Large-Scale Inverse Problems and Quantification of Uncertainty-猫眼课题宝

DOI：

10.1002/9780470685853

发表时间：

1994

期刊：

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通讯作者：

中科院分区：

其他

文献类型：

作者：

L. Biegler;G. Biros;O. Ghattas;M. Heinkenschloss;D. Keyes;B. Mallick;Y. Marzouk;L. Tenorio;B. V. B. Waanders-B.-V.-B.-Waanders-1863062;K. Willcox

1简介1.1简介1.2统计方法1.3近似方法1.4卡尔曼滤波1.5优化2反问题中的频率论与贝叶斯推理入门2.1简介2.2先验信息与参数：你知道什么，你想知道什么？2.3评估者：你能用你测量的东西做什么？2.4评估人员的表现：你能做得多好？2.5基于BNM的贝叶斯估计的频域性能2.6摘要文献3主观知识还是客观信念？斜视贝叶斯方法3.1绪论3.2信念信息和概率3.3贝叶斯公式和更新概率3.4涉及超模型的计算示例3.5信念的动态更新3.6讨论参考文献4反问题的贝叶斯和地统计学方法4.1简介4.2贝叶斯和频率方法4.3先验分布4.4地统计学方法4.5总结参考文献5使用贝叶斯框架将模拟和物理观测结合起来进行统计推断5.1介绍5.2贝叶斯模型公式5.3应用：宇宙微波背景5.4讨论参考文献6用于地下表征的贝叶斯划分模型6.1介绍6.2模型方程和问题设置6.3利用贝叶斯划分模型和两阶段MCMC逼近响应面6.4数值结果6.5结论参考文献7代理和降阶建模：大规模统计反问题的方法比较7.1导论7.2降低求解统计反问题的计算成本7.3一般公式7.4模型约简7.5随机谱法7.6举例说明7.7结论参考文献8参数化抛物偏微分方程的约基近似和后验误差估计在贝叶斯参数估计中的应用8.1导论8.2线性抛物方程8.3贝叶斯参数估计8.4结语参考文献9多变量输出计算机模拟的校准与不确定性分析9.1简介9.2高斯过程模型9.3贝叶斯模型校准9.4案例研究10昂贵的多变量计算机实验的贝叶斯校准10.1计算机实验的校准10.2主成分仿真10.3多变量校准10.4摘要参考文献11集成卡尔曼滤波器及相关滤波器11.1简介11.2模型假设11.3传统卡尔曼滤波器（KF） 11.4集成卡尔曼滤波器（EnKF） 11.5随机最大似然滤波器（RMLF） 11.6粒子滤波（PF） 11.7结束语11.8附录A: EnKF算法的特性11.9附录B：RMLF算法的性质参考文献12利用集成卡尔曼滤波进行复杂油藏模型的历史匹配与不确定性量化12.1导论12.2逆问题的表述与求解12.3 EnKF历史匹配工作流12.4现场实例12.5结论参考文献13阻抗成像大规模非线性病态问题的优化实验设计13.1导论13.2阻抗层析成像13.3优化实验设计背景13.4非线性不适定问题的最优实验设计13.5优化框架13.6数值结果13.7讨论与结论14求解随机逆问题：稀疏网格配置方法14.1简介14.2数学发展14.3数值例子14.4摘要参考文献15地震逆问题的不确定性分析：两个实际例子15.1简介15.2速度测定的走时反演15.3叠前地层反演15.4结论参考文献16离散ODE伴随解逆问题16.1简介16.2龙格-库塔法16.3自适应步骤16.4线性多步骤方法16.5数值结果16.6在数据同化中的应用16.7结论参考文献待定

1 Introduction 1.1 Introduction 1.2 Statistical Methods 1.3 Approximation Methods 1.4 Kalman Filtering 1.5 Optimization 2 A Primer of Frequentist and Bayesian Inference in Inverse Problems 2.1 Introduction 2.2 Prior Information and Parameters: What do you know, and what do you want to know? 2.3 Estimators: What can you do with what you measure? 2.4 Performance of estimators: How well can you do? 2.5 Frequentist performance of Bayes estimators for a BNM 2.6 Summary Bibliography 3 Subjective Knowledge or Objective Belief? An Oblique Look to Bayesian Methods 3.1 Introduction 3.2 Belief, information and probability 3.3 Bayes' formula and updating probabilities 3.4 Computed examples involving hypermodels 3.5 Dynamic updating of beliefs 3.6 Discussion Bibliography 4 Bayesian and Geostatistical Approaches to Inverse Problems 4.1 Introduction 4.2 The Bayesian and Frequentist Approaches 4.3 Prior Distribution 4.4 A Geostatistical Approach 4.5 Concluding Bibliography 5 Using the Bayesian Framework to Combine Simulations and Physical Observations for Statistical Inference 5.1 Introduction 5.2 Bayesian Model Formulation 5.3 Application: Cosmic Microwave Background 5.4 Discussion Bibliography 6 Bayesian Partition Models for Subsurface Characterization 6.1 Introduction 6.2 Model equations and problem setting 6.3 Approximation of the response surface using the Bayesian Partition Model and two-stage MCMC 6.4 Numerical results 6.5 Conclusions Bibliography 7 Surrogate and reduced-order modeling: a comparison of approaches for large-scale statistical inverse problems 7.1 Introduction 7.2 Reducing the computational cost of solving statistical inverse problems 7.3 General formulation 7.4 Model reduction 7.5 Stochastic spectral methods 7.6 Illustrative example 7.7 Conclusions Bibliography 8 Reduced basis approximation and a posteriori error estimation for parametrized parabolic PDEs Application to real-time Bayesian parameter estimation 8.1 Introduction 8.2 Linear Parabolic Equations 8.3 Bayesian Parameter Estimation 8.4 Concluding Remarks Bibliography 9 Calibration and Uncertainty Analysis for Computer Simulations with Multivariate Output 9.1 Introduction 9.2 Gaussian Process Models 9.3 Bayesian Model Calibration 9.4 Case Study: Thermal Simulation of Decomposing Foam 9.5 Conclusions Bibliography 10 Bayesian Calibration of Expensive Multivariate Computer Experiments 10.1 Calibration of computer experiments 10.2 Principal component emulation 10.3 Multivariate calibration 10.4 Summary Bibliography 11 The Ensemble Kalman Filter and Related Filters 11.1 Introduction 11.2 Model Assumptions 11.3 The Traditional Kalman Filter (KF) 11.4 The Ensemble Kalman Filter (EnKF) 11.5 The Randomized Maximum Likelihood Filter (RMLF) 11.6 The Particle Filter (PF) 11.7 Closing Remarks 11.8 Appendix A: Properties of the EnKF Algorithm 11.9 Appendix B: Properties of the RMLF Algorithm Bibliography 12 Using the ensemble Kalman Filter for history matching and uncertainty quantification of complex reservoir models 12.1 Introduction 12.2 Formulation and solution of the inverse problem 12.3 EnKF history matching workflow 12.4 Field Case 12.5 Conclusion Bibliography 13 Optimal Experimental Design for the Large-Scale Nonlinear Ill-posed Problem of Impedance Imaging 13.1 Introduction 13.2 Impedance Tomography 13.3 Optimal Experimental Design - Background 13.4 Optimal Experimental Design for Nonlinear Ill-Posed Problems 13.5 Optimization Framework 13.6 Numerical Results 13.7 Discussion and Conclusions Bibliography 14 Solving Stochastic Inverse Problems: A Sparse Grid Collocation Approach 14.1 Introduction 14.2 Mathematical developments 14.3 Numerical Examples 14.4 Summary Bibliography 15 Uncertainty analysis for seismic inverse problems: two practical examples 15.1 Introduction 15.2 Traveltime inversion for velocity determination. 15.3 Prestack stratigraphic inversion 15.4 Conclusions Bibliography 16 Solution of inverse problems using discrete ODE adjoints 16.1 Introduction 16.2 Runge-Kutta Methods 16.3 Adaptive Steps 16.4 Linear Multistep Methods 16.5 Numerical Results 16.6 Application to Data Assimilation 16.7 Conclusions Bibliography TBD

Large-Scale Inverse Problems and Quantification of Uncertainty

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