论文标题
具有自动差异的阴影灵敏度的混乱时期系统中的变分优化和数据同化
Variational optimization and data assimilation in chaotic time-delayed systems with automatic-differentiated shadowing sensitivity
论文作者
论文摘要
在这篇计算论文中，我们使用阴影算法对混乱制度中的长期（或集合）平均进行敏感性分析。我们引入自动分化，以消除阴影算法中使用的切线/伴随方程求解器。在基于梯度的优化中，我们使用计算的阴影灵敏度来最大程度地减少混乱的时间延迟系统的不同长期平均功能，并通过最佳参数选择。在数据同化的合并状态和参数估计中，我们使用计算的灵敏度来预测模型中的最佳轨迹给定信息，以及超出可预测性时间的测量结果。将算法应用于热声模型。由于计算框架相当笼统，因此本文介绍的技术可用于集合平均值的敏感性分析，参数优化和其他混乱问题的数据同化，这些问题适用于阴影方法。
In this computational paper, we perform sensitivity analysis of long-time (or ensemble) averages in the chaotic regime using the shadowing algorithm. We introduce automatic differentiation to eliminate the tangent/adjoint equation solvers used in the shadowing algorithm. In a gradient-based optimization, we use the computed shadowing sensitivity to minimize different long-time averaged functionals of a chaotic time-delayed system by optimal parameter selection. In combined state and parameter estimation for data assimilation, we use the computed sensitivity to predict the optimal trajectory given information from a model and data from measurements beyond the predictability time. The algorithms are applied to a thermoacoustic model. Because the computational framework is rather general, the techniques presented in this paper may be used for sensitivity analysis of ensemble averages, parameter optimization and data assimilation of other chaotic problems, where shadowing methods are applicable.
