Solution of Inverse Problems with Adaptive Models

自适应模型反问题的求解

• 批准号: 0635194
• 负责人: Adrian Sandu
• 金额: $ 18.61万
• 依托单位: Virginia Polytechnic Institute and State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-09-15 至 2010-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0635194&HistoricalAwards=false
• 关键词: Solution; Inverse; Problems; Adaptive; Models

Inverse problems like parameter estimation, data assimilation, and optimalcontrol for large scale systems governed by partial differential equations(PDEs) are of considerable importance in many fields including atmosphericscience and oceanography, optimal flow control, and homeland security.State-of-the-art solvers for large scale PDEs adaptively refine the timestep and the mesh, and adjust the computational pattern in order tocontrol the numerical errors and to preserve the qualitative features ofthe solution. In contrast, most inverse problems to date have been solvedusing non-adaptive methods due to the considerable challenges associated with obtaining gradients for adaptive simulations. The goal of the project is to advance the fundamental algorithms neededfor solving inverse problems in the context of adaptive models. Theintellectual merit of this work is substantiated by the following researchelements: (1) understand the discrete adjoints for methods that use adaptive mesh refinement, adaptive time stepping, and adaptive computational patterns (e.g., upwinding or flux limiting);(2) develop techniques to minimize the inconsistencies between the discrete adjoint scheme and the (continuous) adjoint PDE;(3) develop apriori adjoint error estimates;(4) assess the impact of different adjoint approaches on the performance of several numerical optimization schemes; and(5) apply the new algorithms to real data assimilation problems in oceanography.The general algorithms and methodologies for solving inverse problems withadaptive forward models are expected to have a broad impact on many fieldsincluding atmospheric sciences, oceanography, environmental sciences,optimal control of flows, structural mechanics, homeland security, etc.

在许多领域，包括大规模微分方程（PDE）控制的大规模系统的参数估计，数据同化和最佳控制等反问题在许多领域都非常重要保留解决方案的定性特征。相反，由于与获得自适应模拟梯度相关的巨大挑战，迄今为止的大多数反问题已经解决了非自适应方法。该项目的目的是推进在自适应模型中解决反问题所需的基本算法。这项工作的智慧优点得到了以下研究详细的证实：（1）了解使用适应性网状精炼，自适应时间步进和自适应计算模式的方法的离散伴随，例如上风或变化的限制）；（2）开发了（2）在相邻方面的临近（2）（2）（2）（2）（2）（2）（2）（2）（2）（2）（2）（2）（2）（2）（2）（2）（2）（2）（2）（2）（2）（2）（2）（2）（2）（2）（2）（2）（2）（2）（2）（2）（2）（2）（2）（2）（2）（2）（2）（2）（2）（2）（2）（2）（连续）（3 APRIORI伴随误差估计；（4）评估不同伴随方法对几种数值优化方案的性能的影响； （5）将新算法应用于海洋学中的真实数据同化问题。预计解决适应性前向模型的逆问题的一般算法和方法将对许多田间的大气科学，海洋学，环境科学，最佳控制，结构机械师，家庭机制，家庭机械师的最佳控制，结构机械师，家庭机制，家庭机制，家庭机械师的最佳控制，构成大气科学的影响很大。