Numerical Methods for Multiscale Inverse Problems and Applications to Sonar Imaging

多尺度反问题的数值方法及其在声纳成像中的应用

基本信息

批准号：
1720306
负责人：
Christina Frederick
金额：
$ 10万
依托单位：
New Jersey Institute of Technology
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2017
资助国家：
美国
起止时间：
2017-09-01 至 2021-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1720306&HistoricalAwards=false
关键词：
Numerical Methods Multiscale Inverse Problems

项目摘要

The principal investigator aims to develop mathematical and computational tools for data-driven research by using theoretically-sound prediction models and adaptive numerical methods that capture intrinsic features of complex physical processes. This research project is intended to provide new guarantees for the solvability of a class of inverse problems important in mathematics, commercial industries, and defense operations. The project will involve undergraduate and graduate students, who will receive training in numerical methods, analysis, and scientific applications. The principal investigator will pursue an original strategy for extracting details from large scale datasets using a new class of efficient methods that exploit problem-dependent features of processes occurring on multiple scales. The design of numerical schemes is adaptable to qualitative scientific knowledge and has the potential to significantly enhance the accessibility and performance of current inversion methods. The basis of the approach is the selection of a low-dimensional parameter that describes key microscopic details and the development of numerical methods that retain an intrinsic knowledge of parameter values while solving large-scale models, substantially reducing computational costs. Deliverables of the project will be the new methodology, as well as scientific applications to large scale inverse problems in sonar imaging, where the main challenge is to capture the appropriate physics while maintaining computational time and memory demands acceptable for current computer architectures.

首席研究者旨在通过使用理论上的预测模型和自适应数值方法来开发用于数据驱动研究的数学和计算工具，从而捕获复杂物理过程的内在特征。该研究项目旨在为在数学，商业行业和国防运营中重要的一类反问题提供新的保证。该项目将涉及本科生和研究生，他们将接受数值方法，分析和科学应用的培训。首席研究者将使用新的有效方法从大规模数据集中提取细节的原始策略，以利用在多个尺度上发生的流程的问题依赖性特征。数值方案的设计适用于定性科学知识，并有可能显着增强当前反转方法的可访问性和性能。该方法的基础是选择一个低维参数，该参数描述了关键的显微镜细节和数值方法的开发，这些方法在求解大规模模型的同时保留了参数值的内在知识，从而大大降低了计算成本。该项目的可交付成果将是新方法，以及对声纳成像中大规模反问题的科学应用，其中主要挑战是捕获适当的物理学，同时维持计算时间和内存需求对于当前的计算机架构可接受。