工程，宾夕法尼亚州立大学，University Park分校，PA 16802）；Aerospace Engineering and the Institute of Computational and Data Science (ICDS), The Pennsylvania State University, University Park, PA 16802（航空工程和计算与数据科学研究所（ICDS），宾夕法尼亚州立大学，University Park分校，PA 16802）
Surrogate-assisted parallel tempering for Bayesian neural learning
University of New South Wales（新南威尔士大学）；The University of Sydney（悉尼大学）；Indian Institute of Technology Guwahati（印度理工学院古瓦哈提分校）；SRM Institute of Science and Technology（SRM科学技术学院）；Indian Institute of Technology Delhi（印度理工学院德里分校）
Stochastic Modeling of Inhomogeneities in the Aortic Wall and Uncertainty Quantification using a Bayesian Encoder-Decoder Surrogate
Graz University of Technology（格拉茨工业大学）；Graz Center for Computational Engineering（格拉茨计算工程中心）；University Medicine Essen（埃森大学医学院）；Norwegian University of Science and Technology (NTNU)（挪威科技大学）
Surrogate-assisted Bayesian inversion for landscape and basin evolution models
University of New South Wales（新南威尔士大学）；University of Sydney（悉尼大学）；SRM Institute of Science and Technology（SRM科学技术研究所）
景观演化模型的复杂性和计算成本高的性质在未知参数的推断和优化方面提出了重大挑战。贝叶斯推断提供了一种用于未知模型参数的估计和不确定性量化的方法。在我们以前的工作中，我们开发了并行回火贝叶斯作为参数估计和不确定性量化的荒地景观演化模型的框架。并行回火Bayeslands具有高性能计算功能，具有数十个并行运行的处理核心，以提高计算效率。虽然我们使用并行计算，但该过程仍然具有计算挑战性，因为需要绘制和评估数千个样本。\textcolor{black}{In large-scale landscape and basin evolution problems, a single model evaluation can take from several minutes to hours, and in some instances, even days. Surrogate-assisted optimisation has been used for several computationally expensive engineering problems which motivate its use in optimisation and inference of complex geoscientific models.}代理模型的使用可以通过开发计算成本低廉的模型来模拟昂贵的模…
SCORE: A 1D Reparameterization Technique to Break Bayesian Optimization's Curse of Dimensionality
Laboratoire de Physique des Interfaces et des Couches Minces (LPICM)（界面与薄膜物理实验室（LPICM））；Ecole Polytechnique, Institut Polytechnique de Paris (IP Paris)（巴黎综合理工学院，巴黎理工学院（IP Paris））；Institut Photovoltaïque d’Île-de-France (IPVF)（法兰西岛光伏研究所（IPVF））
Uncertainty quantification in mechanics: A unified Bayesian perspective
Courant Institute of Mathematical Sciences, New York University（纽约大学柯朗数学科学研究所）；Division of Applied Mathematics, Brown University（布朗大学应用数学系）；Institute of Applied Mechanics, Friedrich-Alexander-Universität Erlangen-Nürnberg（埃尔朗根-纽伦堡大学应用力学研究所）；Institute of Biomechanics, Graz University of Technology（格拉茨工业大学生物力学研究所）；Department of Structural Engineering, Norwegian University of Science and Technology (NTNU)（挪威科技大学结构工程系）；Department of Mechanical Engineering, Stanford University（斯坦福大学机械工程系）
Data-driven inverse uncertainty quantification: application to the Chemical Vapor Deposition Reactor Modeling
University of Luxembourg（卢森堡大学）；Luxembourg Institute of Science and Technology（卢森堡科学与技术研究所）；Johns Hopkins University（约翰斯·霍普金斯大学）；CERATIZIT Luxembourg S.à r.l.（CERATIZIT 卢森堡有限公司）；CERATIZIT Austria GmbH（CERATIZIT 奥地利有限公司）；School of Chemical Engineering, National Technical University of Athens（雅典国立技术大学化学工程学院）
Variable Selection with Rigorous Uncertainty Quantification using Deep Bayesian Neural Networks: Posterior Concentration and Bernstein-von Mises Phenomenon
Leveraging Industry 4.0 -- Deep Learning, Surrogate Model and Transfer Learning with Uncertainty Quantification Incorporated into Digital Twin for Nuclear System
Bangladesh University of Engineering and Technology（孟加拉国工程技术大学）；Jashore University of Science and Technology（杰索尔科技大学）；Indian Institute of Technology Delhi（印度理工学院德里分校）；University of Bristol（布里斯托大学）；Missouri University of Science and Technology（密苏里科技大学）
Surrogate Modelling of Proton Dose with Monte Carlo Dropout Uncertainty Quantification
Institute for Mathematical Innovation University of Bath, Bath, UK（数学创新研究所 英国巴斯大学）；Department of Mathematical Sciences University of Bath, Bath, UK（数学科学系 英国巴斯大学）
