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.

首席研究员的目标是通过使用理论上合理的预测模型和自适应数值方法来捕获复杂物理过程的内在特征，为数据驱动的研究开发数学和计算工具。该研究项目旨在为数学、商业工业和国防行动中重要的一类反问题的可解性提供新的保证。该项目将涉及本科生和研究生，他们将接受数值方法、分析和科学应用方面的培训。首席研究员将寻求一种原始策略，使用一类新的有效方法从大规模数据集中提取细节，这些方法利用多尺度上发生的过程的问题相关特征。数值方案的设计适用于定性科学知识，并有可能显着提高当前反演方法的可访问性和性能。该方法的基础是选择描述关键微观细节的低维参数，并开发数值方法，在求解大型模型时保留参数值的内在知识，从而大大降低计算成本。该项目的成果将是新的方法，以及声纳成像中大规模反演问题的科学应用，其中主要挑战是捕获适当的物理现象，同时保持当前计算机体系结构可接受的计算时间和内存需求。