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

本项目进行数值方法的研究， 分布参数系统的参数估计 几 重要的话题都在讨论。 参数估计问题 通常被公式化为优化问题， 使用梯度方法求解。 第一个主题是效率 使用协态方法计算梯度， 时间Galerkin方法 第二个主题是选择 正则化（即，稳定）参数 优化配方 与此相关的是 选择系统输入和观测以最大化信息 内容 这些数值方法用于开发计算机模型 它描述了分析仪器中的离子流， 化学. 这些技术也可以应用于广泛的领域。 使用数学模型来描述类似的 现象。 实例包括通过多孔介质的流动建模 媒体，其中有重要的应用程序，在清理 污染的地下水和提高石油采收率。

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.