论文标题
高维逆问题的客观敏感主组件分析
Objective-Sensitive Principal Component Analysis for High-Dimensional Inverse Problems
论文作者
论文摘要
我们提出了一种新颖的方法，用于自适应，可区分的大规模随机场。如果该方法与任何基于梯度的优化算法相结合，则可以应用于各种优化问题，包括历史记录匹配。开发的技术基于主成分分析（PCA），但修改了考虑目标函数行为的主要组件的纯粹数据驱动基础。为了定义有效的编码，对梯度敏感的PCA使用目标函数梯度相对于模型参数。我们提出了该技术的计算有效实现，其中两个基于固定扰动理论（SPT）。测试，验证和讨论新编码方法的最佳，正确性和低计算成本。提出了三种用于最佳参数分解的算法，并将其应用于2D合成历史匹配的目标。结果表明，关于目标函数最小化和所需场的分布模式的编码质量的改善。提出了可能的应用和扩展。
We present a novel approach for adaptive, differentiable parameterization of large-scale random fields. If the approach is coupled with any gradient-based optimization algorithm, it can be applied to a variety of optimization problems, including history matching. The developed technique is based on principal component analysis (PCA) but modifies a purely data-driven basis of principal components considering objective function behavior. To define an efficient encoding, Gradient-Sensitive PCA uses an objective function gradient with respect to model parameters. We propose computationally efficient implementations of the technique, and two of them are based on stationary perturbation theory (SPT). Optimality, correctness, and low computational costs of the new encoding approach are tested, verified, and discussed. Three algorithms for optimal parameter decomposition are presented and applied to an objective of 2D synthetic history matching. The results demonstrate improvements in encoding quality regarding objective function minimization and distributional patterns of the desired field. Possible applications and extensions are proposed.
