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、生物和工程科学中普遍存在。这些模型通常被称为仿真器，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反问题。然而，解决反问题并量化不确定性是具有挑战性的。该项目用新颖的方法、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。这个项目的一个特殊应用是遥感中的反问题。这项研究项目综合了统计学、应用数学、数据科学和遥感方面的进展。它将提供评估遥感数据产品的质量和不确定性的方法，以解决科学假设问题。PIS将在碳监测遥感反问题的背景下应用和评估这些新方法，但这些方法也可以用于许多其他领域的数据密集型反问题，包括气候学、地球物理和医学成像。该项目将直接培训学生研究人员，并将开发教材。这一合作研究项目将有助于在统计建模、不确定性量化和解决与高维系统相关的大规模逆问题的高效可扩展方法方面取得重大进展。PIS将建立新的方法来建立具有计算效率和统计保证的统计模拟器。可伸缩性是通过对输入和输出空间进行联合降维来实现的，而所得到的仿真器的理论逼近性质将被推导出来。由此产生的仿真器将促进基于模拟的大规模遥感数据不确定性量化实验。这一统计仿真框架也将被集成到算法中，以推断反问题的解决方案，从而实现更快的计算。所开发的方法将特别侧重于遥感中遇到的高维系统，将导致遥感中复杂推理问题和不确定性量化的统计方法的新范式，并改变目前的遥感检索做法。将向广大科学家和工程师提供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的研究人员具有实用价值。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.