Mathematical Sciences: Numerical Methods for Parameter Estimation in Distributed Parameter Systems

本课题研究分布参数系统参数估计的数值方法。讨论了几个重要的主题。参数估计问题通常被表述为最优化问题，用梯度法求解。第一个主题是利用共轭态方法和时间伽辽金方法进行梯度的有效计算。第二个主题是优化公式中正则化（即稳定化）参数的选择。与此相关的是选择系统输入和观察以最大化信息内容的主题。这些数值方法被用来开发计算机模型来描述分析化学中使用的仪器中的离子流。这些技术也可以应用于使用数学模型来描述类似现象的广泛学科。例如通过多孔介质的流动建模，这在污染地下水的清理和提高石油采收率方面具有重要应用。

This project undertakes research on numerical methods for parameter estimation in distributed parameter systems. Several important topics are addressed. Parameter estimation problems are typically formulated as optimization problems, which are solved using gradient methods. The first topic is the efficient computation of gradients using costate methods coupled with time-Galerkin methods. The second topic is the choice of regularization (i.e., stabilization) parameters in the optimization formulation. Related to this is the topic of choosing system inputs and observations to maximize information content. These numerical methods are used to develop computer models that describe ion flow in instruments used in analytical chemistry. These techniques may also be applied to a broad range of disciplines that use mathematical models to describe similar phenomena. Examples include the modelling of flow through porous media, which has important applications in the cleanup of polluted groundwater and in enhanced oil recovery.