反问题的数学建模、计算及应用

In this project, we propose to study mathematical modeling, computation and applications of several classes of inverse problems that arise in a diverse set of scientific areas including optics, electromagnetics, environmental sciences and medical imaging. The methodology and techniques developed will be novel and general. They will be applicable to inverse problems in many physical processes with common difficulties: high nonlinearity, ill-posedness and large-scale computation. A distinctive feature of the proposed project is to combine the scientific algorithm with high-performance, computable modeling techniques to develop novel computational methods for solving many challenging inverse problems. The developed methods are expected to make a substantial impact on many inverse problems from important scientific and industrial applications.

本项目致力于研究反问题的数学建模、计算和实际应用等方面。针对一些重要的实际问题领域，如光与电磁学，环境科学（如PM2.5等污染物的监测与扩散等）和数理医学，我们将发展一些新的可计算数学模型和高性能科学算法来求解与这些领域密切相关的反问题。这些方法可以克服一般反问题的共性难点，即：高度非线性、不适定性和计算大规模性。我们也计划将这些新的可计算数学模型和高性能科学算法应用到一些实际问题，从而力争解决一些国家的重大需求。 本项目的主要特色就是面向国际前沿，将可计算建模与高性能科学算法相结合，解决相关共性难题，力争在理论、算法、建模及应用上取得突破。