CAREER: New Foundations for Multi-Fidelity Prediction, Estimation, and Learning Under Uncertainty in Dynamical Systems

这笔学院早期职业发展(Career)补助金将用于资助研究，使自主系统能够评估预测不确定性对规划和控制决策的影响，并将其应用于飞行中的飞机和城市环境中的自动飞行，从而促进科学进步和促进国家繁荣。自动飞行飞机为旅行、侦察和观测提供了新的省油方法，包括在大气中难以到达的区域。他们的内置模拟器对大气边界层和上升气流的存在进行假设，以最佳地从盛行的风中提取能量。计算模型还集成在无人机的规划和控制架构中，因为它们基于对周围流场的估计来预测通过城市基础设施的最佳路径。如果不评估其预测中的不确定性，这样的模拟器可能会导致次优或灾难性的决策，因为错过了最佳性能的机会或违反了安全约束。该项目通过开发新的、快速和自动化的算法来严格量化不确定性并相应地更新计算模型，并通过在受控但复杂的风力条件下使用实验飞机验证这些算法来应对这一挑战。这项研究与教育工作相结合，旨在通过围绕相关案例研究建立的一系列研讨会，为航空航天工程课程开设新的数据科学课程，以及与Ann Arbor动手博物馆合作开发K-8学生及其家长可访问的展品，将建模、数据科学和统计学的计算视角带给工科学生和公众。本研究旨在开发自动化方法的基础，以获得针对特定问题的多保真度不确定性量化技术。这些技术旨在融合来自不同保真度和成本的模拟和数据源的信息，以比最高保真度模型所需的计算成本低得多的计算成本实现准确的预测。目前的实现是基于启发式的，不适用于给定问题的数据源之间的特定关系。为了克服这一局限，这项研究将通过分析仅具有可用信息而不是启发式的贝叶斯后验和最大熵分布来得出新的统计估计器；使用这些估计器来开发新的过滤、状态估计和贝叶斯推理技术；并展示这些技术如何应用于挑战在复杂风场中飞行的飞机的规划和控制背景下产生的非线性、混沌和非高斯动力系统。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。

This Faculty Early Career Development (CAREER) grant will fund research that enables autonomous systems to estimate the effects of prediction uncertainty on planning and control decisions, with application to autonomous flight of soaring aircraft and in urban environments, thereby promoting the progress of science and advancing the national prosperity. Autonomous soaring aircraft offer new fuel-efficient approaches for travel, reconnaissance, and observation, including in hard-to-reach areas of the atmosphere. Their built-in simulators make assumptions about the presence of atmospheric boundary layers and updrafts to optimally extract energy from the prevailing winds. Computational models are also integrated in the planning and control architecture of unmanned aerial vehicles as they predict optimal paths through urban infrastructure based on estimates of the surrounding flow fields. Without assessing the uncertainty in their predictions, such simulators may result in suboptimal or catastrophic decisions, as opportunities for optimal performance are missed or safety constraints are violated. This project addresses this challenge by developing new, fast, and automated algorithms for rigorously quantifying uncertainty and updating computational models accordingly, and by validating these algorithms using experimental aircraft in controlled but complex wind conditions. The research is integrated with educational efforts aiming to bring a computational perspective on modeling, data science, and statistics to engineering students and the public through a series of workshops built around relevant case studies, a new data science class for an aerospace engineering curriculum, and a partnership with the Ann Arbor Hands-On Museum to develop exhibits accessible to K-8 students and their parents.This research aims to develop the foundations of automated approaches for deriving problem-specific multi-fidelity uncertainty quantification techniques. Such techniques aim to fuse information from simulation and data sources of varying fidelity and cost to achieve accurate predictions at a significantly lower computational cost than that required by the highest fidelity model. Current realizations are based on heuristics that are not adapted to the specific relationships between data sources of a given problem. To overcome this limitation, the research will derive new statistical estimators through analysis of Bayesian posteriors and maximum entropy distributions endowed with only the information available rather than heuristics; use these estimators to develop new filtering, state estimation, and Bayesian inference techniques; and demonstrate how these techniques may be applied to challenging nonlinear, chaotic, and non-Gaussian dynamical systems arising in the context of planning and control of soaring aircraft in complex wind fields.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.