Collaborative Research: Inference and Uncertainty Quantification for High Dimensional Systems in Remote Sensing: Methods, Computation, and Applications

复杂的数学模型在物理、大气、生物和工程科学中无处不在。这些模型通常被称为模拟器，用于描述系统中许多变量和过程之间的复杂相互作用，有时伴随着大量数据。从模拟器和观测数据中提取信息和知识的过程可以称为逆问题。然而，解决反问题和量化的不确定性是具有挑战性的。该项目通过新颖的方法，高效的算法和软件工具来解决这些挑战，以实现快速模拟和逆问题解决方案。该项目的一个特殊应用是遥感中的逆问题。该研究项目整合了统计学，应用数学，数据科学和遥感的进步。它将提供评估遥感数据产品质量和不确定性的方法，以解决科学假设问题。PI将在碳监测遥感逆问题的背景下应用和评估这些新方法，但这些方法也可用于许多其他领域的数据密集型逆问题，包括气候学，地球物理学和医学成像。该项目将直接培训学生研究人员，并将编制教育材料。该合作研究项目将在统计建模、不确定性量化和有效的可扩展方法方面取得重大进展，以解决与高维系统相关的大规模逆问题。PI将建立新的方法来构建具有计算效率和统计保证的统计仿真器。通过对输入和输出空间的联合降维实现了可扩展性，同时将推导出所得仿真器的理论近似特性。由此产生的模拟器将促进大规模的基于模拟的遥感数据的不确定性量化实验。这种统计仿真框架也将被集成到算法中，以推断逆问题的解决方案，从而实现更快的计算。特别关注在遥感中遇到的高维系统，开发的方法将导致一个新的范例，复杂的推理问题和不确定性量化的统计方法在遥感和改造目前的做法遥感检索。将向广大科学家和工程师提供用于拟议新方法的开放源码软件。通过与遥感领域的合作者合作，该项目开发的方法将对包括碳监测在内的各种应用领域的研究人员具有实际效用。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Complex mathematical models are ubiquitous in physical, atmospheric, biological, and engineering sciences. These models, often called simulators, are used to describe complicated interactions among many variables and processes in the systems and are sometimes accompanied by massive data. The process of extracting information and knowledge from the simulators and observational data can be called an inverse problem. However, solving inverse problems and quantifying the uncertainty is challenging. This project addresses these challenges with novel methods, efficient algorithms, and software tools to enable fast simulations and inverse problem solutions. A particular application in this project is inverse problems in remote sensing. This research project integrates the advancements in statistics, applied mathematics, data science, and remote sensing. It will provide ways to assess the quality and uncertainty of remote sensing data products to address scientific hypotheses. The PIs will apply and evaluate these new methods in the context of inverse problems in remote sensing for carbon monitoring, but these methods can also be used for data-intensive inverse problems in many other areas including climatology, geophysics, and medical imaging. This project will directly train student researchers and will develop educational materials. The project findings will be shared via journal publications and conference presentations.This collaborative research project will contribute to significant advances in statistical modeling, uncertainty quantification, and efficient scalable methods to solve large-scale inverse problems associated with high-dimensional systems. The PIs will establish new methods to build statistical emulators with computational efficiency and statistical guarantees. The scalability is achieved by joint dimension reduction for both the input and output spaces, while theoretical approximation properties of the resulting emulators will be derived. The resulting emulators will facilitate large-scale simulation-based uncertainty quantification experiments for remote sensing data. This framework of statistical emulation will also be integrated into the algorithms to infer inverse problem solutions to enable faster computation. With a particular focus on high-dimensional systems encountered in remote sensing, the methods developed will lead to a new paradigm of statistical methods for complex inference problems and uncertainty quantification in remote sensing and transform the current practice of remote sensing retrieval. Open-source software for the proposed new approaches will be made available to a wide community of scientists and engineers. By partnering with collaborators in remote sensing, the methods developed in this project will be of practical utility for researchers in various applications including carbon monitoring.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.