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

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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.