CDS&E: ECCS: Accurate and Efficient Uncertainty Quantification and Reliability Assessment for Computational Electromagnetics and Engineering

不确定度量化(UQ)允许对灵敏度和可靠性进行分析，这在所有工程领域都是至关重要的。的确，在所有工程应用中，不确定性都是不可避免的。例如，生物医学计算电磁学(CEM)应用中的UQ涉及电磁场对场激励器的位置和方向以及生物物体的尺寸和材料的不确定性的敏感性的研究。通过严格的UQ，分析和设计的有效性和可靠性可能会大大提高。随着消费者(例如手机)或国家安全(例如隐形技术)对高精度组件、设备和系统的需求不断增长，不确定性分析变得极其重要。事实上，在实际系统和方法的设计中，低概率但高风险的事件往往主导着设计关注点。为了实现这些关键目标，该项目将对确定性和统计错误进行连贯的分析和处理，以通过自动和严格的技术改进工程设计。所提出的用于CEM和计算工程中的差错控制和UQ的方法提高了设计和模拟数据的质量和置信度，同时也提高了效率。虽然该项目专注于需要高质量严格UQ的安全关键和任务关键应用，但拟议的新方法也可以在其他CEM和数值模拟应用中提供显著优势。与现有技术在不确定参数空间的维度、计算开销以及可靠、准确地建模和计算故障概率，特别是对于高风险事件的能力方面的挑战相比，该方法具有广泛的适应性，对高维问题达到了精度，并能快速计算任意事件的概率。该项目的教育活动包括为研究生提供咨询和培训，从STEM中代表性不足的少数群体中招收学生，开发新的教育和课程材料，以及参加各种保留/推广计划。该项目的主要目标是制定、开发、分析和演示一种完全自适应误差控制(确定性和统计学)和不确定性量化的新的协同方法，以极大地提高包括电磁系统和设备在内的工程应用的可靠性评估的效率、准确性和可用性。该项目开发了一种全面的方法来约束确定性错误(以消除显著的错误传播影响)和统计错误(以确保高质量地解决成功和失败概率)。这种新的方法承诺显著节省计算资源，并提高高维不确定性的性能。该方法将显著改进对需要高质量UQ的安全关键和任务关键问题的分析。用现有的UQ方法分析不确定事件，特别是小概率和高风险事件，在实际应用中是站不住脚的。与现有方法相比，所提出的自适应局部分辨降维UQ方法具有几个独特的特征：(A)相对于独立的过程，具有全面的确定性和统计差错控制协同作用，以有效地驱动局部分辨增强；(B)自动UQ过程中对多个目标的集成支持，并加速收敛到指定的误差容限；(C)新的基于伴随的相似性指标通过感兴趣的数量聚类来进行显著的效率增强；(D)对高维不确定性的高弹性，同时支持多个目标并提供显著增强的收敛速度；(E)通过伴随数据指标和参数敏感度量度，采用了解故障概率的降维技术；(F)确定参数空间中的临界点，以推动智能资源分配和确定不稳定区域。总体而言，建议的方法具有很强的潜力来满足严格、自动和有效的不确定性量化的需求。这一奖项反映了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。

Uncertainty quantification (UQ) permits analyses of sensitivity and reliability, which is of critical importance in all areas of engineering. Indeed, uncertainty is unavoidable in all engineering applications. Just as one example, UQ in biomedical computational electromagnetics (CEM) applications involves studies of electromagnetic field’s sensitivity to uncertainties in position and orientation of field exciters as well as dimensions and materials of biological objects. Through rigorous UQ, the effectiveness and reliability of analyses and designs may be improved drastically. With the growing demand for high-precision components, devices, and systems for consumer use (e.g., cellphones) or national security (e.g., stealth technology), the analysis of uncertainty is extremely important. In fact, in the design of practical systems and methods, the low-probability but high-risk events often dominate design concerns. To achieve these critical objectives, this project will conduct a cohesive analysis and treatment of deterministic and statistical errors to enhance engineering designs through automatic and rigorous techniques. The proposed methodology for error control and UQ in CEM and computational engineering enhances both quality and confidence in designs and simulation data while also increasing efficiency. Although the project focuses on safety-critical and mission-critical applications requiring high-quality rigorous UQ, the proposed new approach can also provide significant advantages in other CEM and numerical modeling applications. Compared to existing techniques facing challenges of severe limitations in the dimension of uncertain parameter space, the computational expense, and the ability to reliably and accurately model and calculate failure probabilities, particularly for high-risk events, the proposed approach has advantages of extensive adaptivity, achieving accuracy for high-dimensional problems, and computing the probabilities of arbitrary events rapidly. The project’s educational activities include advising and training of graduate students, recruiting students from underrepresented minority groups in STEM, developing new educational and course materials, and participating in various retention/outreach programs. The principal objective of this project is to formulate, develop, analyze, and demonstrate a novel synergistic approach of fully adaptive error control (both deterministic and statistical) and uncertainty quantification to greatly enhance the efficiency, accuracy, and usability of reliability assessment for engineering applications including electromagnetic systems and devices. The project develops a comprehensive approach to constrain deterministic error (to eliminate significant error propagation effects) and statistical error (to ensure high-quality resolution of success and failure probabilities). The novel approach promises significant savings in computational resources and enhanced performance for high-dimensional uncertainty. The approach will significantly improve the analysis of safety-critical and mission-critical problems demanding high-quality UQ. The analysis of uncertain events, particularly those with low-probability and high-risk, is untenable in practical applications through existing UQ approaches. Compared to existing methods, the proposed novel adaptive local resolution with dimension reduction UQ method has several unique features: (A) comprehensive deterministic and statistical error control synergy, as opposed to independent processes, to efficiently drive local resolution enhancements; (B) integral support for multiple objectives in the automated UQ processes with accelerated convergence to specified error tolerances; (C) novel adjoint-based similarity indicators to conduct significant efficiency enhancements through quantity of interest clustering; (D) high-resiliency to high-dimensional uncertainty while supporting multiple objectives and providing significantly enhanced convergence rates; (E) failure-probability-aware dimension reduction techniques through adjoint data indicators and parametric sensitivity metrics; and (F) identification of critical points in the parameter space to drive intelligent resource allocations and identify unstable regions. Overall, the proposed approach has a strong potential to fulfill the needs of rigorous, automatic, and efficient uncertainty quantification.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.