A Posteriori Error Estimates for the Solution of Variational Inverse Problems
A Posteriori Error Estimates for the Solution of Variational Inverse Problems
复制标题
变分反问题求解的后验误差估计
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
Adrian Sandu
中科院分区：
文献类型：
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作者：
Vishwas Rao;Adrian Sandu
动态数据驱动的应用系统在共生反馈控制系统中集成了计算模拟和物理测量。该框架中的反问题使用来自测量的数据以及数值模型来估计感兴趣的物理系统的参数或状态。测量和计算模型中的不确定性都会导致不准确的估计。这项工作发展了一种方法来估计不同误差对反问题变分解的影响。重点是用微分方程描述的时间演化系统，以及一类特殊的反问题，即数据同化。该算法采用一阶和二阶共轭模型。在确定性设置中，该方法提供了逆解的后验误差估计。在概率环境中，在给定模型和数据中的不确定性的情况下，它提供了逆解中的不确定性的后验量化。
Dynamically data-driven application systems integrate computational simulations and physical measurements in a symbiotic feedback control system. Inverse problems in this framework use data from measurements along with a numerical model to estimate the parameters or state of a physical system of interest. Uncertainties in both the measurements and the computational model lead to inaccurate estimates. This work develops a methodology to estimate the impact of different errors on the variational solutions of inverse problems. The focus is on time evolving systems described by differential equations, and on a particular class of inverse problems, namely, data assimilation. The computational algorithm uses first order and second order adjoint models. In a deterministic setting the methodology provides a posteriori error estimates for the inverse solution. In a probabilistic setting it provides an a posteriori quantification of uncertainty in the inverse solution, given the uncertainties in the model and data....